Superinfection and the evolution of resistance to antimalarial drugs

Proc. R. Soc. B (2012) 279, 3834–3842

* Autho

Electron10.1098

doi:10.1098/rspb.2012.1064

Published online 11 July 2012

ReceivedAccepted

Superinfection and the evolution ofresistance to antimalarial drugs

Eili Y. Klein1,3,*, David L. Smith3,4,5, Ramanan Laxminarayan2,3

and Simon Levin1

1Department of Ecology and Evolutionary Biology, and 2Princeton Environmental Institute,

Princeton University, Princeton, NJ 08544, USA3Center for Disease Dynamics Economics and Policy, Washington, DC 20036, USA

4Department of Epidemiology, and 5Malaria Research Institute,

Johns Hopkins Bloomberg School of Public Health, Baltimore, MD 21205, USA

A major issue in the control of malaria is the evolution of drug resistance. Ecological theory has demon-

strated that pathogen superinfection and the resulting within-host competition influences the evolution

of specific traits. Individuals infected with Plasmodium falciparum are consistently infected by multiple

parasites; however, while this probably alters the dynamics of resistance evolution, there are few robust

mathematical models examining this issue. We developed a general theory for modelling the evolution of

resistance with host superinfection and examine: (i) the effect of transmission intensity on the rate of resist-

ance evolution; (ii) the importance of different biological costs of resistance; and (iii) the best measure of the

frequency of resistance. We find that within-host competition retards the ability and slows the rate at which

drug-resistant parasites invade, particularly as the transmission rate increases. We also find that biological

costs of resistance that reduce transmission are less important than reductions in the duration of drug-

resistant infections. Lastly, we find that random sampling of the population for resistant parasites is likely

to significantly underestimate the frequency of resistance. Considering superinfection in mathematical

models of antimalarial drug resistance may thus be important for generating accurate predictions of

interventions to contain resistance.

Keywords: Plasmodium falciparum; malaria; superinfection; drug resistance; evolution

1. INTRODUCTIONMore than a century ago, the Nobel prize-winning German

scientist Paul Ehrlich predicted that pathogens subjected to

drugs would evolve resistance [1]. The conjecture has been

proven true so often and in so many contexts that it can

be regarded as Ehrlich’s Law. There is, nevertheless, uncer-

tainty about virtually every other question of academic or

public health interest—in particular, the role of superinfec-

tion, defined as the simultaneous infection with multiple

strains of the same pathogen, and its influence on the

evolution of drug resistance. Even though superinfection

has been shown to alter the evolution of specific traits,

particularly virulence [2–4], a robust theory of the effect

of superinfection on the evolution of drug resistance is

still lacking. This is important in the study of malaria,

because superinfection, with the concomitant increase in

within-host competition, is likely to change the dynamics

of resistance evolution and have ramifications for control

efforts. Here, we extend some of the classic models

in malaria to consider the consequences of within-host

competition among drug-sensitive and drug-resistant

Plasmodium falciparum malaria parasites, the species of

malaria associated with the highest levels of morbidity

and mortality.

r for correspondence ([email protected]).

ic supplementary material is available at http://dx.doi.org//rspb.2012.1064 or via http://rspb.royalsocietypublishing.org.

9 May 201220 June 2012 3834

Early studies of P. falciparum malaria suggested that

high rates of exposure to malaria could result in simul-

taneous infection with multiple parasites, termed

superinfection [5]. This was not conclusively confirmed

until the 1970s [6], but it is now known that P. falciparum

malaria infections are typically composed of several

genetically distinct lineages, called the multiplicity of

infection (MOI), even in areas of low transmission [7].

Because of the complexity of the parasite’s life cycle, in

which parasite meiosis and recombination occurs in the

mosquito, genetic and phenotypic variation between

clonal P. falciparum populations can be significant,

which can impact their competitive ability.

Antimalarial drug resistance is encoded by mutations

in, or changes to, the copy number of genes relating to

the drug’s target or influx–efflux pumps that affect intra-

parasitic concentrations of the drug [8]. These changes,

which are beneficial in the presence of drugs, also have

a biological fitness cost to the parasite, lowering its

competitiveness [9,10]. In the presence of therapy, the

drug-resistant parasites have an advantage. Removal of

the drug exposes the parasites to increased competition

and can lead to a decline in the frequency of resistance-

conferring mutations, as occurred in Malawi after the

country stopped using chloroquine (CQ) [11]. However,

in areas with lower transmission (and lower MOI and

lower rates of competition), the frequency of resistance

has declined at a slower rate [12]. Thus, understanding

how superinfection affected historical examples of resist-

ance to the former first-line antimalarial drugs CQ and

This journal is q 2012 The Royal Society

no. d

rug-

resi

stan

t par

asite

s

0,0 1,0 2,0 3,0

0,1 1,1 2,1

0,2 1,2

0,3

drug use

no. drug-sensitive parasites

Figure 1. The MOI model with sensitive and resistant types.

The state variables describe the proportion of the populationwith a given MOI for both drug-sensitive and drug-resistantparasites, and the solid lines show changes that are the resultof transmission and clearance. Antibiotic use (dashed lines)reduces the MOI of drug-sensitive parasites, but not drug-

resistant ones. Biological costs of resistance are introducedas an increased propensity to clear or a reduced propensityto transmit drug-resistant types.

Superinfection and drug resistance E. Y. Klein et al. 3835

sulphadoxine-pyrimethamine (SP) is of great interest for

understanding the factors that are likely to be important

for the evolution of resistance to artemisinin-class drugs

and to the artemisinin combination therapies that are

now the first-line treatment for falciparum malaria in

much of the world.

The existing mathematical theory describing the evol-

ution of resistance is poorly developed with respect to

superinfection and within-host competition. Models of

superinfection in other organisms [2,3] either have

assumed that a dominant strain could displace another

pathogen and take over the host, but not vice versa, or

have not allowed for transmission from coinfected states

[13,14]. Neither of these approaches is biologically rel-

evant in malaria, where superinfection is the rule rather

than the exception, and evidence from the field [15,16]

and murine models [17–19] has demonstrated the

impact of within-host competition on the survival and

transmissibility of genetically distinct malaria clones.

In malaria, the mathematical theory of superinfection

was developed by Walton, Macdonald, Irwin, Dietz and

Bailey [5,20–24]. Their models allow for superinfection,

meaning that multiple genetically distinct clones coinfect a

host, and were developed to aid in matching assumptions

of the transmission rate with clearance rates. Although the

models generally fit the data on prevalence better than the

assumption that additional infections have no effect on the

clearance rate [20], epidemiological models of this type

have not been applied to problems of within-host compe-

tition and drug resistance, where it is often assumed

that individuals are infected by either drug-resistant or

drug-sensitive parasites only [25–27].

In their model of antimalarial resistance, Koella &

Antia [28] assume that individuals can be superinfected

by both drug-resistant and drug-sensitive infections (het-

erotypic) but not by two drug-resistant or drug-sensitive

types (homotypic). They assume that individuals with

heterotypic infections transmit both parasites at the

same rate regardless of the composition of drug-resistant

and drug-sensitive parasites in the population. This

significantly biases transmission, particularly when resist-

ance is first emerging, and drug-resistant parasites

are rare. As has been shown in species coexistence

models [29,30], the only way that one species can exclude

another is if there is significant competition in superin-

fected hosts, and in malaria, there is strong evidence

that drug-resistant and drug-sensitive parasites compete

in a host, and removing one will increase the fitness

advantage of the other [31]. Because the full costs of com-

petition are not embedded in the model (i.e. individuals

cannot be multiply infected by the same type of parasite),

when the fitness cost of resistance is low (but not zero),

the model predicts coexistence even when there is no

treatment in the population [28], a result that is not bio-

logically plausible (see electronic supplementary material,

appendix SI).

In this paper, using a general formulation of malaria

superinfection, we present a general theory for the evol-

ution of resistance when superinfection occurs. Building

on population genetics models for malaria [32–34] as

well as past epidemiological models [25], the approach

presented here allows for an examination of some of the

basic questions involved in how competition affects

the spread of drug resistance in different environments.

Proc. R. Soc. B (2012)

Our model provides a new way of thinking about model-

ling antimalarial drug resistance, incorporating many

of the concepts that are in common use in malaria

epidemiology today [35], and suggests ways to better

understand the important control points and identify

new directions for future research.

2. METHODS(a) Superinfection model

To model the evolution of resistance with superinfection, we

modified a Markov chain model for superinfection and clear-

ance to include clinical malaria and antimalarial drugs; the

original model was developed for malaria [22]. MOI (the

number of pathogens per host individual) increases as new

infections occur, but decreases as they clear. The state vari-

ables in the model represent the fraction of the population

that has a given MOI: Xi denotes the fraction of hosts with

an MOI of i. We have extended the model to track the

MOI of sensitive and resistant types (figure 1). Let Xi,j

denote the fraction of the population with i sensitive and j

resistant strains. The equations are formulated so thatPi;j Xi;j ¼ 1, and hence the sum of the time derivativesPi;j

_Xi;j ¼ 0. Thus, the values of the state variables describe

the joint distribution of resistant and sensitive phenotypes in

a population.

(b) Entomology

The dynamics of infection in the model follow a notation

similar to that of single-infection models by Macdonald

[36], as modified by Smith & McKenzie [37]. Vectorial

capacity (V ), the number of infectious bites by a mosquito

over its lifetime, is given by the formula V ¼ ma2e2gn/g,

where m denotes the number of mosquitoes per human

and a is the number of bites on humans per mosquito per

3836 E. Y. Klein et al. Superinfection and drug resistance

day. The instantaneous death rate is g (e2g is the probability

of a mosquito surviving 1 day) and n is the number of days

required for sporogony.

The daily entomological inoculation rate (EIR), the

number of infectious bites per person per day, is calculated

as the product of vectorial capacity and the fraction of mos-

quitoes that are infectious (P/(1 þ aP/g)), where P is the

proportion of the bites on the infected human population

that infect mosquitoes, assuming transmission efficiency c

from humans to mosquitoes (P ¼ cXi,j, where i = 0 or j =

0). The force of infection, or happenings rate (h), is bEIR,

where b, the infectivity rate, is the fraction of bites on

humans that produce a patent infection.

(c) Competition and a biological cost of resistance

The model ignores fluctuations in the abundance of parasites

within a host, but competition is naturally incorporated into

the model as a transmission bottleneck at the mosquito. In

the absence of any biases, the probability of a mosquito trans-

mitting either a resistant or a sensitive parasite is a function of

the proportion of each type ingested (assuming there is no

preference for selfing). We assume that resistant genotypes

in each gamete in the mosquito are lower than the proportion

of the resistant genotypes in the human infection; thus, the

parameter l weighs all the factors that could produce a bio-

logical cost of resistance in the dynamics of parasites from

hepatocyte to gametocyte.

The number of genotypes that are transmitted by each

infectious bite is limited both by the number of ookinetes

that have contributed sporozoites, and by the number of

liver-stage schizonts that arise from each infectious bite.

The proportion of sporozoites in a mosquito’s salivary

glands injected during a feeding event is typically small

[38–40], though the number of genetically distinct sporo-

zoites injected is unclear [41]. Because the bottlenecks

inherent within the system are likely to make the infection

of an individual with a large number of genetically diverse

sporozoites an uncommon event [42], we assume that each

mosquito transmits the offspring of only one gamete,

regardless of the MOI of the host that infected it.

Because competition for transmission occurs only when

a mosquito bites an individual with a mixed infection,

the overall probability that an individual sporozoite in the

next generation is sensitive (~Xw) or resistant (~X r) can be

represented as

~Xw ¼X

i

Xj

i2 þ lij

ði þ ljÞ2Xi;j ð2:1aÞ

and

~X r ¼X

i

Xj

ðljÞ2 þ lij

ði þ ljÞ2Xi;j ; ð2:1bÞ

where l , 1 (see electronic supplementary material, appen-

dix SII for derivation). Thus, the frequency of resistance in

new infections is ~X r=ð ~Xw þ ~X rÞ, and the force of infection

for sensitive (hw) and resistant (hr) parasites is defined as

hw ¼ h~Xw

~X r þ ~Xw

� �ð2:2aÞ

and

hr ¼ h~X r

~X r þ ~Xw

� �: ð2:2bÞ

Proc. R. Soc. B (2012)

We also assume that resistant parasites face an additional

cost in clearance. This is denoted by q, where qi,j ¼ [(i þ j)/j]a

and a . 0. Thus, a describes the bias in the proportion of

cleared parasites that are drug-resistant, relative to the fre-

quency of drug-resistant types among all types in a host.

While numerous reports have presented evidence of fitness

costs of resistance in malaria [10–12], there is no clear

understanding of how these costs are paid [10]. However,

as the resistance alleles are seemingly lost at a much higher

rate in high-transmission areas relative to low-transmission

areas [11,12], we assume that within-host competition is

the most important driver, and thus drug-resistant parasites

are assumed to have a biased clearance rate only when in

competition with drug-sensitive parasites.

(d) Clinical infections and drug use

Drug use is assumed to be associated with clinical symptoms

(primarily fever), which develop at rate c. The rate at which

clinical symptoms arise is independent of MOI. A fraction, r,

of symptomatic patients are assumed to use drugs and suc-

cessfully clear all sensitive parasites. The drug usage rate is

assumed to be constant over each simulation, but is varied

among simulations as noted. Treatment of resistant parasites

is assumed to be ineffective.

(e) Equations

The dynamics of the state variable, Xi,j, which denotes the

fraction of the population with i sensitive and j resistant

strains, are thus described by the following set of coupled

ordinary differential equations.

The equation describing the change in the proportion of

uninfected hosts (i ¼ 0, j ¼ 0) is

_X0;0 ¼ �hX0;0 þ r1;0X1;0 þ r0;1X0;1 þXNi¼1

rcXi;0; ð2:3aÞ

where r is the recovery rate of an infection consisting of i sen-

sitive and j resistant strains, h is the force of infection, c is the

rate that clinical symptoms develop, and r is the fraction of

those patients that are treated and clear the infection

successfully.

For individuals infected only with drug-sensitive clones

(i . 0, j ¼ 0),

_Xi;0 ¼ �hXi;0 � ri;0Xi;0 þ riþ1;0Xiþ1;0 þ ri;1qi;1Xi;1

þ hwXi�1;0 � rcXi;0; ð2:3bÞ

where q is the reduction in the duration of infection owing

to the biological cost of resistance, and hw is the force of

infection for drug-sensitive parasites.

For individuals infected only with drug-resistant clones

(i ¼ 0, j . 0),

_X0; j ¼ �hX0; j � r0; jX0; j þ r0; jþ1X0; jþ1 þ r1; jX1; j

þ hrX0; j�1 þXNi¼1

rcXi; j ; ð2:3cÞ

where hr is the force of infection for drug-resistant parasites.

For individuals infected with both drug-sensitive and

drug-resistant clones (i . 0, j . 0),

_Xi; j ¼� hXi; j � ri; jXi; j þ riþ1; jXiþ1; j þ ri; jþ1qi; jþ1Xi; jþ1

þ hwXi�1; j þ hrXi; j�1 � rcXi; j : ð2:3dÞ

The equations are constrained such that the model has a

‘triangular’ formulation (as in figure 1).

Superinfection and drug resistance E. Y. Klein et al. 3837

(f) Triangularity and the neutrality condition

The model presupposes coexistence in the parasite population

of a large number of distinct genotypes, but it considers com-

petition solely between drug-sensitive and drug-resistant

parasites, which differ both genetically and phenotypically.

To describe the effect of competition on the evolution of resist-

ance, it was necessary to establish that the model satisfied

general principles of ecological and population genetic neu-

trality as described by Lipsitch et al. [43]. These principles

note that the models of competition between genotypically

different but phenotypically similar strains should meet two

criteria: (i) the relative fraction of infected and uninfected

hosts should not depend on the frequency of either strain;

and (ii) the relative frequency of both strains should remain

stable for all time greater than zero. In other words, the struc-

ture of the model should not, in and of itself, generate

coexistence of indistinguishable strains, but mechanisms that

could induce coexistence should be introduced explicitly.

These principles suggest that the prior superinfection model

published by Koella & Antia [28] needs modification because,

as formulated, the model structure itself promotes coexistence.

In the electronic supplementary material, appendix SI, we

describe a model with similar properties to the Koella &

Antia superinfection model, in which homotypic superinfec-

tion was not allowed, and rigorously demonstrate that

coexistence is always an outcome of the model, even when

the resistant strain has a fitness cost.

To ensure that coexistence in our model of superinfection,

described earlier, is not an artefact of the model formulation,

we analysed a special case of the general form of the model,

in which the maximum MOI was two. In this case, the model

allows for both heterotypic superinfection and homotypic

superinfection. Numerical simulations confirm that in the

absence of drug treatment, drug-resistant parasites can neither

invade nor persist when they have a cost of resistance. We also

found that in the absence of either drug pressure or a biological

cost of resistance, the model is neutrally stable, provided

the transmission rate and the recovery rate of each type in a

heterotypic superinfection are exactly equal to each type

in a homotypic superinfection. In other words, the rate that

individuals become doubly infected with either the same type

or a different type must be equal, and the transmission rate of

heterotypic and homotypic infections must be the same regard-

less of strain composition, with an equal rate of transmission of

each type from heterotypic infections. Thus, the model in this

form does not predict coexistence when there is no specific

mechanism promoting its spread.

Both conditions remain true as MOI increases, provided

that the model structure maintains a triangular formulation

in which every possible combination of the maximum MOI

is included (i.e. in a model with a maximum MOI of three,

all possible states where the MOI is equal to three must be

possible: X3,0 and X2,1 and X1,2 and X0,3). Otherwise, the

model structurally creates a niche that allows for coexistence.

All our numerical simulations were done using a general

form of the model with the triangularity condition in place

and in which the maximum MOI was 30. Parameters used

in simulations were consistent with malaria epidemiologi-

cal literature [35,37,44], and are listed in the electronic

supplementary material, table S1.

(g) Frequency of resistance

We employ two measures of the frequency of resistance in

complex infections: (i) the fraction of the population that is

Proc. R. Soc. B (2012)

infected by at least one resistant strain, 1�P

i Xi;0; and

(ii) the fraction of the parasite load that is resistant,Pij j=ði þ jÞXi ; j: The former is important because it tracks

nearly exactly with the frequency that a treated clinical infec-

tion is resistant, which is the measure by which resistance is

often tracked in a population [45,46]. On the other hand, the

latter is particularly useful when discussing the role that

asymptomatic infections play in the spread of resistance.

3. RESULTSThe model is based on the ideas of malaria superinfection

as first laid out by Walton [24] and Macdonald [5] and

written down in equation form by Bailey [22]. However,

unlike previous models of drug resistance in malaria

[25,28], we explicitly model the effect of within-host

competition between drug-resistant and drug-sensitive

parasites. This allows for an examination of the impor-

tance of different types of fitness costs as well as how

competition affects the rate at which resistance spreads

across differential transmission rates.

To evaluate the model, we ran the system to equilibrium

without resistance and then introduced resistance at a low

frequency (1027). At low transmission rates (an annual

EIR of approximately one or less), the model predicts

that drug-resistant parasites will invade and spread,

and eventually dominate the drug-sensitive parasites.

However, as the transmission rate increases, the ability of

drug-resistant parasites to competitively exclude drug-

sensitive parasites decreases (see electronic supplementary

material, figure S1). This is because the mean MOI

increases with the intensity of transmission, measured in

terms of either vectorial capacity or EIR, and so compe-

tition increases. Thus, at low transmission rates, most

individuals are infected with approximately one infection

only, and the influence of within-host competition is

limited. As the mean MOI increases, it becomes more

difficult for resistant parasites to invade because competition

within the host increases, overcoming the ability of resistant

parasites to spread when they are rare. This is consistent with

historical suggestions that resistance to the former first-line

malaria drugs, CQ and SP, both emerged from areas of

low or unstable transmission [47,48]. Changing the drug

treatment rate for any particular transmission level increases

the competitive ability of resistant parasites, allowing them to

invade even when within-host competition increases at

higher transmission levels.

The model also predicts that superinfection modu-

lates coexistence. This result depends on the biological

fitness costs as well as the treatment rate. At high treatment

rates (80% of clinical infections treated), the drug-resistant

parasite competitively excludes the drug-sensitive parasite

at all fitness costs at low transmission. As the transmission

rate increases (annual EIR approx. 7), coexistence can

occur over a large range of fitness costs—even where the

fitness cost of clearance is zero (figure 2). At higher

transmission rates (annual EIR approx. 25), the range

over which coexistence is possible contracts. Lowering

the treatment rate (20% of clinical cases treated) shifts

the results and allows for coexistence at lower transmis-

sion rates, and shrinks the parameter range over which

coexistence can occur at higher transmission rates

(see electronic supplementary material, figure S2).

fitness cost of clearance (%)

013

2434

4350

56fitness cost

of transmission (%)7563

5343

per

cent

res

ista

nt

0204060

80

100

fitness cost of clearance (%)

013

2434

4350 fitness cost

of transmission (%)6343

2713

0

0204060

80

100

per

cent

res

ista

nt(a)

(b)

Figure 2. Fitness costs and coexistence. The cost of resist-ance can occur through either transmission or clearance.The transmission cost is measured as the relative differencein the contribution of resistant and sensitive parasites to

transmission when in equal abundance. The fitness cost ofclearance is measured as the reduction in the rate of clear-ance of a resistant parasite relative to a sensitive parasitewhen in competition. Thus, when there is little or no costof clearance but a significant cost of transmission, the

result is coexistence. As the transmission rate is increased(b), the parameter space over which coexistence can occuris abrogated. In addition, there are significant differences inthe range of each parameter over which coexistence canoccur. Areas of coexistence are marked by low to moderate

fitness costs of clearance and high costs of transmission.In fact, in low-transmission areas, resistant parasites cancoexist with sensitive parasites even when there is no fitnesscost of clearance. (a) Moderate transmission is defined as an

annual EIR of approximately 7, and (b) high transmission isan annual EIR of approximately 25. The treatment ratewas assumed to be 80%.

0 0.2 0.4 0.6

0

0.02

0.04

0.06

0.08

0.10

log of vectorial capacity

resi

stan

ce f

requ

ency

Figure 3. Measuring the frequency of resistance. There are

multiple ways to calculate the frequency of resistance in apopulation: (i) the prevalence of resistance (the fraction ofindividuals infected with a resistant parasite); (ii) the fractionof clinical infections that fail treatment; and (iii) the resist-ance load (the proportion of the parasite population that is

resistant). Depending on the measurement, the frequencyof resistance could be wildly different. To measure thesedifferences, we calculated the resistance load at the point intime when the percentage of clinical infections that faildrug treatment reached 10%. Although both measures

increase nearly concurrently at low transmission rates, astransmission increases (and thus so does competition), thefraction of the parasite population (dashed line) that is resist-ant soon peaks and then begins to fall, even as the proportion

of clinical infections harbouring resistant parasites (solidline) increases.

3838 E. Y. Klein et al. Superinfection and drug resistance

The fitness of drug-resistant parasites is proportional

to both the average duration of an infection and the ability

to transmit. The former is a function only of within-host

competition, whereas the latter is a function of both

within-host and among-host competition, because trans-

mission potential is a function of both transmissibility to

a susceptible vector (a function of competition between

clones within the host) and the propensity for infectious

vectors to infect a new host (the relative fraction of each

type). Results from the model suggest that resistant para-

sites can invade even with significant fitness costs of

transmission, but not when the fitness cost of clearance

increases significantly. This suggests that the ability to

remain competitively infectious within hosts is a stronger

determinant of the invasion capacity of drug-resistant

Proc. R. Soc. B (2012)

parasites than their probability of transmission at any

single event.

Competition also affects the rate that resistance

spreads in a population. At low transmission rates,

increasing the transmission intensity increases the rate

that resistance spreads in a population because, as noted

earlier, most infected individuals have an MOI of one

and there is no competition. Thus, the ability of drug-

resistant parasites to competitively exclude drug-sensitive

parasites increases as transmission increases. However, as

the average MOI increases and competition begins to

inhibit the ability of the drug-resistant parasite to exclude

drug-sensitive parasites, the rate at which resistance

spreads in a population decreases—or, stated another

way, the waiting time for resistance to reach a certain

threshold value grows longer (electronic supplementary

material, figure S3). This change is rapid at first, but as

the transmission rate continues to increase, the rate of

increase slows.

Superinfection also affects how the frequency of resist-

ance is calculated. Although the prevalence of resistance

(the fraction of infected people that harbour at least one

resistant parasite) increases concomitantly with the fraction

of the population that harbours at least one resistant para-

site, the resistance load (the proportion of types that are

resistant) changes at a different rate (figure 3). As the trans-

mission intensity increases, the resistance load increases at

a rate that is similar to the other measures. However, the

rate of increase slows after a point and then falls, while

Superinfection and drug resistance E. Y. Klein et al. 3839

the prevalence of resistance continues to increase. At

high transmission levels, this spread can be more than five

percentage points different when the fraction of clinical

infections reaches 10 per cent.

4. DISCUSSIONA prior model of superinfection in malaria with

drug-resistant and drug-sensitive parasites assumes that

heterotypic superinfection is possible but homotypic super-

infection is not [28]. However, this assumption means that

coexistence will always occur (see electronic supplementary

material, appendix SI). The structure of this prior model

[28] is also similar to earlier models of species coexistence

[29,30], which always predict coexistence unless there is

some type of competition in individuals heterotypically

superinfected. Thus, coexistence is an artefact of the math-

ematical model, not a generic property of the underlying

biological process.

In this paper, we replace those assumptions with a

model that implements a more robust competition frame-

work that allows for a thorough examination of the effect

of competition on the spread of drug-resistant malaria

parasites in an epidemiological context. We found general

conditions for the evolution of resistance as the outcome

of within- and among-host competition between two

classes of parasite types with differing fitness; the con-

ditions depend on competition, drug pressure and the

biological cost of resistance.

Results from a general model demonstrate that the

estimate of disease prevalence as a function of the trans-

mission rate was qualitatively similar to that found in

other models [5] and similar to estimates of the same

relationship in the field [49–51]. Our results also support

earlier studies showing a strong relationship between the

fitness cost of resistance and transmission [25,33].

When the fitness cost of resistance is low, drug-resistant

parasites are able to invade and spread across all trans-

mission levels. However, as the fitness cost of resistance

increases, the ability of drug-resistant parasites to invade

and spread is reduced. One possible reason previously

suggested for this relationship is that the parasite is exposed

to a higher level of drug pressure per infection in low-

transmission areas because a higher fraction of infections

in these areas result in clinical symptoms [33]. Our results

suggest that the low force of infection when recolonization

of infected individuals is rare plays a significant role in

low-transmission areas as well. After drug use eliminates

drug-sensitive parasites, individuals harbouring resistant

parasites are less likely to be recolonized by drug-sensitive

parasites, reducing within-host competition.

Although a biological cost of resistance has been

measured in in vitro experiments [52,53] and estimated

from the field [11,12], reductions in the competitive abil-

ity of the parasite are not expected to be equal across

different axes of competition. This has significant biologi-

cal and epidemiological importance. On the basis of

in vitro experiments in which CQ-resistant parasites had

an estimated 25 per cent loss of fitness per generation

[52], as well as murine models demonstrating slower

growth of drug-resistant parasites in the mouse [54,55],

it has been suggested that mutations conferring resistance

decrease the reproductive efficiency of the parasite and

slow growth [10]. The end result of the lower growth

Proc. R. Soc. B (2012)

rate is assumed to be a decrease in the probability of a

parasite being transmitted when a mosquito feeds on

blood because of the lower relative numbers of gameto-

cytes. A similar mechanism is also presumed to affect

the duration of infection; however, evidence on the rela-

tive cost of resistance on clearance is lacking, particular

in relation to transmissibility. We found that although

the reductions in transmission probability were impor-

tant, the ability to persist in an infection may be a more

important measure of the resistant parasite’s competi-

tive ability, particularly in lower-transmission settings.

These results can be partly explained by the vast time-

scale differences between these processes. Because the

time from infection of a susceptible mosquito to infection

of a human is an order of magnitude faster than the dur-

ation of infection, the benefit of increasing the duration of

infection is significantly greater than the benefit of

increasing infectiousness within an infection. The result

is that resistant parasites can invade even with significant

fitness costs of transmission, but not when the fitness cost

of clearance increases significantly.

Because the parasite has evolved an extremely long

duration of infection to maximize transmission opportu-

nities and can transmit efficiently at very low densities

[56], it is not surprising that the effect of changes in the

clearance rate is more pronounced on the viability of

drug-resistant parasites than on reductions in trans-

mission. However, the effect on attempts to control the

spread of resistance is important. Recent evidence has

shown the emergence of a delayed clearance phenotype

to the drug artemisinin in western Cambodia [57],

which has led to calls for implementing a resistance

containment strategy. Our results suggest that interven-

tions that can shorten the duration of infection for

resistant parasites, such as mass drug administration or

mass screening and treating, may be more beneficial

than has been recognized by earlier models that ignored

superinfection [58].

Within-host competition can also produce coexistence

of the two different parasite phenotypes at the population

level. Coexistence can occur when the relative advantage

of the sensitive parasite, measured as transmission poten-

tial over recovery rate, is greater in mixed infections.

However, the parameter range over which coexistence

can occur is altered by the transmission rate. At low

transmission rates, competition is lessened between

different phenotypes as well as with the same phenotypes.

Individuals with drug-resistant parasites can then be

easily reinfected because they have only a few parasites.

Thus, if drug-sensitive parasites have an advantage in

mixed infections, the result for a fixed treatment rate

will be a greater tendency to coexist. On the other

hand, as the transmission rate increases, individuals who

are treated with drugs are likely to harbour multiple

drug-resistant parasite clones. In this case, the invasion

capability of drug-sensitive parasites is reduced, making

the range over which coexistence can occur smaller.

In terms of designing control strategies, the time until

resistance reaches a critical level, which is critically influ-

enced by the transmission and treatment rates, may be a

more important measure than the final equilibrium level

of resistance. Currently, there is no standardized method-

ology for assessing the frequency of resistance, though it is

generally measured as the proportion of a type specimen

3840 E. Y. Klein et al. Superinfection and drug resistance

isolated from a clinical infection that did not adequately

respond to treatment [46]. However, screening surveys

of the human population using in vitro tests to determine

resistance of a type specimen has also been suggested as a

means to ascertain the frequency of resistance in the

population [59]. These sampling mechanisms are not

identical when individuals have complex infections,

and it is important to understand how these sampling

differences may end up measuring radically different

quantities. In high-transmission areas, when the fre-

quency of resistance is low, complex infections will

primarily consist of drug-sensitive parasites. Because

sampling is imperfect, the probability of false negatives

(i.e. at least one resistant parasite is present but was not

detected) is high [45], which suggests that random

screening surveys as a measure of resistance in higher-

transmission areas may result in biased results. This is

probably also true when withdrawing a drug. For

instance, even though the detection of CQ-resistant

mutations has dropped to undetectable levels in Malawi

[11,60], the complexity of malaria infections suggests

that drug-resistant parasites may still be present at low fre-

quencies and that the reintroduction of CQ may be

followed by a rapid resurgence in resistant infections.

In this model of malaria superinfection, which was

extended to incorporate competition between drug-sensi-

tive and drug-resistant parasites, our results are limited to

examining only the axis of competition between drug-

resistant and drug-sensitive phenotypes. The evolution

of antimalarial drug resistance is obviously a complicated

process involving superinfection and many interacting

processes, including immunity [25], the patterns of

drug use and heterogeneous biting [49]. The results of

this simple model clearly demonstrate that within-host

competition is a significant component in the emergence

and spread of drug resistance even at lower transmission

rates. Models that examine the best ways to control or

contain the emergence of resistance must take account

of superinfection and a variable degree of within-host

competition across the spectrum of transmission. In par-

ticular, the assumption of a blanket fitness cost of

resistance is less reasonable when the duration of infec-

tion dominates the probability that resistance will

spread. Future studies in this area will include how het-

erogeneous biting by the mosquito vector changes the

dynamics of competition, particularly in low-transmission

areas, and how host immunity interacts with virulence to

change the dynamics of the emergence of drug resistance.

This work was funded by Princeton University’s HealthGrand Challenges Program. This publication was alsomade possible by grant no. 1R01GM100471-01 from theNational Institute of General Medical Sciences (NIGMS)at the National Institutes of Health. Its contents are solelythe responsibility of the authors and do not necessarilyrepresent the official views of NIGMS. E.Y.K. wassupported by Princeton University (Harold W. DoddsFellowship). D.L.S. is funded by the RAPIDD program ofthe Science and Technology Directorate, Department ofHomeland Security, and the Fogarty International Center,National Institutes of Health.

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