Estimating spatial and temporal variations of the reproduction number for highly pathogenic avian influenza H5N1 epidemic in Thailand

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Preventive Veterinary Medicine 106 (2012) 143– 151

Contents lists available at SciVerse ScienceDirect

Preventive Veterinary Medicine

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stimating spatial and temporal variations of the reproduction numberor highly pathogenic avian influenza H5N1 epidemic in Thailand

. Marquetouxa,b, M. Paulb,c, S. Wongnarkpetd, C. Poolkhetd, W. Thanapongtharme,. Rogerc, C. Ducrotb, K. Chalvet-Monfraya,b,∗

Université de Lyon, VetAgro Sup, Campus Vétérinaire de Lyon, 69280 Marcy l’Etoile, FranceINRA, UR 346 Epidémiologie Animale, 63122 Saint-Genès-Champanelle, FranceCIRAD, UR 22-AGIRs, Campus international de Baillarguet, 34398 Montpellier, FranceFaculty of Veterinary Medicine, Department of Veterinary Public Health and Diagnostic Services, Kasetsart University, 50 Phahon Yothin Road, Chatuchak,angkok 10900, ThailandBureau of Disease Control and Veterinary Services (BDCVS), Department of Livestock Development, Ministry of Agriculture and Cooperatives, Bangkok0400, Thailand

r t i c l e i n f o

eywords:ighly pathogenic avian influenza (HPAI)eproduction numberpatial modeling5N1hailand

a b s t r a c t

Since 2003, highly pathogenic avian influenza (HPAI) H5N1 virus has spread, causing apandemic with serious economic consequences and public health implications. Quanti-tative estimates of the spread of HPAI H5N1 are needed to adapt control measures. Thisstudy aimed to estimate the variations of the reproduction number R in space and timefor the HPAI H5N1 epidemic in Thailand. Transmission between sub-districts was analyzedusing three different and complementary methods. Transmission of HPAI H5N1 was intense(R(t) > 1) before October 2004, at which point the epidemic started to progressively fade out

(R(t) < 1). The spread was mainly local, with 75% of the putative distances of transmissionless than 32 km. The map of the mean standardized ratio of transmitting the infection (sr)showed sub-districts with a high risk of transmitting infection. Findings from this studycan contribute to discussions regarding the efficacy of control measures and help target

ms.

surveillance progra

. Introduction

Since the disease first emerged in China in 1996, out-reaks of highly pathogenic avian influenza (HPAI) H5N1irus have occurred worldwide, causing important losses innimal production (Kilpatrick et al., 2006). The HPAI H5N1risis appears to represent the greatest threat to animal

ealth that the veterinary community has ever been calledo face, with very serious implications for public healthCapua, 2007). Controlling the spread of the disease in

∗ Corresponding author at: Université de Lyon, VetAgro Sup, Campusétérinaire de Lyon, 69280 Marcy l’Etoile, France.el.: +33 (0) 478 872 668; fax: +33 (0) 478 872 793.

E-mail address: [email protected]. Chalvet-Monfray).

167-5877/$ – see front matter © 2012 Elsevier B.V. All rights reserved.oi:10.1016/j.prevetmed.2012.01.021

© 2012 Elsevier B.V. All rights reserved.

poultry should help to limit the number of human casesof HPAI infection. Prevention and control measures tar-geting HPAI outbreaks in poultry are mainly based on theprohibition of movement, pre-emptive culling, and vacci-nation around infected areas (Yee et al., 2009). However,the temporal and spatial scales used for implementingcontrol measures often rely on empirical knowledge ofdisease spread mechanisms. Despite the range of controlstrategies that have been implemented, recent outbreakshave occurred, indicating that the disease remains difficultto control.

Mathematical models have become important tools toprovide quantitative estimations of the main parameters

that characterize the dynamic of human and animaldisease epidemics in space and time (Diekmann et al.,1990; Cross et al., 2007). The reproduction number is akey notion of disease dynamics (de Jong, 1995). Previous

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studies on the dynamics of the 2001 foot-and-mouth-disease epidemic in Great Britain (Haydon et al., 2003)showed the informative value of reproduction numberestimations for policy-making in veterinary public health.The estimation of the reproduction number is basedon the original Susceptible–Infectious–Removed (SIR)model proposed by Kermack and McKendrick (1991),which is a deterministic model that assumes a large,well-mixed population. The SIR model shows the evidenceof an epidemic threshold for successful disease invasion(Hethcote, 2000). This threshold is estimated by the‘basic reproduction number’ (R0), which is the expectednumber of secondary infections caused by a primary casein a completely susceptible population (Diekmann et al.,1990). The infection is expected to spread when R0 > 1,otherwise it will die out. By definition, R0 is an idealizedquantity that is virtually impossible to observe directlybut can be estimated indirectly (Mishra et al., 2011). Onthe other hand, the ‘effective’ reproduction number, Rt,is defined as the actual mean number of secondary casesper primary case at time t, in a population in which not allhosts are susceptible. The value of Rt is typically smallerthan the value of R0. Time variations of Rt can be assessedfrom epidemiological data. Rt allows the calculation of thereproductive number to be refined by estimating it at eachtime interval instead of a mean value. The recent epidemicof HPAI H5N1 was analyzed in previous studies usingmethods that enabled estimations of R0 (Tiensin et al.,2007; Ward et al., 2009; Soares Magalhaes et al., 2010).

Estimations of the within-flock reproduction numberwere discussed in Vietnam (Soares Magalhaes et al., 2010)and Thailand (Tiensin et al., 2007) in the context ofeffectiveness of poultry vaccination. The disease controlstrategies followed in Thailand differ from other Asiancountries as the vaccination of poultry against the H5N1subtype always has been prohibited there. Thailand wasinfected by HPAI H5N1 during the first and second waveof influenza (2004–2005), with 2045 outbreaks reported.Sporadic outbreaks have been reported since 2006. In theabsence of vaccination, control measures rely mainly onpre-emptive slaughter of poultry and movements restric-tions within a given perimeter around outbreaks.

The aim of the present study was to estimate the vari-ation of R0 in space and time for the HPAI epidemic inThailand. Ward et al. (2009) compared three methodsfor estimating R0 on HPAI H5N1 using the village as theepidemiological unit. In this present work, similar comple-mentary methods were combined to describe the spread ofthe disease. The unit of interest was the sub-district, a smalladministrative area used as the base unit in the design ofsurveillance and implementation of sanitary control mea-sures (Paul et al., 2010). Findings from this study shouldfacilitate further discussions on the efficiency of controlmeasure policies.

2. Material and methods

2.1. Data

Data on HPAI H5N1 outbreaks in Thailand were col-lected since January 2004 by official veterinarians of the

ry Medicine 106 (2012) 143– 151

Department of Livestock Development (DLD, Bangkok,Thailand). The DLD is in charge of the surveillance and mon-itoring of avian influenza in poultry (Paul et al., 2010). Thepresence of the HPAI H5N1 virus were confirmed by diag-nostic laboratories using reverse-transcriptase polymerasechain reaction and virus isolation in cloacal samples fromsick or dead poultry (Tiensin et al., 2009). The DLD out-breaks database included for each HPAI H5N1 outbreakthe following data: the detection date, location (code ofthe infected sub-district) and species of dead or sick poul-try (Tiensin et al., 2009). The present study is restrictedto outbreaks in poultry, which occurred during the secondwave of HPAI in Thailand (July 2004–May 2005). Duringthis period, both the passive and active components of thesurveillance system for detecting the disease were fullyimplemented. Passive surveillance of highly pathogenicavian influenza has been carried out in Thailand since 1997,when the H5N1 virus was detected in Hong Kong. It is basedon the compulsory notification by farmers of any clinicalsuspicion of HPAI outbreaks in poultry. The active com-ponent of the surveillance systems includes pre-slaughterand pre-movement testing and AIV monitoring programin layer, breeders and exporting pet birds. To strengthenthe surveillance, the Government has been implementingsince October 2004, an intensive survey known as the “X-ray campaign”. Twice a year and for the duration of onemonth, 990,000 volunteers conduct door-to-door surveysto collect field samples and to look for clinical suspicionsof HPAI on poultry in every house nationwide (Buranathaiet al., 2007).

A week number was assigned to each outbreak, withweek 1 corresponding to 1–7 January 2004. The DLDoutbreaks database included records of 1314 laboratory-confirmed cases (flocks of affected poultry) dating from 3July 2004 (week 27) to 12 April 2005 (week 67).

The epidemiological unit of interest for the study wasthe sub-district (‘Tambon’ in Thai), which covers a meanarea of 69.7 km2. The sub-districts located in the south ofPhetchaburi province (on the Kra isthmus of Thailand) wereexcluded from the analysis. As the few outbreaks reportedin that area were assumed to play a minor role in diseasetransmission because of its remoteness and minor geo-graphical connection with the main part of the country.As a result, 6277 out of the 7408 sub-districts of Thailandwere considered for statistical analysis.

An outbreak was defined as a sub-district with atleast one laboratory-confirmed case during a given week.Two farm outbreaks in the same sub-district during thesame week were considered as a unique outbreak at thesub-district level. In the period of interest, a total of1208 outbreaks were defined per week and sub-district.If successive confirmed cases within the same sub-districtoccurred more than 1 week but less e.g., than 2 weeks, thesewere considered to be a persistent outbreak. Otherwise, itwas considered as a new outbreak.

2.2. Estimation of the basic reproduction number (R0)

from the intrinsic growth rate

The R0 was estimated for the early phase of the epi-demic, during which interventions were absent and effects

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f susceptible depletion were small. An initial exponentialrowth is usually assumed for this phase, which is char-cteristic of most infectious diseases (Anderson and May,991). Two methods were used in this study to compute0, which both aimed at estimating the initial exponential-rowth rate (�) from the cumulative rate of cases.

The first method used a linear regression to estimate �.ith the logarithm of the cumulative number of cases as

he dependent variable and time as the predictor variable,he parameter � corresponded to the slope of the straightegression line. The regression must be calculated only dur-ng the exponential phase (Chowell et al., 2007; Vynnyckyt al., 2007).

The second method consisted of estimating � dur-ng the same exponential growth period by plotting the

ean number of new cases by unit of time (the week)gainst the cumulative number of cases. The slope ofhe corresponding straight regression line was the initialxponential-growth rate � (Favier et al., 2006).

The key point was to determine when the exponentialhase ended, in other words, when the curvature of theurve overtook the stochastic noise around the initial lin-ar trend. There are several methods for determining thisut-off (Wearing et al., 2005; Favier et al., 2006). Given theimited number of observations in the study’s dataset, theut-off was defined as the culmination point of the epi-emic, which corresponded to the 16th week (with 141 newutbreaks for a refractory period of 1 week, 122 new out-reaks for a refractory period of 2 weeks). The refractoryeriod represented the period of time following a case noti-cation and during which a new notification in the sameub-district was not considered as a new outbreak, but as

persistence of the previous outbreak.The reproduction number then was computed by sub-

tituting the estimate for � into an expression derived fromhe linearization of the SIR deterministic epidemic modelChowell et al., 2007). The method used here was adaptedrom Degallier et al. (2005) and Favier et al. (2006):

0 = 1 + �

�= 1 + � × T

With � = recovery rate (at the sub-district level); = initial exponential rate, T = length of the infectiouseriod (at the sub-district level), and T ≤ refractory period.

.3. Spatial scale of spread: distance to the nearestnfectious neighbor

The distribution of the distance between two successiveutbreaks located in different sub-districts, as defined inhe data section, was analyzed. The package” fitdistrplus”f R software (Pouillot and Delignette-Muller, 2010) wassed to find the best fit for this distribution.

.4. Estimation of the time variation of the effectiveeproduction number

First, the transmission dataset was constructed using similar method to previous work (Tiensin et al., 2007;ard et al., 2009). Assuming that all newly infected sub-

istricts were infected by an infectious sub-district during

ry Medicine 106 (2012) 143– 151 145

this phase of the epidemic, a simple deterministic SImodel (Anderson and May, 1991) was used to describethe transmission of HPAI H5N1 between sub-districts. Thetransmission rate of HPAI H5N1 between sub-districts (ˇ)was estimated from the relationship between the numberof newly infected sub-districts each week (new outbreaks,C(t)), the number of Infectious sub-districts each week(Infectious sub-districts, I(t)) and the number of suscepti-ble sub-districts each week (susceptible sub-districts, S(t)).At the sub-district level, it would be irrelevant to considera recovered (R) category in the model. Indeed, pre-emptiveslaughter was restricted to suspected farms or villages(Paul et al., 2010) during the period of interest (secondwave of the epidemic). In the absence of general culling,as soon as a sub-district was no longer infectious, it wasassumed to be immediately susceptible again.

A latency period of 1 week was used to take the timeinterval between the real date of infection for a sub-districtand the notification date registered in the database intoaccount. This latency period corresponded to the delay ofthe expression of clinical signs in the poultry flocks, addedto the delay before declaration or discovery of the outbreakby the surveillance system. As a result, with no restrictionin the remote transmission, the number of newly infectedsub-districts for a given week, C(t), was equal to the numberof infectious sub-districts in the following week.

According to the model, susceptible sub-districts S(t)in contact with the virus enter the infectious class at therate × I(t)/N(t), where is the transmission rate; I(t)is the number of infectious sub-districts at time t; andN(t) = S(t) + I(t) is the total number of sub-districts exposedto the risk of HPAI H5N1.

By calculating C(t), I(t), S(t) and N(t) at each week t, thetransmission rate could be deduced from the followingequation (Ward et al., 2009):

= C(t) × N(t)S(t) × I(t)

where is the transmission rate; C(t) is the number of newcases at the week t; S(t) is the number of susceptible to theinfection at the week (t), I(t) is the number of infected atthe week t;

N(t) = S(t) + I(t)

The effective reproduction number of the epidemiclies in the following equation (Anderson and May, 1991;Tiensin et al., 2007):

R = × T

where T is the duration of the infectious period.The calculation of the number of sub-districts cate-

gorized as infectious at each week (I(t)) depends on theduration of the infectious period. The calculation was per-formed for 2 hypotheses: an infectious period of 1 week oran infectious period of 2 weeks.

The calculation of the number of sub-districts exposed

at each week (N(t)) also depended on epidemiologicalfeatures, especially the geographical scale of the transmis-sion of HPAI between sub-districts. Two hypotheses wereexplored: ‘national’ versus ‘local’ transmission. In the case

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of a national transmission, the transmission between twosub-districts can occur even when the two sub-districtsare far apart. Consequently, the number of exposed sub-districts N(t) is equal to the overall number of sub-districtsincluded in the study. Indeed, all sub-districts in Thailandwere assumed to have poultry and thus to be at risk ofan HPAI H5N1 outbreak. In the case of a local transmis-sion, as suggested by Souris et al. (2010), the transmissionbetween two sub-districts can occur only when the dis-tance between sub-district centroids is less than a distanced. In this case, the number of exposed sub-districts N(t) isequal to the number of sub-districts in Thailand for whichthe distance between the centroid of the exposed sub-district and the centroid of an infectious sub-district is lessthan d. The 80% and the 90% quantiles of the fitted distri-bution of the distance to the nearest infectious neighborfor each sub-district were used to determine d. As a result,the model was performed for a national transmission andtwo different radius of local transmission. With the outputof this model, the curve representing the time variation ofthe effective reproduction number could be drawn underthe different hypotheses.

2.5. Estimation of the spatial variation of thetransmission of HPAI in Thailand

Despite the absence of detailed information concerningthe infectious network, it was possible to reconstruct anepidemic tree from the notification data. The nearest infec-tious neighbor method, a deterministic method adaptedfrom Haydon et al. (2003) and Ward et al. (Haydon et al.,2003; Ward et al., 2009) was used to build the infectiousnetwork. Under this method, a putative source of infection(referred to as a “parent”) was attributed to each outbreak.For each outbreak, previously reported outbreaks withinthe infectious period (for example, up to 1 week before fora one-week infectious period) were selected. This estima-tion consequently depended on the hypothesis concerningthe duration of the infectious period at the sub-districtlevel. Estimations of the length of individual-based infec-tious periods for HPAI in poultry vary in the literature. Fromexperimental studies, it widely is admitted that the periodduring which birds shed the virus after inoculation is lim-ited, being generally less than 1 week in chicken or ducks.Mortality occurs only within 2 or 4 days in inoculatedchicken (Webster et al., 2006; Lee et al., 2009). However,at the sub-district level, a between-flocks transmission ispossible; therefore the overall infectious period for a sub-district was assumed to be longer than for an individual.Based on the results of Ward et al. (2009) (1 week infectiousperiod at the village level for HPAI H5N1 in Romania) andSouris et al. (2010) (3 weeks infectious period at the sub-district level), the model was tested for both a one-weekinfectious period and a two-week infectious period.

The closest outbreak (Euclidian distances between sub-district centroids) during the last week or the last 2 weekswas selected as the putative parent of the outbreak, until

each outbreak had a putative source. Then the number ofputative daughter outbreaks different from itself (persis-tent outbreaks) arising from each outbreak at each weekcould be deduced. This number, corresponding to the local

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effective reproduction rate, was called Ri(t), i referring tothe sub-district source of the infection and t referring tothe week considered.

It then was possible to calculate a weekly mean R(t), byaveraging the local Ri(t) of each week:

R(t) =(∑nt

i=1Ri(t))

nt

With Ri(t) representing the number of putative daugh-ters outbreaks different from itself arising from sub-districti at week t, nt representing the number of outbreaks (sub-districts) identified as the putative source of infection atweek t (outbreaks of week t − 1 or outbreaks of week t − 1and of week t − 2, depending on the duration of the infec-tious period of 1 week versus 2 weeks).

This value R(t) corresponds to a mean value of the effec-tive reproduction number for all of the areas where theepidemic occurs at week t.

For each sub-district i identified as a potential parent, aweekly standardized ratio of transmission sri(t) was calcu-lated. It was the ratio of the value the Ri(t) on global value ofthe weekly mean R(t) over all of the affected sub-districts,defined as:sri(t) = Ri(t)

R(t)Finally, for each sub-district i a global standardized ratio

sri was calculated by averaging the sri(t) over the wholeepidemic course, defined as:

sri =∑ki

t=1sri(t)

ki

In this equation, sri represents the mean standardizedratio of transmission for the sub-district i over the entireperiod of interest. The term ki represents the total num-ber of weeks during which the sub-district i was infectious(during which this sub-district was identified as the puta-tive source of infection for other infected sub-districts).The term sri is a local measure of the transmission at thesub-district level over the entire period of interest.

The mean standardized ratio sri was mapped usinggeographical information systems (ArcGIS© software). Thespatial autocorrelation of these sri were analyzed using theglobal and the local Moran test with the Sphere of Influenceneighbors (Bivand et al., 2009), using the package” spdep”of R software (Bivand et al., 2008).

3. Results

3.1. Basic reproduction number

Two methods and two assumptions were used to esti-mate R0 during the second wave of the epidemic, based onthe data of the epidemic curve. Depending on the methodand assumption used, R0 ranges from 1.27 [1.18–1.36] to1.60 [1.44–1.75] (Table 1).

3.2. Spatial scale of spread: distance to the nearestinfectious neighbor

A gamma distribution was fitted to the log-transformeddistance to the nearest infectious neighbor. The distribu-tion was very similar independent of the length of the

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Table 1Estimation of the R0 during the initial exponential-growth phase of the second wave of the HPAI H5N1 epidemic in Thailand, using two different methodsadapted from the literature and two refractory periods.

Refractory period of 1 week Refractory period of 2 weeks

Method adapted from(Vynnycky et al., 2007)

Method adapted from(Favier et al., 2006)

Method adapted from(Vynnycky et al., 2007)

Method adapted from(Favier et al., 2006)

Initial exponential-growth rate (SE) � = 0.27 � = 0.31E = 0.038

� = 0.26 � = 0.30

= 1.31.23–1.39

io

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3

hoaRo

Fahtd

(SE = 0.045) (SR0 [95% CI] R0 = 1.27

[1.18–1.36]R0

[1

nfectious period (1 or 2 weeks). The distribution for ane-week infectious period is shown in Fig. 1.

The nearest infectious neighbor was located on averaget 29.9 km with a min at 1.606 km and a max at 348 km (forn infectious period of 1 week) or 25.9 km with a min at.606 km and a max at 348 km (for an infectious period of 2eeks) from an outbreak. More than 75% of the outbreaksad a parent outbreak within a 32.1 km range. The spreadetween sub-districts appeared to be predominantly andtrongly local, on average less than 31 km, compared tohe mean distance between all sub-districts of this part ofhailand, which is 343.4 km with a min at 0.341 km and aax at 330 km.

.3. Temporal variation of transmission of HPAI

Estimates of R(t) were very similar whatever theypothesis regarding the length of the infectious period (1

r 2 weeks). Fig. 2 presents the output of the SI model for

one-week infectious period, with the time variations of(t) according to different hypotheses concerning the scalef the spread (local versus global).

Empirical and theoretical distribution

log(nearest infectious neigbor distance)

De

nsity

6543210

0.4

0.3

0.2

0.1

0.0

400 km150 km55 km20 km7.4 km2.7 km0 km

ig. 1. Distribution of the logarithm of the distance between an outbreaknd the nearest infectious neighbor, for a one-week infectious period. Theistogram represents the empirical distribution and the curve representshe density of probability of the theoretical fitting distribution (gammaistribution with a shape parameter of 7.54 and a scale parameter of 2.74).

) (SE = 0.044) (SE = 0.039)

]R0 = 1.53[1.35–1.67]

R0 = 1.60[1.44–1.75]

The variations of R(t) were the same regardless of theconsidered spatial scale for the spread of HPAI. How-ever, the effect of long-distance jumps was visible onthe spread at the beginning and end of the epidemic. Inthese parts, a national transmission, allowing long-distancejumps between outbreaks, increases the value of R(t) com-pared to more local transmission hypothesis (Fig. 2).

The course of the epidemic can be graphically dividedinto two sections. Before week 40, R(t) was on average highwith several peaks. In contrast, after week 40, R(t) remainedalmost steadily under the epidemic threshold except forone large peak.

3.4. Spatial variation of transmission of HPAI

3.4.1. Distribution of Ri(t)One thousand two hundred and eight outbreaks (sub-

districts with at least one case notified during a given week)

occurred during the second wave of HPAI H5N1 in Thailand.For a 1 week infectious period, the reconstruction of theinfectious network showed that out of these 1208 out-breaks, the sub-district was infectious the previous week

60504030

10

86

42

0

Week

R(t

)

Fig. 2. time variation of the effective reproduction number of the HPAIH5N1 epidemic in Thailand, for a one-week infectious period: graph cor-responding to a local spread, over the whole territory of Thailand (—);graph corresponding to a local spread, within a radius of less than 90%quantile of the nearest infectious neighbor distance distribution (- - -);graph corresponding to a local spread, within a radius of less than 80%quantile of the nearest infectious neighbor distance distribution (· · ·· · ·);line corresponding to the epidemic threshold (- · - · -).

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Standardized ratio (sr)

[0,0.7]

]0.7, 1.3]

]1.3,∞]

Subdistrict boundary

2001000 Kilometers50

district

Fig. 3. Choropleth map of the transmission standardized ratio at the sub-a one-week infectious period.

for 199 outbreaks (outbreaks persisting for at least 2 weeks)and 1009 outbreaks were new outbreaks (Table 2). More-over, for the sub-districts identified as a source of infectionfor other sub-districts, the proportion of outbreaks thathad no putative daughter outbreaks the following week

were 47% for an infectious period of 1 week and 73% for aninfectious period of 2 weeks. Mapping of the standardizedratio (sri) was obtained using a choropleth map catego-rizing the risk at three levels: high (sri > 1.3), intermediate

Table 2Distribution of Ri(t), the number of putative daughter outbreaks.

Infectious period

1 week 2 weeks

Number of outbreaks(a sub-district infectiousfor a given week)

New outbreaks 1009 918

Persistent outbreaks 199 209

All Ri(t) Min 0 0Max 25 13Average 0.83 0.41

Ri(t) > 0 Min 1 1Max 25 13Average 1.86 1.51

level during the second wave of the HPAI H5N1 epidemic in Thailand, for

(0.7 < sri < 1.3) and low standardized ratio (sri < 0.7) (Fig. 3).A standardized ratio equal to one (sri = 1) from a specificsub-district i corresponds to the mean risk of transmissionbetween all sub-districts in the same period. The Moran’sI test applied to the overall distribution of sri was not sig-nificant (using the Sphere of influence neighbors, Moran’sI = 0.0196, p-value = 0.228). However, the local test of spa-tial autocorrelation detected 17 significant sub-districts(p = 0.046) among the 752; and for 7 of them, the localMoran’s I was highly significant (p = 8.6 × 10−6). So, globallythe sri were not correlated with those of its neighbors, nev-ertheless in few area there is was strong spatial autocorre-lation (i.e., the sri are correlated with those of its neighbors),Furthermore, these areas corresponded to a high level of sri.

4. Discussion

In this paper, the variation of the key parameters ofthe dynamic during the second wave of the HPAI H5N1epidemic in Thailand were analyzed in time and in space.

The use of several methods provided complementaryinformation to characterize the main features of thespread of HPAI from one sub-district to another from July2004 to April 2005.

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The nearest infectious neighbor method used to buildhe infectious network avoided the computational bur-en of a numeric method. Under this method, a putativeource of infection (referred to as a “parent”) was attributedo each outbreak eliciting to Ri(t) estimate as directly asossible from the data. This Ri(t) is a very local and tem-oral estimation of the transmission, varying with theub-district and the week.

It should be noted that the main methodologicalssumption underlying this work involved the length ofhe infectious period at sub-district level. In accordanceith previous work (Ward et al., 2009; Souris et al., 2010),

he sensitivity of our model to the length of the infectiouseriod was tested using two hypothetical infectious peri-ds, the first of 1 week, the second, 2 weeks. All resultsere very similar for both hypotheses. Another important

ssumption, one common to all methods adapted from theearest neighbor method, was that proximity in both timend space are the strongest factors driving the spread of aontagious disease such as HPAI. However, the same pat-erns can arise from the presence of other risk factors thatre spatially correlated. In this study, it was assumed thathe infectious sub-district closest to each outbreak serveds the source of that outbreak. Information on the contactetwork of sub-districts, with respect to the movement ofoultry, would improve the validity of such assumptionWard et al., 2009). Concerning the assumption about theeriod of latency, the same duration of 1 week was used

n a previous paper on HPAI H5N1 outbreaks (Ward et al.,009).

This study also implicitly assumed that all outbreaksere detected and reported. This assumption was rea-

onable as the two complementary surveillance systemspassive surveillance, and a reinforced, nationwide, active

onitoring program called, “X-ray survey” (Tiensin et al.,007; Paul et al., 2010)) were implemented during thetudy period ensuring the detection of outbreaks (Tiensint al., 2009). In addition, under-reporting may have beenimited at the sub-district level. As the number of flocks in

sub-district is large, there should be at least one infectedarm being notified if an outbreak appears in a sub-district.

The basic reproduction number R0 at the beginning ofhe epidemic was estimated to be between 1.27 and 1.60epending on the method of estimation and the hypothe-is of infectious period at the sub-district level that weresed. This value corresponds to the average total numberf sub-districts contaminated from a single contaminat-ng sub-district. It is noteworthy that, for both methods,alues of R0 always were significantly higher than the epi-emic threshold value 1 (none of the confidence intervals

ncluded the value 1).These estimated values for R0 were slightly lower than

he R0 calculated by Ward (1.95–2.68) for the epidemic ofPAI H5N1 in Romania (Ward et al., 2009). This may reflect

difference in HPAI spread patterns between Thailand andomania. The difference also could be explained by the dif-

erent intensities of the epidemics (110 outbreaks in 25

ays in Romania compared to 1210 outbreaks in 294 days

n the present study), or by the difference in the size ofhe epidemiological units (Romanian village versus Thaiub-district).

ry Medicine 106 (2012) 143– 151 149

This study showed that the spread of HPAI during thesecond wave of the epidemic in Thailand was predom-inantly a local process, with a mean distance betweenthe centers of two successively infected sub-districts of29.9 km (for an infectious period of 1 week) or 25.9 km (foran infectious period of 2 weeks). These results are similarto those of Ward et al. (2009) who found a mean distancebetween outbreaks of 23.36 km (95% CI 18.19–28.53). Inthe present study, 75% of the outbreaks were located at adistance of less than 32 km from the closest outbreak. Thisis consistent with previous work concerning the H5N1 epi-demic in Thailand (Souris et al., 2010), which estimated60 km as the maximum distance for the transmission pro-cess, with rare long range transmission jumps. Given theshort distances involved in transmission, control measuresthat reduce the transmission between neighboring areasare very important. With the prohibition of vaccination inThailand, the control of movement played an importantrole in limiting the spread of HPAI. Our results support thepolicy currently implemented in Thailand, with a restric-tion on movements within, at the minimum, a 10-kmradius around an outbreak.

The number of putative daughter outbreaks rangedfrom 0 to 25 for a one-week infectious period, and from0 to 13 for a two-week infectious period. These resultsare very similar if they are calculated on the overall infec-tious period. The highest numbers of putative daughteroutbreaks were observed at the beginning of the epidemiccurve, when transmission peaked. The mean number ofputative daughter outbreaks each week was 0.83 and 0.41respectively for an infectious period of 1 week or 2 weeks.This corresponds to an estimation of the mean effectivereproduction number (0.83 for an infectious period of 1week, and 0.82 (=0.41 × 2) for an infectious period of 2weeks). These values are lower than the value of basicreproduction number. This is logical, as the effective repro-duction number was estimated from an average of thevalues of R(t) over the epidemic curve while the basic repro-duction number was estimated from the early epidemicphase only, when few control measures were in place.Moreover, the outputs of a deterministic SI model gave atime variation of R(t). A peak was observed for week 54,but it would be excessive to conclude that there was avery high spread at this period of time. Indeed, this out-put could be due to the fact that only one outbreak wasobserved in week 54, while 8 outbreaks were recorded forweek 55. However, the present study demonstrated a tem-poral pattern in the variations of R, with high values of R0at the beginning of the epidemic, which then decreasedand remained stable under the epidemic threshold. Theperiod (1 July–29 September 2004) before week 40, witha high R(t) and some peaks, corresponded to an intensespread of HPAI between sub-districts. Whereas controlmeasures (pre-emptive slaughter, movement restrictions)were fully implemented in July 2004, variations of theR(t) showed that the disease spread was under controlonly after week 40. It is noteworthy that week 40 (30

September 2004–6 October 2004) corresponded to thebeginning of the first X-ray survey. The X-ray survey wasdesigned to reinforce the surveillance of HPAI in Thailand.During the month of October 2004, 990,000 volunteers

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conducted door-to-door surveys to check poultry nation-wide and collect samples. The goal of the X-ray also wasto cull suspected and positive flocks without delay, when-ever the infection was suspected or detected based on theHPAI H5N1 clinical case definition or as a result of lab-oratory confirmation (Tiensin et al., 2007). Tiensin et al.(2007) noticed a sharp increase in the amount of outbreaksdetected during October–November 2004. Results from ourstudy suggest that the considerable efforts made to controlthe disease were fruitful as the transmission parametersdecreased remarkably at that time.

Soares Magalhaes et al. (2010) observed at the flock levelthe same tendency in the temporal variations of R as theone we evidenced at the sub-district level. However, theR0, estimates that we produced at the sub-district level forHPAI H5N1 (ranging from 1.27 to 1.6) were lower thanthose estimated by Tiensin et al. (2007) for within-flocktransmission of the same disease (from 2.26 to 2.64). Thismight be due to the divergent scale of interest, the largestepidemiologic study leading naturally to a smaller valueof R0 or R(t) for the same epidemics. Indeed, within a herd,the contacts are closer favoring transmission and infectiousperiod is not significantly changed.

The standardized ratio (sr) we produced showed thespatial variations of the capacity of each sub-district totransmit HPAI H5N1 to other sub-districts. The over-all spatial pattern of standardized ratios was randomlydistributed. However, sub-districts with significant localautocorrelation were identified. The implementation ofcontrol measures in the field may have differed betweensub-districts, and may have contributed to spatial varia-tions of the sub-district reproduction number. However,the characteristics of these ‘hot-spots’, i.e. sub-districtswith a high potential for transmitting the disease toanother, should be explored. Intrinsic features such as ele-vation, rice cultivation, presence of free-grazing ducks orproximity to main transportation axes have been foundto influence the spatial distribution of HPAI H5N1 out-breaks (Gilbert et al., 2006; Paul et al., 2010). It is natural toask whether the risk factors associated with transmissionbetween sub-districts would be the same.

This study illustrates how complementary methodscan be used to study the temporal and spatial pattern ofdisease spread. With regard to the spread of HPAI betweensub-districts in Thailand during the second wave, thevariation in time of the reproductive number likely wasassociated with the efficacy of disease control measuresthat were implemented at that time. Control measuresalso may partially explain the spatial variations of trans-mission capacity that were highlighted in our study, butfurther work is needed to precisely identify which factorsunderlie the geographical pattern of transmission.Conflictof interestNone declared.

Conflict of interest

None declared.

Acknowledgments

We are grateful to Dr. Yukon Limlaemthong and Dr.Sakchai Sribunsue for supporting this work. We thank

ry Medicine 106 (2012) 143– 151

the National Institute of Animal Health and the ProvincialLivestock Offices of the Department of Livestock Develop-ment (Thailand), for their support. We are grateful to theFrench-Thai PHC program which provided us additionalsupport. We also thank Grace Delobel for verifying ourwritten English.

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