1 ECONOMICALLY OPTIMAL MANAGEMENT OF HUANGLONGBING IN FLORIDA CITRUS By ABDUL WAHAB SALIFU A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013
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ECONOMICALLY OPTIMAL MANAGEMENT OF HUANGLONGBING IN FLORIDA CITRUS
By
ABDUL WAHAB SALIFU
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY
Background ............................................................................................................. 13 Problem Statement ................................................................................................. 14
Strategies of Control ............................................................................................... 16 Objectives ............................................................................................................... 20 Scope of Research ................................................................................................. 20
2 LITERATURE REVIEW .......................................................................................... 22
HLB Disease Incidence, Latency, and Spread ........................................................ 22
The Impact of HLB .................................................................................................. 25
HLB Control ............................................................................................................ 26
Social Consequences of HLB Persistence .............................................................. 29 Effects of HLB on Yield and Cost of Production ...................................................... 30 Economics of Disease Control Strategies ............................................................... 33
Bioeconomic Models of Disease Control (with Incorporated Discount Rates) ........ 36
Optimal Investment Theory ..................................................................................... 38 Overview .......................................................................................................... 38 Optimal Capital Investment Model .................................................................... 39
The Economic Model .............................................................................................. 40
The Biological Model............................................................................................... 40
4 MODEL RESULTS ................................................................................................. 44
Model Estimation Assumptions ............................................................................... 44
Empirical Results of Model ............................................................................... 45 Conclusions ...................................................................................................... 49
The Effects of a Price Decline ................................................................................. 63
The Effects of a Price Increase ............................................................................... 64 The Effects of a Lower Annual Rate of Spread ....................................................... 65
The Effects of an Increased Annual Rate of Spread ............................................... 66 The Effects of a Lowered Latency Period ............................................................... 67
6 CONCLUSIONS, RECOMMENDATIONS AND LIMITATIONS .............................. 86
LIST OF REFERENCES ............................................................................................... 90
4-2 Non-Valencia Orange Yield Estimated Boxes per Tree, by Age Group in Florida, 2004-2005 through 2008-2009 .............................................................. 51
4-3 NPV1 for Strategy 1 (Do Nothing) ....................................................................... 52
4-4 NPV1 for Strategy 2 (Symptomatic Tree Removal) ............................................. 53
4-6 NPV1 for the Three Strategies for Age Classes 0 and 3 ..................................... 55
4-7 NPV1 for the Three Strategies for Age Classes 6 and 10 ................................... 56
4-8 NPV1 for the Three Strategies for Age Classes 14 and 17 ................................. 57
4-9 NPV1 for the Three Strategies for Age Classes 0 and 3 at Different Yield Penalty2 Levels for Strategy 3 ............................................................................ 58
4-10 NPV1 for the Three Strategies for Age Classes 6 and 10 at Different Yield Penalty2 Levels for Strategy 3 ............................................................................ 59
4-11 NPV1 for the Three Strategies for Age Classes 14 and 17 at Different Yield Penalty2 Levels for Strategy 3 ............................................................................ 60
5-1 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Decline2 ... 69
5-2 NPV1 for the Three Strategies for Age Classes 6 and 10 from a Price Decline2 .............................................................................................................. 70
5-3 NPV1 for the Three Strategies for Age Classes 14 and 17 from a Price Decline2 .............................................................................................................. 71
5-4 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Increase2 ............................................................................................................ 72
5-5 NPV1 for the Three Strategies for Age Classes 6 and 10 from a Price Increase2 ............................................................................................................ 73
5-6 NPV1 for the Three Strategies for Age Classes 14 and 17 from a Price Increase2 ............................................................................................................ 74
5-7 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Decline in Beta2 ................................................................................................................... 75
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5-8 NPV1 for the Three Strategies for Age Classes 6 and 10 from a Decline in Beta2 ................................................................................................................... 76
5-9 NPV1 for the Three Strategies for Age Classes 14 and 17 from a Decline in Beta2 ................................................................................................................... 77
5-10 NPV1 for the Three Strategies for Age Classes 0 and 3 from an Increase in Beta2 ................................................................................................................... 78
5-11 NPV1 for the Three Strategies for Age Classes 6 and 10 from an Increase in Beta2 ................................................................................................................... 79
5-12 NPV1 for the Three Strategies for Age Classes 14 and 17 from an Increase in Beta2 ................................................................................................................... 80
5-13 NPV1 for the Three Strategies for Age Classes 0 and 3 from a Lowered Latency Period2 .................................................................................................. 81
5-14 NPV1 for the Three Strategies for Age Classes 6 and 10 from a Lowered Latency Period2 .................................................................................................. 82
5-15 NPV1 for the Three Strategies for Age Classes 14 and 17 from a Shortened Latency Period2 .................................................................................................. 83
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LIST OF FIGURES
Figure page 4-1 Net Present Value per Acre as a Function of Disease Incidence and Average
Age (Years) of Trees at First Detection with Contour Lines for the Do Nothing Strategy .............................................................................................................. 61
4-2 Net Present Value per Acre as a Function of Disease Incidence and Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 2 ......... 61
4-3 Net Present Value per Acre as a Function of Disease Incidence and Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 3 (30% Yield Penalty) ............................................................................................ 62
4-4 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age (Price = $1.50/pound solid, 30% yield penalty for strategy 3) ........... 62
5-1 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Price: Top Subplot is Baseline, Middle and Bottom Subplots Shows Price Decline (from $1.50 to $1.20) and Increase (from $1.50 to $1.80), respectively ..................................................................... 84
5-2 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Beta: Top Subplot is Baseline, Middle and Bottom Subplots Shows Beta Decline and Increase, respectively ...................... 84
5-3 Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Latency: Top Subplot is Baseline, Bottom Subplot Shows Decline in Latency from 1 year to 6 Months for Groves with Average Age of 0 and 3 while the Latency for Groves 6 Years or Larger Remain at 2 Years .............................................................................................. 85
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Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
ECONOMICALLY OPTIMAL MANAGEMENT OF HUANGLONGBING IN FLORIDA
CITRUS
By
Abdul Wahab Salifu
May 2013
Chair: Thomas H. Spreen Major: Food and Resource Economics
Following the declaration of the endemic status of Huanglongbing (HLB) in
Florida in 2005 with no formal control policy for the disease, it is natural that an
empirical examination and justification of the management protocols implemented at the
farm-level to control HLB be made. We develop farm level decision rules to judge when
it is economically justified to implement a particular control strategy. Models are
developed that allow economic assessment of each strategy and determine the
scenarios for which each strategy is optimal or yield a positive net present value,
considering average grove age at first detection, and rates of infection at first detection.
Our results justify the heterogeneous decisions of growers regarding their choice among
control strategies, in a way that optimizes each grower’s utility. As hypothesized, the
superiority of either strategy depends upon the level of infection at the time when the
disease is first found in a particular block, the rate of spread of the disease, the average
age of the grove at first infection, expectations of future fruit prices, and the latency
period. Our research identifies important efficacy targets that must be achieved for the
long-term economic viability of a citrus grove. Our results provide a recommendation of
12
the optimal control strategy for a given set of conditions such as the age of the planting
and initial rate of infection.
13
CHAPTER 1 INTRODUCTION
Background
Huanglongbing (HLB) is a bacterial disease that affects all varieties of citrus. It is
commonly referred to as citrus greening. HLB was first discovered in Florida in 2005
and is now found in all counties where commercial citrus is produced (Manjunath et al.
2008). It is spread by a small leaf-feeding insect, the Asiatic citrus psyllid (ACP). The
ACP was first found in June 1998 in Delray Beach, and it is noted for its short-range
maneuverability and long range drift by wind, which facilitates its ability to spread HLB
far and wide. HLB acts to disrupt the phloem of the tree thereby limiting its ability to
uptake nutrients. Initially this leads to yellowing of leaves, promotion of premature fruit
drop, and production of small, misshapen fruit that contain bitter juice with no economic
value. As the disease spreads through the tree, the amount of usable fruit produced
diminishes until eventually the tree is of no economic value (Brlansky et al. 2011).
Worldwide, three different bacteria are known to cause HLB: Candidatus
Liberibacter asiaticus (LAS), Candidatus Liberibacter africanus (LAF), and Candidatus
Liberibacter americanus (LAM). The most prevalent of these is LAS, which is found
worldwide, including the United States. Asiatic HLB is caused by LAS, and it is
transmitted by the Asian citrus psyllid (ACP), Diaphorina citri. While LAM is found to be
prevalent in Brazil and China, the African HLB caused by LAF, can be found in Africa,
Saudi Arabia, and the South Asia, and is spread by its vector, the African citrus psyllid
(Trioza erytreae) (Gottwald 2010).
HLB is the single most vicious and debilitating citrus disease responsible for the
destruction of almost 100 million trees in major citrus growing areas of the world where
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the disease has become endemic (Aubert et al. 1985, Bové 1986). This is partly due to
its elusiveness to various regionally specific management prescriptions. At the present
time, the only known way to effectively combat the disease is through early detection
and a strict eradication program of infected trees. The standard control strategy adopted
by HLB affected regions of the world is an integrated control program that involves
psyllid control, symptomatic tree removal, restricted movement of citrus propagation
materials, and distribution of disease-free seedlings and budwood (Gottwald et al. 2012,
Aubert 1990).
Problem Statement
Florida is the leading citrus-producing state in the United States, with nearly
600,000 acres devoted to commercial production. HLB poses as the most serious
obstacle faced by the state’s $9.3 billion citrus industry (National Research Council
2010), which supports almost 80,000 jobs. In its eight-year presence in Florida, it is
estimated that over 10 million of the 60 million orange trees are currently infected with
HLB (Irey et al. 2011), and $1.3 billion in citrus revenue have been lost (Hodges and
Spreen 2012; Bolton 2012). To appreciate the devastating impact of HLB on Florida
citrus, it is said to cause far worse tree damage than citrus canker, which was
responsible for the destruction of over 4 million trees. Tree removal due to HLB infection
has resulted in the reduction of approximately 10 percent of Florida’s commercial citrus
production, and a 40 percent increase in production costs (Irey et al. 2008). HLB has
already been implicated for loss in land acres allocated to citrus in the state since 2006,
and soaring grower costs in terms of tree eradication, psyllid control, inspections, and
replanting costs (TBO 2008). Hodges and Spreen (2012) estimated that within the last
five years, Florida has lost 8,257 jobs, total revenue of $4.541 billion comprised of
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indirect revenue of $2.717 billion, due to HLB. A more important longer-term
consequence has been the fact that HLB has created huge uncertainty among Florida
citrus growers with respect to future investment/planting.
HLB is a disease with two important characteristics. First, the rate of spread is
strongly affected by tree age because psyllids prefer new growth (Brlansky et al. 2008).
Young trees, which are more vigorous as compared to mature trees, produce more
flushes and thereby are more susceptible to psyllid feeding and disease transmission. In
the case of mature trees, the disease spreads more slowly (Gottwald 2010).
Consequently, an infected mature tree is capable of producing usable fruit for several
years while at the same time serving as a source of infection for other healthy trees.
Other factors that affect the rate of spread of HLB are the ACP population and initial
level of infection at first find of the disease. The density of the ACP population is the
single most important factor because theoretically, if the ACP population is reduced to
zero, spread of HLB will stop with immediate effect. Second, control through tree
eradication is complicated by a latency period between the time a tree first becomes
infected and when it expresses visual symptoms. Once a mature tree is infected, it may
not begin to exhibit symptoms of the disease for up to two years (Gottwald 2010). If the
rate of infection in a particular grove is relatively high at the time the disease is first
discovered, a policy of eradication of symptomatic trees may result in destruction of the
entire grove.
Just a few months after the discovery of HLB in Florida, the citrus canker
eradication program was terminated following the sweeping spread of canker over most
southern Florida groves by a series of hurricanes that blew over the citrus belt in 2004
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and 2005. Later in 2005, an interdisciplinary team of USDA HLB experts declared HLB
endemic to Florida, with no chances of eradication (Gottwald and Dixon, 2006). So far, it
is even more troubling to note that neither the citrus industry nor the state or USDA has
put in place a clear cut and decisive procedure for control of HLB, unlike in the case of
the aborted citrus canker control program.
Strategies of Control
At this time, there are three distinct strategies being employed to deal with
greening. Strategy 1, referred to as “do nothing”, allows the disease to spread and takes
no measures to slow its spread including controlling psyllid populations or mitigating
HLB’s impact on tree health. Strategy 1 has no effect on per acre costs as management
tactics are not modified. Per acre revenues, however, are gradually affected as the
disease spreads and the number of healthy fruit that can be harvested and utilized
gradually declines. At some point, per acre revenues will not cover per acre grove
maintenance costs and at that point, the grove is no longer economically viable. The
disease spreads faster in younger groves, so younger groves cease to be economically
viable at a faster rate compared to an older grove with the same initial level of infection.
Strategy 2 follows the standard plant pathology disease control model and is the
only internationally accepted control strategy for HLB (Aubert 1990). Under Strategy 2,
an aggressive psyllid control program is also put into place to suppress psyllid
populations. In addition, between four and twelve inspections are conducted annually to
identify symptomatic trees. Once found, symptomatic trees are immediately eradicated
(Brlansky et al. 2008). The logic behind Strategy 2 is that by eradicating symptomatic
trees, the level of inoculum in a particular citrus grove gradually will be reduced.
Eventually the incidence of the disease will be reduced to a point where it can be
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economically tolerated. Muraro (2010) has estimated that in Florida, Strategy 2
increased pesticides costs by about $450 per acre. Overall production cost have
increased from $800 (2004, pre HLB) to $1,500 (2009, post HLB + canker). There are
five problems associated with Strategy 2. First, plant pathologists have yet to
characterize the key parameters that would significantly define the timeline by which to
control HLB through eradication of symptomatic trees. These parameters include a
controllable base level of HLB infection, the number of years it would take to achieve
that base level, and the probability that young tree resets will survive to productive
maturity. Second, the latency period of the disease implies that not all diseased trees
will be removed in a timely manner, and these asymptomatic trees will serve as a
reservoir of the disease inoculum. Third, if a grove is already at a high level of known
infection and given that more trees are infected but not yet symptomatic, it may not be
possible to effectively reduce inoculum levels in a particular grove without eradicating
the entire grove. The probability of this outcome is related to the age of the grove and
the level of infection when the first positive tree is found. Fourth, eradication or
suppression of the disease to a tolerable level in one grove may not be possible if
neighboring growers are not adequately suppressing the disease in their groves.
Neighboring groves will serve as sources of the inoculum, and the disease may be
continually re-introduced into the groves of the grower following Strategy 2. Fifth, relying
on visual detection of HLB-infected trees by scouting is estimated to be about 50%–
60% effective in finding all the symptomatic trees in a single survey (Futch et al. 2009;
Spann et al. 2010). One other factor that also impacts the effectiveness of this strategy
18
is the neighbor’s HLB management behavior. If psyllid control or tree removal is not
coordinated with neighbors of a grove, inoculum builds up in the local vicinity.
Strategy 3 is an approach first developed in southwest Florida and is, in part, a
response to the Achilles heel of Strategy 2, namely if Strategy 2 is initiated too late, the
entire grove may be eradicated before the disease can be suppressed. While an initial
high rate of disease incidence is one possible motivation to adopt Strategy 3, it is also
possible that under some conditions, Strategy 3 may yield a higher return than Strategy
2 even though Strategy 2 could successfully reduce HLB inoculums to a manageable
level. Strategy 3 proposes to treat the symptoms of HLB through foliar application of
micro and macro nutrients. The tree’s defense response to an HLB infection is to
produce compounds that block phloem vessels of the tree’s vascular system. This
resulting damage to the root system inhibits the ability of the tree to uptake nutrients
from the ground. In the foliar feeding method, a portion of the nutritional needs of the
tree is applied through foliar sprays including both macro and micro nutrients (Spann et
al. 2010). Formulation of the enhanced nutritional program depends on the program, but
generally the active ingredients include standard essential micronutrients, and
phosphite, and salicylate salts (Gottwald et al. 2012). Symptomatic trees are not
removed and scouting for the disease is discontinued. As with Strategy 2, a strong
psyllid control program is practiced. Roka, et al. (2010) have estimated that the
additional nutrient applications increase production costs between $200 to $600 per
acre, depending on the type and amount of foliar nutritionals a grower decides to apply.
The primary concern among plant pathologists with Strategy 3 is that HLB
inoculum is left unchecked. The economic implications of Strategy 3 include whether it
19
is feasible for young trees (ages 3-8) to reach their productive maturity, whether planting
the next generation of citrus trees is economically viable, and whether the presence of a
grove following Strategy 3 while other growers follow Strategy 2 will cause increased
damage on the latter growers’ fields. Spatial analysis of disease spread in south Florida
suggests that spread between citrus blocks is a more significant portion of disease
spread than the spread of the disease within a citrus block (Gottwald et al. 2008). This
suggests that heterogeneous control methods may reduce the viability of Strategy 2.
This study addresses the economic consequences of the three strategies. In
other words, how does a grower determine which strategy is in her/his best interests
(given average grove age and initial infection rate)? Strategy 1 needs to be considered
as a baseline to reference Strategies 2 and 3. Growers make heterogeneous decisions
regarding their choice among control strategies. Models are developed that allow
economic assessment of each strategy and determine the scenarios for which each
strategy is optimal or yield a positive net present value, considering tree age at first
detection, and rates of infection at first detection. Since the optimal strategy may vary
due to tree age at first detection and the rate of infection at first detection, the optimal
strategy may vary across growers located nearby. Currently, the long term net present
value of the control strategies is unknown because of uncertainty in the efficacy of the
strategies. Our research identifies important efficacy targets that must be achieved for
the long-term economic viability of a citrus grove.
Our results provide a recommendation of the optimal control strategy for a given
set of conditions. It is hypothesized that the superiority of any one strategy depends
upon the level of infection at the time when the disease is first found in a particular
20
block, the rate of spread of the disease, the average age of the grove at first infection,
expectations of future fruit prices, and the latency period. The rate of spread is a
function of psyllid populations and the efficacy of psyllid control measures.
Objectives
The primary objective of this study is to determine the optimal economic
management strategies of citrus greening in Florida. This is accomplished through the
following specific objectives:
1. Identify grove age and level of initial disease incidence at which each strategy yields positive economic returns.
2. Determine the ranges of initial grove age and initial disease incidence for which a given control method is economically preferred over other available methods.
Scope of Research
The study implements a net present value analysis of the control strategies
adapted by Florida citrus growers following the advent of HLB in the state. This is
essential to the determination of which strategy is economically superior, from the
grower’s point of view. It is of more importance to consider the private benefits/cost of
the tree eradication policy to the grower, as no compensation is paid for removed trees.
The impact of HLB on citrus yield is first modeled through a disease spread function; a
discrete logistic function approximated from a Gompertz function. Since the spread rate
of HLB is dependent on the average grove age, the logistic function is approximated for
three average age classes of 0, 3, and 6 or older. Due to lack of available data for the
estimation of model parameters for Florida, we obtain parameter estimates from a
corresponding region of HLB spread. Given this logistic function, disease spread in an
infected grove with a tree density of 150 per acre is simulated for given parameter
values for each age class, while varying the initial level of infection. The logistic curves
21
thus incorporate both asymptomatic and symptomatic trees expressed in a ratio
involving total diseased trees. Total diseased is the sum of the asymptomatic (latently
infected trees without visual symptoms) and symptomatic tree categories. From this, a
spread function is generated and fed into HLB tree and grove severity functions for the
calculation of the relative yield due to HLB presence in the affected grove. The net
present value is then estimated from the corresponding relative yield estimates given
the yield from a healthy grove unaffected by HLB, obtained as estimated boxes of fruit
per tree by age group for non-Valencia oranges from the Florida agricultural statistics
service (Florida citrus statistics 2008-2009). Fruit prices are expressed as delivered-in
(to the processing plant) $/pound solids ($1.50/pound solid is the baseline price) with
pound solids per box values dependent on tree age. The model described above is the
baseline model for the ‘do-nothing’ policy. Hence two other models are developed: the
infected tree eradication model and the enhanced foliar nutrition model. These models
are unique in the sense that they include a latency period of HLB infection, as well as
take into account the average grove age, the natural variation in disease incidence at
first detection across groves in a region, and periodic removal of symptomatic trees
(specific to the tree eradication model). The robustness of each model is tested by a
sensitivity analysis conducted for the main model parameters.
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CHAPTER 2 LITERATURE REVIEW
Responses to stem the devastating effects of HLB or plant diseases in general
especially in academia have been enormous. This chapter reviews relevant literature in
all aspects of related disciplines including HLB epidemiology, the variety of control
methods experimented to date, the impact of HLB across the globe and in Florida as
well as its social ramifications if left unchecked. In addition, the review includes work on
HLB effects on production and yield costs, and general economic and bio-economic
models of disease control.
HLB Disease Incidence, Latency, and Spread
Disease incidence has been estimated using a variety of approaches. Gottwald
et al. (2010) determined disease incidence via a logistic spread rate per year calculated
by linear regression of transformed1 disease incidence in Florida. HLB incidence in
Florida has also been found in similar studies to increase within 10 months from 0.2 %
to as much as 39 % (Gottwald et al. 2007b, 2008; Irey et al. 2008). Spatiotemporal
spread models have also been used to characterize HLB in Florida where simultaneous
within and across grove spread were common (Gottwald et al. 2008). Other studies
have been conducted such as in Vietnam where HLB incidence is found to vary
depending on the management strategy employed (Gatineau et al. 2006) or in Brazil
where incidence has been shown to depend on proximity to HLB-infected citrus groves
and/or on neighbors’ behavior (Bassanezi et al. 2006; 2005, Gatineau et al. 2006;
1 The disease incidence data was first transformed via a logistic linear function given
by )1/ln()(logit yyy .
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Gottwald et al. 2007a; 2007b). Albrecht et al. (2012) showed in a Florida study that
HLB disease incidence is unaffected by the type of rootstock used in propagation.
Disease latency refers to the time between when infection by a pathogen occurs
and the onset of symptoms. HLB latency has also been demonstrated in some studies
where for every symptomatic tree in a given grove, 13 (range 2 to 56) HLB-positive but
asymptomatic trees existed in its neighborhood, which expressed symptoms in
subsequent assessments (Bassanezi et al. 2006). Irey et al. (2006) use PCR
techniques to test for the presence of the bacteria that causes HLB (Candidatus
Liberibacter asiaticus) in plots of about 190 trees and found that 60 percent more
asymptomatic trees existed in addition to the symptomatic trees that were found (Irey et
al. 2006). High correlation (R2 = 0.89) between infected trees and total number of
infected trees among the plots suggests natural disease transition from asymptomatic
trees to symptomatic trees. In some instances, high bacteria titer was found with PCR in
some asymptomatic trees, suggesting the need for roguing asymptomatic trees as well
(National Research Council 2010; Irey et al. 2006). The presence of a high percent
(80%) of infected trees within 25 m of a symptomatic tree also signifies short distance
spread of HLB (Irey et al. 2006).
HLB progression in a grove has also been determined to depend on the vector
population and inoculum levels as well as average grove age at first detection. HLB
progression in Reunion Island, China, and the Philippines is reported to follow a sigmoid
curve, with clustering of diseased trees (Gottwald and Aubert 1991; Gottwald et al.
1989, 1991). In Reunion Island more aggregation towards the direction of prevailing
wind was observed, suggesting that psyllids are dispersed by the wind. Aggregation in
24
China was facilitated by closer tree spacing. Logistic growth rates are more plausible for
both growth of an infested area in space and population density growth than constant
growth rates (Kompas and Che 2009). This suggests that an infected area initially
grows exponentially, slows down and finally stops as the potential range of the species
is attained. Disease progression can reach asymptotic levels faster in young groves
than older groves (Gottwald et al. 2007, 2007a). The dispersal distance for HLB-infected
psyllids have been estimated to range from 0.88 to 1.61 km with a median of 1.58,
which may imply that groves more than 2km apart are unlikely to directly affect each
other with HLB (Gottwald et al. 2007b, Gottwald et al. 2008). Thus HLB spread is
spatially continuous and simultaneous, primarily via psyllid feeding behavior between
groves and secondarily through within grove feeding of the psyllids, necessitating the
need for landscape management practices (neighbors HLB management practices
should be compatible) for effective control. Manjunath et al. (2008) in a study to detect
HLB bacteria from a sample of over 1,200 psyllid adults and nymphs in Florida found
that the bacteria spread in an area may be detected one to several years before
symptom development in plants. Raphael et al. (2012) developed a deterministic
mathematical model that involve susceptible citrus, infectious but asymptomatic citrus,
symptomatic citrus, non-infective adult ACP, and infective adult ACP that acquired HLB
in the adult and nymph stages to study the dynamics of HLB in a citrus grove. Results
show that all trees in the grove are infected after 5 years even after removal of
symptomatic trees with 47% detection efficiency. They concluded that the best control
strategy is the reduction of the vector populations. Chiyaka et al. (2012) used a
mathematical model of HLB transmission to indicate the importance of ACP for initial
25
HLB infection. Their work also underscores the importance of flush production and
latency period in influencing HLB development.
The Impact of HLB
HLB, which in Chinese means “yellow dragon disease”, was first described in
southern China in 1919 and spread widely and devastated citrus establishments in the
Philippines, Indonesia, Thailand, and South Africa between 1960 – 1980. Until recently
(2004/5), symptoms of HLB were found in two countries in the Americas; specifically in
São Paulo State in Brazil, in which nearly three million HLB infected trees were
removed in subsequent years, and in Florida, USA (Bové 2006; National Research
Council, 2010). HLB now occur in other North American areas, such as Cuba, Georgia,
Louisiana, South Carolina, Nayarit (Mexico), California, Texas, Costa Rica, and Belize.
HLB is a very serious, debilitating disease that affects all varieties of citrus. HLB’s
destructive abilities are unwavering no matter the mode of propagation; reducing yield
significantly through fruit drop, dieback and stunted growth, in addition to causing poor
quality of un-harvested fruits (National Research Council, 2010). Depending on the
psyllid vector population, bacteria titer, and age cohort of the grove at first detection,
HLB can take over an entire grove in 3 – 13 years following the expression of first
symptoms (Catling and Atkinson 1974; Aubert et al. 1984; Gottwald et al. 1991;
Gatineau et al. 2006; Gottwald et al. 2007a; Gottwald et al. 2009). Symptoms can
become very severe within one to five years from onset of the disease, depending upon
tree age at time of infection and the range of infection (Lin 1963; Schwarz et al. 1973;
Aubert 1992). The progression of HLB severity in a grove results in yield reduction,
rendering the grove uneconomical within 7 – 10 years after planting. (Aubert et al. 1984;
Aubert 1990; Gottwald et al. 1991; Roistacher 1996).
26
Worldwide, nearly 100 million trees are estimated to be affected by HLB. In some
parts of Thailand in 1981, close to 100 percent of trees were affected. Between 1961
and 1970 in the Philippines, citrus acreage was reduced by 60 percent, which
represents the fallout from the infection of an estimated seven million trees in 1962
(Altamirano et al. 1976; Martinez and Wallace 1969). Three million trees were removed
in Java and Sumatra within that same period, and a loss of 3.6 million trees were
reported in Bali within four years from 1984 to 1987. The HLB havoc extended to
southwestern Saudi Arabia, where most sweet orange and mandarin trees were killed
by 1983. In the 1960s, the entire citrus industry in Reunion Island was devoured by HLB
(Altamirano et al. 1976; Martinez and Wallace 1969).
Since its arrival in São Paul State, Brazil in early 2004, three million HLB affected
sweet orange trees have been removed as part of measures taken to control HLB
(National Research Council 2010). In the wake of the panic from the first reports of HLB
in Florida citrus in 2005, no public policy has emerged to handle HLB, as a result of
which growers evolved their own private stop-gap management strategies, rendering
the citrus industry to be labeled as an endangered industry. Before effective control of
the African psyllid with systemic insecticides was discovered in the late 1980s, HLB
devastated the South African citrus industry across the length and breadth of the
country, affecting four million out of the 11 million trees in South Africa, during the mid-
1970s (National Research Council 2010).
HLB Control
This section outlines the various recommended control measures for a pre- and
post-HLB presence in a given region. These include quarantine, roguing, psyllid control,
27
and use of healthy nursery propagation materials. The effectiveness of some of these
measures as gleaned from the literature is also presented.
So far, the first line of control of HLB is by adoption of quarantine measures to
prevent disease introduction. If however HLB is found in a hitherto HLB-free region, a
series of coordinated actions known as preventative control measures could be taken to
control the disease. Affected areas are mapped through surveys to identify infected
trees, which are later removed to prevent re-infection. A rigorous psyllid control program
should also be put in place. To avoid infection through plant propagation practices,
production of healthy citrus seedlings should be ensured especially if resetting is
required after symptomatic trees are removed. This is because without control, it takes
on average eight years for a grove to reach 100% infection (Bové 2006).
Control by roguing is effective through well-timed and carefully repeated surveys
to identify all affected trees as much as possible. The latency period of HLB, which can
be up to two or more years (Gottwald 2010), reduces the effectiveness of roguing as a
control measure; hence the need for repeated surveys. The quality of roguing is also
affected by the presence of uncontrolled psyllids in the grove in which infected tree
removal is practiced. Roguing must therefore be accompanied with a rigorous psyllid
control regime. Detection of HLB in Florida and São Paulo is done by mounting
platforms that allow for inspection of the tops of mature trees as it is reported that many
affected trees start showing symptoms first on the upper part of the canopy (National
Research Council 2010). Brlansky et al. (2009) recommend four inspections per year,
even though some growers carry out two to three inspections per year. Futch et al.
(2009) indicated that no scouting method is 100% accurate in detecting HLB
28
symptomatic trees. This re-emphasizes the need for multiple inspections within the
year. Irrespective of age or severity of infection, all symptomatic trees should be
removed (Ayres et al. 2005), and prior to removal these symptomatic trees should be
sprayed with a contact insecticide (Rogers et al. 2010). Unlike citrus canker in which
infected trees as well as all surrounding trees at 15 m radii are removed, this practice is
not feasible for HLB (Bassanezi 2005), as the psyllid vector feeds randomly across a
given grove, and can disperse farther to other groves by wind, hurricanes or storms.
The proportion of the infected trees removed depends on the initial disease incidence
and hence the entire grove can be eradicated at very high rates of initial disease
incidence. For instance, a grove with 10% symptomatic trees implies 20% infected
trees, and groves with 20%, 30% and 50% symptomatic trees give rise to 36%, 50%
and 70% infected trees respectively, due to latency and hence the presence of
asymptomatic trees (Bové 2006). Recently, Bové (2012) has been discounting the
latency period saying that it is just incomplete inspections, while Futch et al. (2009)
indicates that the latency period of HLB is unknown within a tree. Resetting can be done
with healthy seedlings, after infected trees are removed.
Application of contact and systemic insecticides as well as use of biological
agents reduces psyllid populations and HLB spread, depending on the species of the
psyllid. Biological control is reported to have been successful in Reunion Island (Aubert
and Bové 1980; Aubert et al. 1980), mainly due to the fact that there were no
hyperparasitoids on the introduced Tamarixia radiata and T. dryi parasitoids to hamper
their effectiveness (Aubert and Quilici 1984). Predators such as spiders, lacewings,
ladybugs, minute pirate bugs, and some wasp parasitoids attack the Asian citrus psyllid.
29
However, the most effective natural enemy is reported to be the coccinellid lady beetles
Olla v-nigram, and Harmonia axyridis (Michaud, 2004). In Florida, attempts have been
made to establish the biological agent T. radiata to control psyllids (Bové 2006) with
little effect on the citrus psyllid population. Major reasons for this failure include
presence of hyperparasites and inadequate number of alternative hosts for the
parasitoids (Halbert and Manjunath 2004, National Research Council, 2010).
In Brazil, encouraging results were obtained in the use of tree removal and
insecticides against psyllids to control HLB. HLB incidence decreased from 7% to
0.03% in the 10th survey of a grove with 71,000 trees (Ayres et al. 2005). The African
version of HLB in South Africa was effectively managed for some period by the adoption
of disease-free nursery stock, intensive psyllid control coupled with rouging of
symptomatic trees. In China, however, the Asian HLB has proven more difficult to
handle with preventative control measures. Aggressive implementation of similar
measures brought some success in Brazil, and gave rise to the identification of factors
that affect HLB preventative control effectiveness. These factors include farm size, age
cohort of grove, HLB incidence frequency in the area of the grove, neighbors HLB
management behavior, HLB incidence at first inspection, date of first scouting, number
of scouting for affected trees, and frequency of insecticide application (Belasque, Jr. et
al. 2009). In Florida, it is also been observed that large grove size with well-maintained
groves in the same area that have low bacteria titer lowers HLB incidence by reducing
the spread across groves.
Social Consequences of HLB Persistence
The $9.3 billion citrus industry in Florida supports almost 80,000 jobs (grove
employees, seasonal pickers, haulers, processors, and packers). With total annual
30
wages of $2.7 billion, these workers earn roughly 1.5 percent of Florida’s wage income
(Norberg 2008). Inefficiency in managing HLB in the state will affect not only these full-
time equivalent job employees of the industry, but also the general public will be
deprived of health benefits derived from citrus products, albeit still enjoyed at a higher
cost from imported juice and fruit. Growers who cherish citrus production as a way of life
will be affected. The worldwide recognition of Florida as a citrus producing state whose
brand name has contributed to the state’s attractiveness to tourists, retirees, and
consumers will also be compromised. To augment shortfalls in both fresh and
processed citrus demand domestically, imports have to rise, putting further strains on
the economy.
Effects of HLB on Yield and Cost of Production
Effective management of HLB implies a dramatic increase in production costs
through adoption of various control measures such as use of disease-free nursery
stock, scouting and roguing symptomatic trees, and psyllid vector control. Other
reasons for reduced profit include declining yield and fruit quality of affected trees,
production of healthy nursery trees, costs of tree replacement and care, and value of
income/production losses from replaced trees. Yield effects of HLB depend on
tree/grove age and severity of infection. Young trees/groves become unproductive
faster than mature trees/groves. Mature trees/groves remain productive for several
years with less severe infection, and productive life could be reduced to as low as two
years with severe infections on a tree/grove (National Research Council 2010).Yield
reduction is high (19%) for younger infected groves (1-5 years olds) 2-4 years after the
onset of infection compared to older groves (over 5 years olds) where high yield
reduction occurs only after 5-10 years of first symptomatic tree onset (Bassanezi et al.
31
2011; Bassanezi and Bassanezi 2008). Optimal control policy for a pest has been
shown to depend significantly on the costs of pest damage per unit of infected area
(Carrasco et al. 2009; Sharov 2004).
Stringent requirements for raising disease free nursery trees in screened houses
have resulted in an increase from $4.50 to $9.00 in the cost per nursery tree. Given the
recommended four inspections per year for symptomatic trees and an estimated cost of
between $25–30/acre per inspection, annual inspection costs could add as much as
$100 to $120 to production costs (Morris et al. 2008). Assuming six trees are detected
for removal each year, tree removal costs add another $34 per acre per year to
production expenses (Muraro 2008b). Morris et al. (2008) suggested little economic
difference between controlling HLB with roguing and doing nothing to ameliorate the
impact of the disease until the grove becomes economically useless.
Psyllid control is accomplished either with soil application of recommended
insecticides or application of foliar insecticides such as zeta-cypermethrin , carbaryl,
Source: Bassanezi and Bassanezi (2008); Bassanezi et al. (2011)
51
Table 4-2. Non-Valencia Orange Yield Estimated Boxes per Tree, by Age Group in Florida, 2004-2005 through 2008-2009
Tree Age Average1 Yield (2004/5 - 2008/9)
Yield2 (boxes/tree)
1
1.2
0
2 0
3 1
4 1.2
5 1.4
6
1.8
1.7
7 1.8
8 1.9
9
2.26
2
10 2.1
11 2.3
12 2.4
13 2.5
14
3.05
2.6
15 2.7
16 2.8
17 2.9
18 3
19 3.1
20 3.2
21 3.3
22 3.4
23 3.5
Sources: Florida Citrus Statistics 2008-2009. FASS 1Average yields of 1.2, 1.8, 1.26, and 3.05 boxes/tree are for groves of ages 3 – 5, 6 – 8, 9 -13, and 14 – 23 years respectively 2 Yield for each tree age is derived from the 5-year average yield in column two
Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
55
Table 4-6. NPV1 for the Three Strategies for Age Classes 0 and 3
Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
56
Table 4-7. NPV1 for the Three Strategies for Age Classes 6 and 10
Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
57
Table 4-8. NPV1 for the Three Strategies for Age Classes 14 and 17
Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
58
Table 4-9. NPV1 for the Three Strategies for Age Classes 0 and 3 at Different Yield Penalty2 Levels for Strategy 3
0.500 -5,482 -10,433 -2,096 -1,180 -722 -4,164 -7,114 1,876 3,123 3,747 1 Cumulative 15-year NPV ($/ac). 2Yield from HLB infected trees reduced 20%, 10% and 5% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
59
Table 4-10. NPV1 for the Three Strategies for Age Classes 6 and 10 at Different Yield Penalty2 Levels for Strategy 3
0.500 1,077 -1,752 5,787 6,869 7,409 3,176 276 8,683 9,864 10,455 1 Cumulative 15-year NPV ($/ac). 2Yield from HLB infected trees reduced 20%, 10% and 5% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
60
Table 4-11. NPV1 for the Three Strategies for Age Classes 14 and 17 at Different Yield Penalty2 Levels for Strategy 3
0.500 4,779 1,784 10,554 11,768 12,375 5,375 2,399 11,164 12,380 12,988 1 Cumulative 15-year NPV ($/ac). 2Yield from HLB infected trees reduced 20%, 10% and 5% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
61
05
1015
0.10.2
0.30.4
0.5-1
-0.5
0
0.5
1
1.5
x 104
Age of Trees at First detectionHLB Incidence at First Detection
Ne
t P
rese
nt
Va
lue
-5000
0
5000
10000
15000
Figure 4-1. Net Present Value per Acre as a Function of Disease Incidence and
Average Age (Years) of Trees at First Detection with Contour Lines for the Do Nothing Strategy
05
1015
0.10.2
0.30.4
0.5-1.5
-1
-0.5
0
0.5
1
x 104
Age of Trees at First detectionHLB Incidence at First Detection
Ne
t P
rese
nt
Va
lue
-1
-0.5
0
0.5
1
x 104
Figure 4-2. Net Present Value per Acre as a Function of Disease Incidence and
Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 2
62
05
1015
0.10.2
0.30.4
0.5-5000
0
5000
10000
Age of Trees at First detectionHLB Incidence at First Detection
Ne
t P
rese
nt
Va
lue
-2000
0
2000
4000
6000
8000
10000
12000
Figure 4-3. Net Present Value per Acre as a Function of Disease Incidence and
Average Age (Years) of Trees at First Detection with Contour Lines for Strategy 3 (30% Yield Penalty)
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
2
4
6
8
10
12
14
16
Disease Incidence at First detection
Cu
mm
ula
tive
Ave
rag
e G
rove
Ag
e
Strategy 3
Strategy 2
Strategy 1
Figure 4-4. Dominant Strategy Given Disease Incidence at First Detection and Average
Grove Age (Price = $1.50/pound solid, 30% yield penalty for strategy 3)
63
CHAPTER 5 SENSITIVITY ANALYSIS
In this chapter, the robustness of the model’s conclusions is tested by performing
sensitivity analysis to determine how changes the main parameters of the model affect
the optimal strategy mix. Changes in the age-dependent rate of spread (β) affect the
disease spread, which in turn alter fruit yield and net returns with a resulting impact on
the optimal strategy. Changes in the price per pound solids directly impacts the net
present value estimates. Other parameters that affect the optimal choice of the model
include the period of latency and fruit yield. This chapter considers the effects of
changing prices, betas (rate of spread) and period of latency on optimal strategy. First,
the impact of a price decrease from $1.50/pound solids to $1.20, followed by a price
increase from $1.50 to $1.80/pound solids are examined for each of the three age
cohorts. Next, the age dependent rate of spread and the latency periods are also
adjusted to observe their effect on model results.
The Effects of a Price Decline
Tables 5-1 through 5-3 presents the net present values for the three strategies
for a delivered-in price from $1.50 to $1.20 per pound solid for each of the three age
categories. In Table 5-1, irrespective of the strategy or disease incidence at first
detection, the age cohorts of 0 and 3 produces negative net present values when price
falls. This trend is reversed for the mature groves with average ages of 6, 10, 14, and
17 where net present values are positive, except at high incidence values of 30% to
50%, where some strategies still yield negative net present values. In Tables 5-2 and 5-
3, at low disease incidence of 0.1% - 10.0% (at high incidence of 20% - 50%), Strategy
1 (Strategy 3) is the superior strategy for groves with average ages of 6, 10, 14, and 17.
64
Overall, the lowered price results in lower net present value for all groves at all levels of
disease incidence. A fall in price favors strategy 1 as it completely replaces strategies 2
and 3 at the lower levels of incidence of 0.1% - 10%.
The Effects of a Price Increase
When price is increase from $1.50 to $1.80 per pound solid, the net present
value is still negative for almost all levels of incidence for groves with average age of 0,
but now positive for groves with average ages of 3 or more except at high incidence of
8% to 50% (30% to 50%) in which Strategy 1 (Strategy 2) posts negative net present
values (Table 5-4). In Table 5-4, at low initial disease incidence (0.1% to 7%), Strategy
2 is better than Strategies 1 and 3 for groves with average age of 3. Thereafter, at initial
disease incidence of 8% to 50%, Strategy 3 overtakes Strategy 2 as the best strategy in
net present value. This result again confirms that at higher rates of infection, Strategy 3
is preferred over Strategy 2 because of the high tree removal rates associated with
Strategy 2. For groves with average age of 6 or more, Strategy 1 is only dominant at
0.1% to 1% level of initial incidence, whereas Strategy 2 is dominant for all initial
incidence rates ranging from 2% to 8%. When the initial incidence rate exceeds 10%,
Strategy 3 takes over from Strategy 2 (Tables 5-5 and 5-6). Increased price results in
higher net present value for all groves at all levels of disease incidence. The switch
point (7%) between Strategy 2 and 3 for groves of average age 3 do not change when
price increase. This may be attributed to the fact that as price increase; net present
value of existing fruits increases making it more expensive to remove trees.
In Figure 5-1 (middle subplot), the ranges of initial grove age and initial disease
incidence for which each strategy maximizes net present value shows that when price
falls, Strategy 1 (Strategy 3) is the optimal strategy for all groves, when disease
65
incidence ranges between 0.1% to 10% (20% to 50%). Therefore, when price is
lowered, Strategy 1 replaces Strategy 2 (and some part of Strategy 3) as the optimal
strategy for all groves when disease incidence ranges from 0.1% to 10%. In Figure 5-1
(bottom subplot), when price increase, the optimal strategy is Strategy 2 for initial
incidence of 2% to 8% for all groves and for groves of 6 years or larger, Strategy 1 is
optimal at incidence of 0.1% to 1%. For all groves at 10% to 50% incidence, Strategy 3
is the best strategy. Strategy 1’s area at 2% initial disease incidence for groves over 6
years is taken over by Strategy 2, and Strategy 2’s area at 1.0% initial disease
incidence for groves older than 14 years is taken over by Strategy 3.
The Effects of a Lower Annual Rate of Spread
Tables 5-7 through 5-9 presents results for a lower annual rate of spread of HLB
0.7440625; for the respective average age category, gives similar results for groves with
average age of 0 and 3, in which the former presents negative net present values, and
the later shows dominance for Strategy 2 at initial incidence of between 0.1% to 2.0%,
and thereafter from 3% to 50%, Strategy 3 is the best strategy. However, for groves with
average age of 6 or larger, Strategy 1 does best for incidences of 0.1% only, Strategy 2
does best for incidences of 1.0% to 6%, and Strategy 3 does best for incidences 7% to
50%. The increased betas have resulted in smaller net present value for all groves at
all levels of disease incidence.
A reduction in the betas also affects the optimal strategy mix (Figure 5-2).
Strategy 1 (Strategy 3) is the optimal strategy for groves 6 years or larger when initial
disease incidence is 0.1% to 10% (20% to 50%). For groves with average age of 0 and
3 (0 or larger, i.e. all groves), Strategy 2 (Strategy 3) is optimal at incidence of 1% to
10% (20% to 50%). As a result of the reduction in the betas, Strategy 1 replaces
Strategy 2 as the dominant strategy for groves older than 6 years at disease incidence
of 3% to 10%. For an increase in the betas (Figure 5-2, bottom subplot), Strategy 1 has
the smallest area of optimality, which occurs only at the lowest level of initial incidence
of 0.1% for groves 6 years or larger. For all groves at incidence of 1% - 6% (7% - 50%),
Strategy 2 (Strategy 3) is the best strategy. Strategy 2 replaces strategy 1 as dominant
strategy for groves older than 6 years when disease incidence is between 1.0% and
2.0%, whereas Strategy 3 replaces Strategy 2 for groves older than 6 years when
disease incidence is from 6% to 8%.
67
The primary consequence of decreased rate of spread is to make Strategy 2
more attractive. This result makes sense as the goal of Strategy 2 is to suppress the
level of disease inoculum. A lower rate of disease spread gives a grower more time to
initiate Strategy 2 and thereby enjoy its benefits. Lower disease spread rate also
means that fewer trees are being removed early in the treatment period. This results in
a smaller decrease in fruit revenue. The contrary effect emerges when the rate of
spread is increased. Faster spread of the disease means the growers have a shorter
window of opportunity to implement Strategy 2; Strategy 3 is preferred at younger ages
of first detection and smaller levels of initial incidences at first detection.
The Effects of a Shortened Latency Period
The latency period refers to the interval between the time a tree first becomes
infected and when is expresses symptoms. The existence of the latency period is one
of the most vexing dimensions of the disease in that a tree removal policy fails to
eliminate all diseased trees. Bové (2012) has recently argued that the latency period
may be shorter than that suggested in earlier literature on HLB. In this section we
investigate the impact of a shorter latency period on the optimal strategy.
Another dimension to this analysis is the efficacy of scouting in detecting the
disease. Futch et al. (2009) argues that one pass through a grove where HLB is present
will result in 50% of symptomatic trees being detected. Bové’s (2012) argument
regarding latency is based upon the observation that symptomatic trees may be
present, but scouts are unable to detect them. Therefore, improved detection
techniques could reduce the latency period.
Tables 5-13 through 5-15 presents results for the scenario when the latency
period is reduced such that groves with ages of 0 and 3 now are assumed to have a
68
latency period of 6 months instead of 1 year, while the latency period of groves 6 years
or larger remain unchanged at 2 years. Results show that all cases in which age of first
detection is 0 display negative net present values. Groves with average age of 3
displays net present values in which Strategy 2 is best when disease incidence is 0.1%
to 10.0%; Strategy 3 is best when disease incidence is 20.0% to 50.0%. For groves 6
years or larger, Strategy 1 does best from disease incidence of 0.1% to 1.0%, after
which Strategy 2 is best at 2.0% to 10.0% disease incidence, followed by Strategy 3,
which is optimal at incidence of 20.0% to 50.0%. In Figure 5-3, the reduction in latency
period favors Strategy 2 more compared to Strategy 1 (and 3), for groves older than 6
years when disease incidence is 2% (10%). Strategy 3 is dominant at disease incidence
of 20% to 50% for all groves. The change in latency has resulted in lower net present
value for all groves at all levels of disease incidence.
Comparison of the results in Table 4-7 and Table 5-13, however, suggest that
shortening the latency period does impact the optimal strategy. Under the baseline
latency period, for groves of three years of age at first detection, Strategy 3 is superior
for initial infection rates of 9% and higher, but with a shortened latency period,
superiority of Strategy 3 shifts to initial infections rates of 10% and higher. While this is a
small change, it does indicate that superior detection methods that could reduce the
period of latency would benefit Strategy 2.
69
Table 5-1. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Decline2
Disease Incidence at First Detection
Average Age of Trees at First Detection
0 3
Strategy Strategy
1 2 3 1 2 3
0.001 -3,986 -3,397 -4,655 521 347 -1,115
0.010 -5,043 -5,902 -4,972 -1,626 -26 -1,759
0.020 -5,321 -6,950 -5,056 -2,320 -418 -1,967
0.030 -5,436 -7,553 -5,090 -2,794 -788 -2,109
0.040 -5,494 -7,969 -5,108 -3,013 -1,137 -2,175
0.050 -5,610 -8,280 -5,142 -3,174 -1,468 -2,223
0.060 -5,653 -8,529 -5,155 -3,480 -1,782 -2,315
0.070 -5,686 -8,730 -5,165 -3,594 -2,080 -2,349
0.080 -5,712 -8,901 -5,173 -3,690 -2,365 -2,378
0.100 -5,747 -9,174 -5,183 -3,843 -2,895 -2,424
0.200 -5,884 -9,922 -5,225 -4,472 -4,979 -2,613
0.300 -5,905 -10,259 -5,231 -4,887 -6,456 -2,737
0.400 -5,970 -10,436 -5,250 -5,218 -7,568 -2,837
0.500 -5,983 -10,532 -5,254 -5,345 -8,433 -2,875 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is reduced from $1.50 to $1.20. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
70
Table 5-2. NPV1 for the Three Strategies for Age Classes 6 and 10 from a Price Decline2
Disease Incidence at First Detection
Average Age of Trees at First Detection
6 10
Strategy Strategy
1 2 3 1 2 3
0.001 5,980 2,852 2,260 8,149 5,025 4,433
0.010 4,562 2,680 1,834 6,684 4,835 3,993
0.020 3,754 2,490 1,592 5,832 4,626 3,738
0.030 3,196 2,302 1,425 5,238 4,420 3,560
0.040 2,848 2,116 1,320 4,858 4,215 3,445
0.050 2,450 1,932 1,201 4,431 4,013 3,317
0.060 2,219 1,750 1,131 4,175 3,812 3,240
0.070 1,875 1,570 1,028 3,805 3,614 3,130
0.080 1,703 1,392 977 3,612 3,418 3,072
0.100 1,412 1,041 889 3,283 3,031 2,973
0.200 152 -609 511 1,872 1,212 2,550
0.300 -578 -2,099 292 1,036 -435 2,299
0.400 -1,389 -3,446 49 105 -1,925 2,020
0.500 -1,673 -4,659 -36 -232 -3,270 1,918 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is reduced from $1.50 to $1.20. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
71
Table 5-3. NPV1 for the Three Strategies for Age Classes 14 and 17 from a Price Decline2
Disease Incidence at First Detection
Average Age of Trees at First Detection
14 17
Strategy Strategy
1 2 3 1 2 3
0.001 9,575 6,452 5,860 10,028 6,904 6,312
0.010 8,103 6,256 5,418 8,555 6,708 5,871
0.020 7,243 6,039 5,160 7,695 6,492 5,613
0.030 6,642 5,826 4,980 7,093 6,278 5,432
0.040 6,253 5,614 4,863 6,705 6,067 5,316
0.050 5,819 5,405 4,733 6,271 5,857 5,185
0.060 5,556 5,197 4,654 6,007 5,650 5,106
0.070 5,180 4,992 4,541 5,630 5,445 4,993
0.080 4,980 4,789 4,481 5,430 5,242 4,933
0.100 4,638 4,389 4,379 5,088 4,841 4,830
0.200 3,174 2,503 3,939 3,620 2,955 4,390
0.300 2,293 793 3,675 2,738 1,245 4,125
0.400 1,316 -757 3,382 1,758 -305 3,831
0.500 948 -2,159 3,272 1,387 -1,706 3,720 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is reduced from $1.50 to $1.20. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
72
Table 5-4. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Price Increase2
Disease Incidence at First Detection
Average Age of Trees at First Detection
0 3
Strategy Strategy
1 2 3 1 2 3
0.001 -1,371 2,108 314 7,165 9,313 7,176
0.010 -3,241 -2,197 -247 3,480 8,671 6,140
0.020 -3,744 -4,006 -398 2,286 7,998 5,712
0.030 -3,956 -5,050 -461 1,469 7,363 5,467
0.040 -4,065 -5,773 -526 1,090 6,762 5,353
0.050 -4,275 -6,315 -557 810 6,194 5,269
0.060 -4,355 -6,749 -581 282 5,655 5,111
0.070 -4,418 -7,102 -600 85 5,142 5,052
0.080 -4,467 -7,402 -615 -83 4,653 5,001
0.100 -4,533 -7,883 -635 -351 3,741 4,921
0.200 -4,791 -9,216 -712 -1,449 157 4,592
0.300 -4,832 -9,828 -724 -2,175 -2,386 4,374
0.400 -4,954 -10,155 -761 -2,758 -4,305 4,199
0.500 -4,980 -10,334 -769 -2,983 -5,796 4,131 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is increased from $1.50 to $1.80. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
73
Table 5-5. NPV1 for the Three Strategies for Age Classes 6 and 10 from a Price Increase2
Disease Incidence at First Detection
Average Age of Trees at First Detection
6 10
Strategy Strategy
1 2 3 1 2 3
0.001 16,947 14,030 13,384 20,952 18,043 17,397
0.010 14,516 13,734 12,655 18,441 17,717 16,643
0.020 13,131 13,409 12,239 16,982 17,359 16,205
0.030 12,176 13,087 11,953 15,964 17,005 15,900
0.040 11,578 12,768 11,773 15,311 16,654 15,704
0.050 10,896 12,453 11,569 14,579 16,307 15,485
0.060 10,500 12,141 11,450 14,140 15,964 15,353
0.070 9,911 11,832 11,273 13,507 15,624 15,163
0.080 9,615 11,527 11,185 13,175 15,287 15,063
0.100 9,117 10,926 11,035 12,610 14,625 14,894
0.200 6,957 8,098 10,387 10,192 11,506 14,169
0.300 5,705 5,542 10,011 8,759 8,683 13,739
0.400 4,314 3,234 9,594 7,163 6,128 13,260
0.500 3,827 1,154 9,448 6,585 3,822 13,086 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is increased from $1.50 to $1.80. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
74
Table 5-6. NPV1 for the Three Strategies for Age Classes 14 and 17 from a Price Increase2
Disease Incidence at First Detection
Average Age of Trees at First Detection
14 17
Strategy Strategy
1 2 3 1 2 3
0.001 23,398 20,488 19,843 24,174 21,264 20,619
0.010 20,873 20,152 19,086 21,649 20,928 19,862
0.020 19,401 19,781 18,644 20,175 20,557 19,420
0.030 18,369 19,415 18,335 19,143 20,191 19,110
0.040 17,703 19,052 18,135 18,477 19,828 18,910
0.050 16,959 18,693 17,912 17,733 19,469 18,687
0.060 16,508 18,338 17,776 17,281 19,114 18,551
0.070 15,863 17,986 17,583 16,635 18,762 18,358
0.080 15,520 17,638 17,480 16,292 18,414 18,254
0.100 14,934 16,952 17,304 15,705 17,728 18,078
0.200 12,424 13,719 16,551 13,190 14,494 17,324
0.300 10,915 10,787 16,098 11,676 11,563 16,870
0.400 9,239 8,130 15,596 9,996 8,906 16,366
0.500 8,609 5,727 15,407 9,362 6,503 16,175 1 Cumulative 15-year NPV ($/ac). 2Price per pound solid is increased from $1.50 to $1.80. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger.
75
Table 5-7. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Decline in Beta2
Disease Incidence at First Detection
Average Age of Trees at First Detection
0 3
Strategy Strategy
1 2 3 1 2 3
0.001 -2,065 46 -1,986 5,872 4,859 3,639
0.010 -3,872 -1,462 -2,529 2,498 4,595 2,627
0.020 -4,228 -2,650 -2,635 1,394 4,308 2,296
0.030 -4,526 -3,540 -2,725 637 4,026 2,068
0.040 -4,649 -4,243 -2,762 274 3,750 1,960
0.050 -4,731 -4,817 -2,786 -262 3,479 1,799
0.060 -4,893 -5,298 -2,802 -489 3,213 1,731
0.070 -4,946 -5,710 -2,851 -677 2,951 1,674
0.080 -4,991 -6,067 -2,864 -1,107 2,695 1,546
0.100 -5,059 -6,663 -2,885 -1,373 2,195 1,465
0.200 -5,294 -8,417 -2,955 -2,422 -62 1,151
0.300 -5,346 -9,330 -2,971 -3,106 -1,987 946
0.400 -5,449 -9,909 -3,002 -3,655 -3,649 781
0.500 -5,470 -10,303 -3,008 -4,112 -5,095 644 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) =1.5148125 – 0.3 = 1.2148125 for the 0 Age Class; Beta (2) = 0.8450625 – 0.3= 0.5450625 for age Class of 3; Beta (3) = 0.4440625 – 0.3= 0.1440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
76
Table 5-8. NPV1 for the Three Strategies for Age Classes 6 and 10 from a Decline in Beta2
Disease Incidence at First Detection
Average Age of Trees at First Detection
6 10
Strategy Strategy
1 2 3 1 2 3
0.001 11,826 8,449 7,931 14,918 11,542 11,025
0.010 11,288 8,285 7,769 14,351 11,361 10,855
0.020 10,759 8,104 7,611 13,791 11,160 10,687
0.030 10,289 7,922 7,469 13,291 10,959 10,537
0.040 9,866 7,742 7,343 12,840 10,759 10,402
0.050 9,483 7,561 7,228 12,430 10,560 10,278
0.060 9,132 7,381 7,123 12,053 10,361 10,165
0.070 8,810 7,202 7,026 11,706 10,162 10,061
0.080 8,513 7,023 6,937 11,383 9,964 9,965
0.100 7,978 6,667 6,776 10,802 9,570 9,790
0.200 6,081 4,914 6,207 8,710 7,629 9,163
0.300 4,827 3,209 5,842 7,306 5,740 8,752
0.400 3,106 1,550 5,393 5,454 3,901 8,266
0.500 1,303 -63 4,774 3,441 2,113 7,582 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) =1.5148125 – 0.3 = 1.2148125 for the 0 Age Class; Beta (2) = 0.8450625 – 0.3= 0.5450625 for age Class of 3; Beta (3) = 0.4440625 – 0.3= 0.1440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
77
Table 5-9. NPV1 for the Three Strategies for Age Classes 14 and 17 from a Decline in Beta2
Disease Incidence at First Detection
Average Age of Trees at First Detection
14 17
Strategy Strategy
1 2 3 1 2 3
0.001 16,854 13,479 12,962 17,469 14,093 13,576
0.010 16,280 13,290 12,790 16,894 13,904 13,404
0.020 15,712 13,081 12,619 16,326 13,695 13,233
0.030 15,205 12,872 12,467 15,818 13,487 13,081
0.040 14,746 12,664 12,329 15,358 13,278 12,943
0.050 14,327 12,457 12,204 14,940 13,071 12,817
0.060 13,943 12,249 12,089 14,555 12,864 12,702
0.070 13,588 12,043 11,982 14,200 12,657 12,596
0.080 13,259 11,837 11,883 13,870 12,451 12,497
0.100 12,663 11,427 11,705 13,274 12,041 12,318
0.200 10,505 9,407 11,057 11,112 10,021 11,669
0.300 9,043 7,440 10,629 9,646 8,054 11,240
0.400 7,138 5,525 10,127 7,738 6,139 10,737
0.500 5,062 3,661 9,424 5,658 4,276 10,033 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) =1.5148125 – 0.3 = 1.2148125 for the 0 Age Class; Beta (2) = 0.8450625 – 0.3= 0.5450625 for age Class of 3; Beta (3) = 0.4440625 – 0.3= 0.1440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
78
Table 5-10. NPV1 for the Three Strategies for Age Classes 0 and 3 from an Increase in Beta2
Disease Incidence at First Detection
Average Age of Trees at First Detection
0 3
Strategy Strategy
1 2 3 1 2 3
0.001 -3,104 -2,466 -2,298 2,514 4,712 2,632
0.010 -4,388 -6,016 -2,683 60 3,327 1,896
0.020 -4,683 -7,247 -2,772 -784 2,110 1,642
0.030 -4,789 -7,836 -2,804 -1,337 1,123 1,476
0.040 -4,966 -8,237 -2,857 -1,444 297 1,395
0.050 -5,039 -8,535 -2,879 -1,810 -409 1,335
0.060 -5,093 -8,771 -2,895 -1,963 -1,023 1,289
0.070 -5,131 -8,964 -2,906 -2,081 -1,564 1,253
0.080 -5,157 -9,126 -2,914 -2,405 -2,047 1,156
0.100 -5,181 -9,387 -2,921 -2,602 -2,877 1,097
0.200 -5,374 -10,110 -2,979 -3,341 -5,532 875
0.300 -5,378 -10,468 -2,980 -3,640 -7,058 786
0.400 -5,473 -10,691 -3,009 -4,042 -8,090 665
0.500 -5,492 -10,479 -3,015 -4,214 -8,832 613 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) = 1.5148125 + 0.3 = 1.8148125 for age class of 0; Beta (2) = 0.8450625 + 0.3= 1.1450625 for age class of 3; Beta (3) = 0.4440625 + 0.3= 0.7440625 for age classes 6 or larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
79
Table 5-11. NPV1 for the Three Strategies for Age Classes 6 and 10 from an Increase in Beta2
Disease Incidence at First Detection
Average Age of Trees at First Detection
6 10
Strategy Strategy
1 2 3 1 2 3
0.001 10,474 8,423 7,525 13,551 11,514 10,615
0.010 7,698 8,025 6,692 10,658 11,082 9,747
0.020 6,637 7,597 6,374 9,514 10,617 9,404
0.030 6,085 7,183 6,208 8,901 10,166 9,220
0.040 5,505 6,781 6,034 8,267 9,728 9,030
0.050 5,187 6,391 5,939 7,909 9,303 8,922
0.060 4,929 6,012 5,862 7,615 8,890 8,834
0.070 4,512 5,644 5,737 7,156 8,489 8,696
0.080 4,317 5,286 5,678 6,932 8,098 8,629
0.100 3,992 4,600 5,580 6,558 7,347 8,517
0.200 2,767 1,641 5,213 5,148 4,100 8,094
0.300 1,926 -718 4,961 4,174 1,498 7,802
0.400 1,237 -2,635 4,754 3,370 -629 7,560
0.500 875 -4,197 4,645 2,940 -2,369 7,432 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) = 1.5148125 + 0.3 = 1.8148125 for age class of 0; Beta (2) = 0.8450625 + 0.3= 1.1450625 for age class of 3; Beta (3) = 0.4440625 + 0.3= 0.7440625 for age classes 6 or larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
80
Table 5-12. NPV1 for the Three Strategies for Age Classes 14 and 17 from an Increase in Beta2
Disease Incidence at First Detection
Average Age of Trees at First Detection
14 17
Strategy Strategy
1 2 3 1 2 3
0.001 15,487 13,450 12,552 16,101 14,064 13,166
0.010 12,580 13,008 11,679 13,193 13,622 12,294
0.020 11,421 12,531 11,332 12,034 13,145 11,946
0.030 10,794 12,068 11,144 11,407 12,682 11,758
0.040 10,147 11,619 10,950 10,760 12,233 11,564
0.050 9,777 11,183 10,839 10,389 11,797 11,452
0.060 9,472 10,758 10,747 10,084 11,372 11,361
0.070 9,002 10,345 10,606 9,613 10,960 11,220
0.080 8,769 9,944 10,536 9,379 10,558 11,149
0.100 8,375 9,171 10,418 8,985 9,785 11,031
0.200 6,889 5,820 9,972 7,495 6,435 10,584
0.300 5,854 3,123 9,662 6,456 3,737 10,272
0.400 4,995 911 9,404 5,594 1,525 10,014
0.500 4,526 -907 9,263 5,121 -293 9,872 1 Cumulative 15-year NPV ($/acre). 2 Beta (1) = 1.5148125 + 0.3 = 1.8148125 for age class of 0; Beta (2) = 0.8450625 + 0.3= 1.1450625 for age class of 3; Beta (3) = 0.4440625 + 0.3= 0.7440625 for age classes 6 or larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
81
Table 5-13. NPV1 for the Three Strategies for Age Classes 0 and 3 from a Lowered Latency Period2
Disease Incidence at First Detection
Average Age of Trees at First Detection
0 3
Strategy Strategy
1 2 3 1 2 3
0.001 -4,195 192 -2,625 1,623 4,861 2,364
0.010 -4,898 -334 -2,836 -940 4,614 1,595
0.020 -5,152 -871 -2,913 -1,417 4,344 1,452
0.030 -5,213 -1,365 -2,931 -2,014 4,077 1,273
0.040 -5,244 -1,821 -2,940 -2,199 3,815 1,218
0.050 -5,259 -2,243 -2,945 -2,340 3,556 1,176
0.060 -5,380 -2,634 -2,981 -2,451 3,301 1,142
0.070 -5,392 -2,999 -2,985 -2,542 3,050 1,115
0.080 -5,402 -3,340 -2,988 -2,950 2,802 993
0.100 -5,417 -3,958 -2,992 -3,075 2,316 955
0.200 -5,437 -6,188 -2,998 -3,751 71 752
0.300 -5,498 -7,590 -3,016 -3,928 -1,907 699
0.400 -5,500 -8,558 -3,017 -4,353 -3,665 571
0.500 -5,501 -9,258 -3,017 -4,440 -5,234 546 1 Cumulative 15-year NPV ($/ac). 2 Latency is now 6 months for ages 0 and 3, and 2 years for ages of 6. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
82
Table 5-14. NPV1 for the Three Strategies for Age Classes 6 and 10 from a Lowered Latency Period2
Disease Incidence at First Detection
Average Age of Trees at First Detection
6 10
Strategy Strategy
1 2 3 1 2 3
0.001 11,287 8,447 7,769 14,372 11,540 10,861
0.010 9,181 8,264 7,137 12,193 11,337 10,207
0.020 8,045 8,061 6,796 10,994 11,112 9,848
0.030 7,457 7,859 6,620 10,355 10,888 9,656
0.040 6,849 7,658 6,438 9,703 10,665 9,460
0.050 6,504 7,457 6,334 9,320 10,443 9,345
0.060 6,006 7,258 6,185 8,785 10,223 9,185
0.070 5,761 7,060 6,111 8,509 10,003 9,102
0.080 5,547 6,863 6,047 8,267 9,784 9,030
0.100 4,944 6,471 5,866 7,608 9,350 8,832
0.200 3,533 4,567 5,443 6,006 7,240 8,351
0.300 2,254 2,754 5,059 4,554 5,230 7,916
0.400 1,453 1,031 4,819 3,623 3,320 7,636
0.500 1,075 -603 4,705 3,174 1,507 7,502 1 Cumulative 15-year NPV ($/ac). 2 Latency is now 6 months for ages 0 and 3, and 2 years for ages of 6. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
83
Table 5-15. NPV1 for the Three Strategies for Age Classes 14 and 17 from a Shortened Latency Period2
Disease Incidence at First Detection
Average Age of Trees at First Detection
14 17
Strategy Strategy
1 2 3 1 2 3
0.001 16,308 13,476 12,798 16,923 14,091 13,412
0.010 14,118 13,265 12,141 14,732 13,879 12,755
0.020 12,907 13,030 11,778 13,521 13,644 12,392
0.030 12,257 12,797 11,583 12,870 13,411 12,197
0.040 11,594 12,565 11,384 12,207 13,179 11,998
0.050 11,202 12,334 11,266 11,814 12,948 11,880
0.060 10,657 12,104 11,103 11,268 12,718 11,716
0.070 10,372 11,875 11,017 10,983 12,489 11,631
0.080 10,120 11,647 10,942 10,731 12,262 11,555
0.100 9,444 11,195 10,739 10,054 11,809 11,352
0.200 7,770 8,997 10,237 8,376 9,611 10,848
0.300 6,255 6,903 9,782 6,857 7,517 10,393
0.400 5,265 4,912 9,485 5,864 5,526 10,095
0.500 4,777 3,023 9,339 5,372 3,637 9,947 1 Cumulative 15-year NPV ($/ac). 2 Latency is now 6 months for ages 0 and 3, and 2 years for ages of 6. Beta (1) = 1.5148125 for the 0 Age Class; Beta (2) = 0.8450625 for age Class of 3; Beta (3) = 0.4440625 for Age Classes of 6 or Larger. Yield from HLB infected trees reduced 30% on “normal” yield for strategy 3.
84
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Strategy 3
Strategy 2
Strategy 1
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Cu
mm
ula
tive
Ave
rag
e G
rove
Ag
e
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Disease Incidence at First detection
Figure 5-1. Dominant Strategy Given Disease Incidence at First Detection and Average
Grove Age from a Change in Price: Top Subplot is Baseline, Middle and Bottom Subplots Shows Price Decline (from $1.50 to $1.20) and Increase (from $1.50 to $1.80), respectively
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Strategy 3
Strategy 2
Strategy 1
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Cu
mm
ula
tive
Ave
rag
e G
rove
Ag
e
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Disease Incidence at First detection
Figure 5-2. Dominant Strategy Given Disease Incidence at First Detection and Average Grove Age from a Change in Beta: Top Subplot is Baseline, Middle and Bottom Subplots Shows Beta Decline and Increase, respectively
85
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Cu
mm
ula
tive
Ave
rag
e G
rove
Ag
e
0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.50
5
10
15
Disease Incidence at First detection
Strategy 3
Strategy 2
Strategy 1
Figure 5-3. Dominant Strategy Given Disease Incidence at First Detection and Average
Grove Age from a Change in Latency: Top Subplot is Baseline, Bottom Subplot Shows Decline in Latency from 1 year to 6 Months for Groves with Average Age of 0 and 3 while the Latency for Groves 6 Years or Larger Remain at 2 Years
86
CHAPTER 6 CONCLUSIONS, RECOMMENDATIONS AND LIMITATIONS
The preceding chapters have sought to develop a management strategy for HLB
at the grove level for citrus producers in Florida. A baseline model was developed to
simulate the economic consequences for the “Do nothing” control strategy. This served
as a benchmark for the modeling of the infected tree removal strategy as well as the
enhanced foliar nutritional strategy. The adoption of a particular strategy by a grower is
seen to be a function of certain grove characteristics. This research has identified the
various zones of optimality for each strategy given a grove’s average age and initial
HLB infection rate.
This research attempted to integrate the intricate biological realities of HLB into
an economic decision making framework for producers. The basis of the biological
model is provided by the works of Bassanezi and Bassanezi (2008) and Bassanezi et
al. (2011). This research demonstrate that the complex biological features of HLB can
be transformed into an economic decision making process for citrus growers. The effect
of latency on control effectiveness especially when employing Strategy 2 for example is
addressed in this analysis. The most important contribution of this research is the
incorporation of both symptomatic and asymptomatic trees in the logistic spread curves
used in the analysis. This ensures that even if symptomatic trees are removed (as in
Strategy 2); spread through asymptomatic trees is still accounted for in the model. The
rate of spread of HLB is a function of the grove’s age cohort, which has been intricately
knitted into each of the three models of control strategies in this analysis. Additionally, in
varying the level of initial infection in the analysis, this research also demonstrates the
heterogeneous effects of HLB to NPV at the landscape level, whereby optimal control
87
decisions varies across neighbors. The significance of this research lies in its ability to
address these characteristics and formulate optimal control policy for effective decision
making.
In summary, we find that groves that contain younger trees at first detection have
low or negative net present value due to the faster spread of the disease in younger
groves in addition to low production from young groves. For Strategy 1, all groves with
an average age of 6 years and larger will yield a positive net present value, irrespective
of the initial level of infection. For Strategy 2, except when initial incidence is 40% to
50%, all groves with an average age of 6 or larger yields a positive net present value.
For Strategy 3, all groves with an average age of 3 or larger at all initial incidence levels
yields a positive net present value. Whether cost exceeds revenue in production is a
function of disease incidence and average grove age. The higher the initial incidence
level (the larger the average grove age), the more likely (less likely) that cost of
production exceeds revenue from production.
Finally, we find that the optimal strategy to adopt by a grower depends on the
average grove age at first detection and the initial rate of disease incidence at first
detection. Irrespective of the average grove age, once initial incidence is 20% or larger
in a grove, Strategy 3 should be implemented. The intuition of this recommendation is
that it is better to incur the extra costs of nutritional supplements than remove 20% or
more of productive but sick trees or even do nothing. The marginal revenue from this
action is more than its marginal cost. At higher rates of infection, Strategy 3 is preferred
over Strategy 2 because of the high tree removal rates associated with Strategy 2.
Implementation of Strategy 2 requires that initial incidence should be 3% to 8% for
88
groves 6 years or larger or 0.1% - 2% for groves of average age 0 or 3. Here, the
intuition is that removing 3% to 8% of infected mature trees or 0.1% - 2% of newly
established trees is more cost effective compared to spraying such trees with nutritional
supplements or doing nothing. When there is virtually no infection (0.1% to 1%) in a
grove of age 6 or larger, doing nothing is in the best interest of the producer. The
relationship between the net present value and model parameters such as delivered-in
price, the rate of spread of HLB, and latency has been established through the
sensitivity analysis. It is found that net present value is positively related to price but
negatively related to the rate of spread and the latency period. Changes in these
parameters also results in changes in the optimal strategy mix. In particular, results
indicate that superior detection methods that could reduce the period of latency would
benefit Strategy 2. Results also suggest that the primary consequence of
decreased/increased rate of spread (our proxy for psyllid control) is to make Strategy
2/Strategy 3 more attractive.
The rate of spread of HLB is related to three factors including average grove age,
initial incidence at first detection, and the psyllid population. Even though our model did
not directly incorporate psyllid control into the analysis, reduction in the annual rate of
HLB spread investigated via the sensitivity analysis can serve as proxy for psyllid
control because total elimination of psyllids notably terminates HLB spread.
Effective control of plant diseases that involves spread by vectors and other
weather factors such as HLB requires a model that recognizes landscape management
characteristics, which is missing in this analysis for now. Neighbor effects negatively
affects heterogeneous management protocols by adjacent growers since buildup of
89
bacteria titer in a grove practicing Strategy 1 or 3 could diminish the inoculum reduction
objective of a neighbor practicing Strategy 2. One other drawback is the lack of HLB
spread data from Florida required to estimate the model parameters. Although the
parameters used may not be representative of the HLB situation in Florida, the results
derived here do serve as a guide and reference point for growers and policy makers in
the industry. The assumption of no resetting greatly simplifies the calculation of disease
spread and the accompanying reduction in fruit production per acre. However, this
assumption clearly is a limitation on the derived results. The lack of knowledge on the
underlying distribution of the key variables that affect net present value in the presence
of HLB has forced us to proceed with the analysis in a deterministic framework. Cleary,
stochastic dominance would have been the best estimator of superiority. It is hoped that
future research can be greatly enhanced when most of these limitations are addressed.
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