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Summary

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices

Objective  Antimalarial drugs kill the asexual parasites responsible for causing disease and some, notably chloroquine and the artemisinins, also kill the sexual transmission stages known as gametocytes. It is invariably argued by malariologists that gametocytocidal activity is beneficial because it reduces the rate at which resistance evolves by ‘reducing the transmission of resistant parasites’. This seems dubious from a population genetics perspective, where intuition would lead to the opposite conclusion. The objective was to reconcile these differing views.

Methods  The effect of gametocytocidal drug activity was quantified mathematically and calibrated using field data.

Results  It appears to be a robust result that gametocytocidal activity actually promotes the spread of resistance through a population; the underlying reason is that gametocytocidal activity reduces transmission of drug-sensitive forms to a greater extent than the drug resistant, thereby increasing the spread of the latter. The increased rate of spread of resistance is quantified and appears to be small providing drug coverage is moderate or low.

Conclusions  Citing reduced spread of resistance as a justification for deploying gametocytocidal antimalarials is unjustified; the deliberate use of a gametocytocidal antimalarial at high coverage to reduce transmission may ultimately be counterproductive through its rapid promotion of drug resistance.

Keywords Plasmodium falciparum

malaria

drug resistance

combination therapy

gametocytocidal

Objectifs  Tous les médicaments antimalariques tuent les parasites asexués qui causent la maladie. Certains, notamment la chloroquine et l'artemisinine tuent également les stades de transmissions sexuelles qui sont les gamétocytes. Il est invariablement soutenu par les malarialogistes que l'activité gamétocytocide est bénéfique car elle réduit la fréquence avec laquelle la résistance évolue ‘en réduisant la transmission des parasites résistants’. Cela semble un argument douteux pour une vision de génétique de populations ou l'intuition conduirait plutôt vers une conclusion opposée. Notre objectif a été de concilier les différentes visions.

Méthodes  L'effet de l'activité des médicaments gamétocytocides a été mathématiquement quantifié et calibrée en utilisant des données de terrain.

Résultats  Il apparaît plutôt consistant qu'en fait, l'activité gamétocytocide favorise la dissémination de résistance dans la population, la raison étant que l'activité gamétocytocide réduit de façon beaucoup plus considérablement la transmission des formes sensibles que celle des formes résistantes au médicament, augmentant ainsi la transmission de ces dernières. L'augmentation du taux de dissémination de résistance a été quantifiée et semble faible lorsque la couverture médicamenteuse est modérée ou faible.

Conclusion  L'argument de la réduction de la dissémination de la résistance comme justificatif au déploiement de médicaments gamétocytocides n'est pas fondé. L'utilisation délibérée d'antimalariques gamétocytocides sur de vastes couvertures afin de réduire la transmission peut en fin de compte s'avérer antagoniste par la favorisation rapide de la résistance aux médicaments.

Mots clés P. falciparum

malaria

résistance aux médicaments

thérapie de combinaison

gamétocytocide

Objetivos  Todos los fármacos antimaláricos terapéuticos matan los estadíos asexuales del parásito, causantes de la enfermedad, y algunos – principalmente la cloroquina y las artemisinas – también matan los estadíos sexuales de transmisión, conocidos como gametocitos. Desde siempre, los malariólogos han argumentado que la actividad gametocida es beneficiosa, puesto que reduce la tasa de evolución de resistencia al ‘‘reducir la transmisión de parásitos resistentes’’. Esto parecería ser dudoso desde la perspectiva de la genética de poblaciones, en donde la intuición lleva a una conclusión opuesta. El objetivo fue reconciliar estos puntos de vista divergentes.

Métodos  El efecto de la actividad gametocida del fármaco fue cuantificado de forma matemática y calibrado utilizando datos de campo.

Resultados  Parece ser un resultado robusto el hecho de que la actividad gametocida promueve la dispersión de resistencias en una población. La razón subyacente está en que la actividad gametocida reduce mayoritariamente la transmisión de las formas sensibles al fármaco y no tanto la de las formas resistentes, con lo cual incrementa la dispersión de estas últimas. El aumento en la tasa de dispersión de resistencia es cuantificable y parece ser pequeño, siempre y cuando la cobertura del fármaco sea moderada o baja.

Conclusiones  El citar la reducción en la dispersión de resistencias como una justificación para la utilización de antimaláricos gametocidas no es justificable; el uso deliberado de antimaláricos gametocidas con una alta cobertura para reducir la transmisión puede en últimas ser contraproducente por su rápida promoción de resistencia a los fármacos.

Palabras clave P. falciparum

malaria

resistencia a fármacos

terapia de combinación

gametocida


Introduction

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices

The life history of a Plasmodium falciparum malarial infection can be broadly categorised into three stages: an expansion phase in the liver, the development of a large asexual parasite load in the blood, and the development of sexual transmission stages known as gametocytes. Only the asexual parasite load causes symptomatic disease, so antimalarial drugs are primarily active against this stage (an activity known as schizontocidal) although some are also active against the developing or mature gametocytes (gametocytocidal), and some may also disrupt the development of the ookinete in the mosquito gut (sporontocidal) (Butcher 1997). Gametocytocidal activity is conventionally regarded as advantageous because it may have a public health benefit in decreasing transmission and, it is hypothesised, because killing the transmission stages will reduce the rate at which resistance spreads. This latter assertion appears to be widely accepted (see, for example, Barnes & White 2005, and references therein) so that, for example, it is one of the properties listed by WHO as having the ‘potential to delay or prevent the development of resistance’ (WHO 2001). It is also one of the mainstays for arguments that antimalarial combination therapy should contain artemisinin drugs. There appear to be no published calculations to substantiate this assertion, and it appears to rest solely on intuition. This intuitive argument is unacceptable from a population genetic perspective, where it is clearly recognised that what drives resistance is not the transmission of resistant forms in isolation, but their transmission relative to the sensitive form. A priori, the impact of gametocytocidal activity is expected to be greater on the sensitive than the resistant forms, so gametocytocidal activity may actually enhance the rate at which resistance spreads. So the intuition of geneticists leads to a completely opposite conclusion to that of malariologists. It is therefore necessary that a detailed quantitative analysis be undertaken to resolve this paradox. The purpose of this manuscript is to examine this effect in more detail, to substantiate the assertion that gametocytocidal activity enhances the spread of resistance, and to quantify the likely size of its impact.

Methods

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices

The selective advantage of drug-resistant parasites is most easily calculated as the number of secondary inoculations produced during the lifespan of a single resistant infection (LSI; the lifetime number of secondary inoculations) compared with the number produced by a drug-sensitive infection. This is achieved by estimating their infective lifespan and multiplying by a constant ‘k’ (Hastings et al. 2002). Assuming the infective lifespan is measured in days, then k represents the number of secondary contacts made via the mosquito vectors (the vectorial capacity) discounted by all the other factors that affect successful transmission such as failure to infect the mosquito, failure of sporozoites to invade the liver, and so on. These factors determine the absolute value of LSI but can remain unknown because k immediately cancels out of the equations, leaving the selective advantage as simply the ratio of the average infective lifespan of resistant to sensitive parasites. So if the mean infective lifespan of resistant parasites is R days and that of the sensitive parasites is S days, the selective advantage of resistance in drug-treated individuals is simply Rk/Sk or R/S as illustrated in Figures 1 and 2 and in the Appendix 1.

image

Figure 1.  A model of complete drug resistance. Resistant parasites are assumed to be completely unaffected by the drug. The life history of malarial infections and a plausible time course are shown: the light grey box represents the liver stage, the dark grey box represents the asexual blood phase and the solid black line represents the presence of mature gametocytes. An untreated infection is assumed to spend 10 days developing in the liver and then 90 days as an asexual blood infection, before host immunity eliminates the asexual forms. It takes 14 days of blood infection before gametocytes appear and they persist for a further 10 days after their progenitor asexual forms are eliminated by host immunity (or by a secondary event such as presumptive drug treatment). In reality, people may remain infective for up to 28 days but with a rapidly decreasing number of gametocytes (Smalley & Sinden 1977) and hence decreasing infectivity. This is approximated as equivalent to 10 days infectivity of a non-treated infection. As ever, the general conclusions are not affected by this approximation (Appendix 1). Thus an untreated infection lasts 100 days in total during which it is infectious for 86 days (because of the total 100 days of infection, 10 days are spent in the liver, 14 days as an asexual infection with no sexual stages and gametocytes persist for a further 10 days after the asexual forms disappear and 100 − 10 − 14 + 10 = 86; examples i and ii). A resistant infection is assumed to be completely unaffected by the drug (but see Figure 2) so follows the same time course irrespective of treatment and has an infective period of 86 days (iii and v). Drug treatment is represented by the arrow and is assumed to occur 30 days after initial infection by which time, allowing for 14 days in the liver and 10 days for gametocytes to appear, it has been infective for 6 days. If the drug is non-gametocytocidal it takes 10 days for the gametocytes to disappear after their progenitor asexuals have disappeared meaning sensitive infections have been infective for a total of 16 days (example iv). If the drug does kill gametocytes (example vi) then the infective period is 6 days. The selection favouring the resistance forms in treated individuals can be calculated as their lifetime secondary inoculations (LSI) relative to that of the sensitive (see main text and Appendix 1). Using this timescale for life-history stages, the selective advantage for resistance in the presence of the drug is 5.4 if the drug is non-gametocytocidal and increases to 14.3 if the drug is gametocytocidal.

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image

Figure 2.  A model of recrudescent drug resistance. The resistant parasites are badly affected by the drug and reduced to low numbers before recrudescing as a detectable infection. The life history and timescale of the malaria infection is the same as for the complete resistance model illustrated on Figure 1 except that, for the purposes of illustration, it is assumed to take 20 days after treatment for the infection to recrudesce back to an infective form (there may be a lag between the recrudescence of asexual parasites and the subsequent reappearance of sexual stages so the recrudescent period is defined as the time between the infection being drug treated and it becoming re-infective). The loss of infective period for a schizontocidal drug with no gametocytocidal activity is 10 days because, during the period before recrudescence, gametocytes persist for 10 days after treatment and 20 − 10 = 10. The loss is 20 days for gametocytocidal drug because it kills all gametocytes present at the time of treatment. This timescale for life-history stages results in a 4.7-fold selective advantage for resistance if the drug is non-gametocytocidal, rising to 11-fold if the drug is gametocytocidal.

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This is a population genetic approach that tracks the number of secondary inoculations as a measure of reproductive success and investigates the spread of resistance on a timescale of parasite generations. Resistance is assumed to be encoded by a single gene so the process is equivalent to competition between sensitive and resistant ‘strains’ and, in principle, it is also possible to track the process on a continuous timescale using an epidemiological approach based on differential equations integrated over time (see Anderson & May 1992 for details). The two approaches are analogous and the same qualitative results would arise. The population genetic approach is preferred here because it can serve as the basis for future studies of resistance whose genetic determination is more complex, for example if two or more genes are required to encode resistance, in which case recombination and linkage disequilibrium become important. The method implicitly assumes that the population is constant over time. If it is expanding (e.g. in an epidemic) or contracting (e.g. because of interventions), then the value of k may alter over time. In an epidemic, for example, transmissions that occur earlier from the infection may have greater ‘reproductive value’ than later transmissions (such as occur after drug treatment). This will not affect the qualitative conclusions although it may slightly affect the quantitative ones (mathematically adept readers can find further details in Charlesworth 1994).

The basic argument can be made both algebraically (Appendix 1) and intuitively. The latter approach is presented graphically in Figures 1 and 2, and explained in the appropriate figure legends. Figure 1 examines the case where the resistant parasites are completely unaffected by the drug and serves as a simple and compelling example. More commonly, ‘resistant’ infections are greatly affected by drug treatment: the vast majority of parasites are killed and the infection becomes sub-patent until the survivors increase in number sufficiently to cause a relapse of ‘drug resistant’ malaria. This is referred to as the ‘recrudescent’ model and is presented on Figure 2.

An operational question arises when considering combinations of antimalarial drugs where the first drug targets only asexual stages while the second is gametocytocidal. Intuitively, the clinical efficacy of this second drug must exceed a critical value to overcome the drawback of its gametocytocidal activity. This critical value can be calculated numerically for the models shown on Figures 1 and 2 as described in Appendix 2.

These models capture the essential elements of malaria infections, and of the drug treatments they encounter. They represent the two ends of the spectrum of drug resistance, one where the parasites with the resistant mutation are entirely unaffected by the drug (Figure 1), and the other where they are instantaneously eradicated and recrudesce some time later (Figure 2). They establish the important basic principles and allow approximate quantification of the effects of gametocytocidal activity. The effects of other aspects of malaria biology can be discussed in the context of these calculations, and shown not to affect the general conclusions (Appendix 3).

Results

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices

Antimalarial drugs with gametocytocidal activity (here assumed to kill both mature and developing gametocytes) select for resistance more strongly than those without. In the model of complete resistance shown on Figure 1, the selective advantage of resistance if the drug is non-gametocytocidal is 5.4-fold rising to 14.3-fold if the drug is gametocytocidal, an increase by a factor of 2.6. In the recrudescent model shown on Figure 2, the corresponding figures are 4.7-fold in the presence of a non-gametocytocidal drug, rising to 11-fold if the drug is gametocytocidal, an increase by a factor of 2.3. The timescales used in these examples, for example the amount of time spent in the hepatic stage, are arbitrary but the arguments are qualitatively robust and not dependent on their exact values (Appendix 1).

The ratio of LSI values gives the selective advantage in the presence of the drug. Many infections are not drug treated so the overall selective advantage for resistance has to be calculated taking this into account [Eqns (A1.1–A1.4) in Appendix 1]. Figure 3a shows the increased rate of evolution of resistance to gametocytocidal drugs over a single generation for various drug treatment rates. As might be expected, the increase was small when drug use was rare, becoming much larger as the proportion of people treated increases. As a specific example, using the lifecycle timeframes shown on Figures 1 and 2 and drug treatment rate of 0.3, resistance to a gametocytocidal drug spreads 5% faster than a purely schizontocidal drug in the model of complete resistance and 1% faster in the recrudescence model. Although small, these differences become somewhat larger when compounded over the numerous parasite generations that occur during the evolution of resistance. Figure 3b shows how these differences of 5% and 1% per parasite generation can affect the useful therapeutic lifespan (UTL) of the antimalarial drug. Assuming that UTL finishes once resistance exceeds 20%, under a model of complete resistance the UTL of gametocytocidal drug is 6.2 years against 7.2 years for a non-gametocytocidal drug – a reduction in UTL of nearly 15%. The selective differences in the recrudescence model are much lower and UTL only falls from 8.3 to 8 years, a reduction in UTL of 4%.

image

Figure 3.  The increase in resistance to gametocytocidal and non-gametocytocidal antimalarial drugs. (a) The increased rate of evolution of resistance if a drug is gametocytocidal compared with that for a non-gametocytocidal drug that targets only the asexual stages. The upper line represents the increase calculated for a model of complete resistance using the time periods illustrated on Figure 1, while the lower line is calculated from the recrudescent model illustrated on Figure 2. The rates are over a single parasite generation and drug treatment rate is the proportion of infections treated. (b) The evolution of resistance over time (calculated on a timescale of parasite generations and converted to years by assuming five parasite generations per year) based on the models of complete or recrudescent drug resistance and depending on whether the drug is gametocytocidal or non-gametocytocidal. The lifecycle timescales used to illustrate Figures 1 and 2 were used, starting frequency of resistance is 10−5 and drug treatment rate is 0.3.

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The critical values of clinical efficacy that need to be exceeded to overcome gametocytocidal activity in drug combinations are shown in Figure 4. At low to moderate levels of drug use, even a marginally effective gametocytocidal drug retards the evolution of resistance. For example, even if 30% of infections are treated, the second drug only needs to increase cure rates by 16% in the full resistance model, or by 4% in the recrudescence model, to significantly retard the evolution of resistance. The critical threshold of its protective efficacy becomes much higher at high levels of drug coverage. For example, at 70% coverage, the second drug must increase cure rates by 29% or 19% in the complete resistance and recrudescence models respectively.

image

Figure 4.  The minimum clinical efficacy of a gametocytocidal partner drug that must be exceeded before its inclusion into a combination therapy slows the spread of resistance. Shown as a function of drug treatment rate for models of Complete and Recrudescent resistance, using the infective lifespan used to illustrate Figures 1 and 2 (Further details in Appendix 2).

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Discussion

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices

It may be difficult to accept that a factor such as gametocytocidal activity that appears intuitively beneficial could have counter-productive properties. However the underlying logic appears robust and the conclusions seem inescapable. The verbal assertion that gametocytocidal activity slows the spread of resistance is invariably along the lines that gametocytocidal activity ‘reduces the transmission of resistant forms thereby slowing the spread of resistance’ (see Barnes & White 2005 for a recent illustrative example). This is true but is quite literally only half the equation [the numerators of Appendix Eqns (A1.4 and A2.1) to be precise]. The important comparison is the extent to which gametocytocidal activity also reduces the spread of sensitive forms. Since the latters’ infective lifespans are, by definition, terminated by the drug, it stands to reason that the loss of infective lifespan due to gametocytocidal activity will constitute a bigger proportion of the sensitives’ infective lifespan than it will of the resistants’ infective lifespan. This inevitably results in an increased selective advantage for the resistant form. The algebraic equivalent of this argument is to note that subtracting a constant amount from each LSI disproportionately affects the sensitive form, thereby increasing the ratio of resistant to sensitive transmissions (Appendix 1). For example, if resistant forms generate 20 inoculations, and sensitive forms generate 10, then the advantage of resistance is 20/10, i.e. twofold. If gametocytocidal activity prevents two inoculations from each LSI, this results in an advantage of 18/8, i.e. 2.2-fold, preventing five inoculations from each LSI results in an advantage of 15/5, i.e. threefold, and so on.

The models described above provide a simple method to establish the basic impact of gametocytocidal activity in antimalarial drugs. Additional impacts of gametocytocidal activity and putative differences in malaria biology and epidemiology can be incorporated and shown not to affect the basic qualitative conclusion; these are discussed separately in Appendix 3 to avoid disrupting the main argument. Gametocytocidal activity gives an extra impetus to the spread of resistance, and it is necessary to quantify the effect. The increased rate of evolution appears to be small if drug treatment rates are low to moderate (Figure 3a). Furthermore, the addition of a gametocytocidal drug to a non-gametocytocidal monotherapy will remain beneficial (Figure 4) in these circumstances. Artemisinin derivatives used in a combination therapy typically reduce drug failure rates to around 20–50% that of the equivalent monotherapy (International Artemisinin Study Group 2004) so adding artesunate to another antimalarial drug remains a beneficial strategy, despite the former's slight gametocytocidal activity. This was one of the key reasons for assuming that the drug is completely gametocytocidal and kills both developing and mature gametocytes. If complete gametocytocidal activity can be shown to have only a minimal impact on the rate of evolution of resistance, it is a highly robust conclusion that the lesser gametocytocidal activity of drugs such as CQ and artesunates (which kill developing, immature gametocytes, not the mature, infective stages (Kumar & Zeng 1990; Butcher 1997; Pukrittayakamee et al. 2004) will have little impact on the rate of evolution of resistance. However, at high levels of drug coverage the effects of gametocytocidal activity may become far more serious. Firstly, the increased rate of resistance to a single drug becomes much higher: for example, if 80% of infections are treated, gametocytocidal activity increases the evolution of resistance by 36% and 22% per generation under assumptions of complete resistance and recrudescence, respectively (Figure 3a). Secondly, gametocytocidal drugs in a combination therapy need to be much more clinically effective to overcome the inherent drawback of their gametocytocidal activity; for example if 80% of infections are treated then the partner drug's additional clinical effect must exceed 26% or 20% under models of complete resistance or recrudescence, respectively (Figure 4). This has operational implications because past attempts at mass drug administrations often employed the gametocytocidal drug primaquine, the justification being that high drug coverage may have a substantial impact on local transmission intensity, with a corresponding decrease in the disease burden (von Seidlein & Greenwood 2003). This may be the case but policy makers need to be aware that this strategy may greatly increase the spread of resistance.

There are sound theoretical reasons why antimalarial drugs should be used in combination (see White 1999 and Hastings & D'Alessandro 2000 for access to the literature). Combinations reduce the probability of spontaneous resistance mutations surviving and spreading from the ‘biomass’ of parasites within a drug-treated individual, the spread of resistance is slowed because resistant parasites are less likely to survive treatment with a combination, and sexual recombination in the Plasmodium lifecycle means that parasite genotypes resistant to both drugs will be broken down by genetic recombination. None of these factors are affected by the presence or absence of gametocytocidal activity, and it is important to note that nothing in this manuscript should be interpreted as detracting from the desirability of deploying antimalarial drugs as combination therapies. The only possible exception, considered above, arises if the first drug targets only asexual stages while the second is gametocytocidal because the undesirable gametocytocidal action of the second drug could, in principle, outweigh its advantage in protecting the first drug if deployed at high coverage. However, the results shown on Figure 4 clearly support the policy that antimalarials be deployed as combinations. At low to moderate levels of drug use, even a marginally effective second drug retards the evolution of resistance irrespective of whether or not it is gametocytocidal. In summary, a second drug with gametocytocidal activity is much preferable to no second drug.

It appears that gametocytocidal activity is counterproductive and stimulates the spread of drug resistance. However this effect seems to be small, provided drug use is low to moderate (Figure 3). The neutral reader is therefore entitled to wonder why it was deemed necessary to write this manuscript. This can be justified for several reasons. Firstly, the erroneous idea that gametocytocidal activity reduces the evolution and spread of resistance permeates much malaria epidemiological thinking (see the final paragraph of an otherwise excellent paper by Nair et al. 2003 for a recent, but by no means unique, example) and, more importantly, permeates much of the strategic thinking underlying antimalarial deployment policies. It has been used unchallenged to inform and guide regional drug policies over an extended period. There were several proposals in the 1960s (e.g. Rieckmann et al. 1968) to add primaquine to existing antimalarials. Primaquine has no significant effect on asexual forms of P. falciparum, so has no therapeutic benefit, and its inclusion was justified by the assertion that its gametocytocidal effect ‘reduced the spread of resistance to its partner drug’. The added cost, and the possibility of adverse reactions to primaquine, was therefore incurred to achieve an effect that was probably counterproductive. The modern equivalent is the proposal to add primaquine to Artecom (to form a drug called CV8), a policy that has undergone clinical trials over an extended period of time in Vietnam (World Health Organisation 2001); its inclusion may be justified by its action against Plasmodium vivax but it is important to note that it could not be further justified by its gametocytocidal activity against P. falciparum. Finally, gametocytocidal activity has been cited by WHO as one of the factors justifying the selection of artesunate within antimalarial combination therapy. Artesunate has some useful properties making it a suitable partner drug in combination therapies but its slight gametocytocidal activity is unlikely to be one of them. Interestingly, Professor Louis Molineaux raised exactly the same basic point (i.e. that gametocytocidal activity promotes the evolution of resistance) in an unpublished discussion document presented to the WHO Scientific Group on the Chemotherapy of Malaria in 1989 (Louis Molineaux, personal communication), but it was apparently poorly received and disregarded. Herein the effect has been investigated in detail to guide drug policy more objectively. Gametocytocidal activity has been regarded in policy considerations as being unambiguously beneficial with the potential to both reduce transmission and to slow the evolution of resistance. Gametocytocidal activity may have a putative beneficial impact in reducing local transmission intensity but this has to be carefully weighed, and justified, against its impact in increasing the rate at which resistance spreads through these populations.

Acknowledgements

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices

I thank many colleagues for helpful discussions on this topic and/or comments on the manuscript, particularly Bill Watkins, Colin Sutherland, Tim Anderson and three anonymous reviewers. This work was supported by the DFID-funded Malaria Knowledge Programme of the Liverpool School of Tropical Medicine. However, the Department for International Development accepts no responsibility for any information or views expressed.

References

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices
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Appendices

  1. Top of page
  2. Summary
  3. Introduction
  4. Methods
  5. Results
  6. Discussion
  7. Acknowledgements
  8. References
  9. Appendices

Appendix 1: Gametocytocidal monotherapy vs. non-gametocytocidal monotherapy

This is the algebraic formulation of the arguments outlined on Figures 1 and 2. The life-history timings used in Figures 1 and 2 are arbitrary and will vary according to local epidemiology, particularly prevailing levels of human immunity. It is therefore necessary to demonstrate that the conclusions are qualitatively robust by developing an equivalent algebraic argument. The following symbols are used in this derivation and the values in square brackets are the default values used in the examples:

  • ni is the average time until an infection is eliminated by host immunity [100 days];
  • nd is the average time until an infection is drug treated (measured from the day of its inoculation) [30 days];
  • th is the average time an infection spends in the hepatic phase [10 days];
  • td is the average time an infection takes to become infective after emerging from the hepatic stage [14 days];
  • tp is the average time an infection remains infective after the asexual forms have disappeared [10 days].

It is easiest to work in terms of expected infective lifespan, L(i, j), where i is the parasite genotype, either s for sensitive or r for resistant, j is the treatment, either n if no treatment, a if the person is treated with a schizontocidal drug that only targets asexual stages, and g if the person is treated with a drug that targets gametocytes. Thus:

  • image
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If the proportion of infections drug treated is d, it is straightforward to calculate the genetic ‘fitness’ of a genotype as the weighted average of its expected infective lifespan in the absence and presence of drug treatment:

  • image
  • image
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where w(i, j) is average infective lifespan and, as above, i is parasite genotype (s for sensitive and r for resistant) and j is mode of drug action (a if the drug kills only asexuals, g if it is gametocytocidal).

Thus the selective advantage of resistance in the presence of a drug that only targets the asexual forms, v(a), is

  • image((A1.1))

and selective advantage of resistance in the presence of a gametocytocidal drug, v(g), is

  • image((A1.2))

The numerators of Eqns (A1.1 and A1.2) are identical so v(g) will always be larger than v(a) provided tp > 0, i.e. whenever gametocytes persist after treatment with a non-gametocytocidal drug which will, by definition, always be the case.

The analogous derivation can be made for the recrudescence model of Figure 2 using an additional parameter, tr, which is the average time a ‘resistant’ infection takes to recrudesce after drug treatment and become infective again. All the infective lifespans are unchanged except L(r, a) and L(r, g) which become

  • image
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Both periods of infectivity lose a period of time tr while they are recrudescing and tp enters L(r, a) twice because there are two periods during which gametocytes persist after asexual forms have been eliminated: first after the infection has been drug-treated, and second after its eventual elimination by host immunity.

The selective advantage of resistance in the presence of a non-gametocytocidal drug is now

  • image((A1.3))

and to a gametocytocidal drug is

  • image((A1.4))

setting x = ni − th − td − tr + tp and y = nd − th − td allows the equations to be rewritten as

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and

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and, as before, v(g) is always larger than v(a) provided tp > 0.

These are the changes over a single generation and were used to produce Figure 3a. It is assumed that the frequency of resistance alleles is negligible so the mean fitness of the population is simply the average fitness of the sensitive parasites. Growth of resistance is exponential so most of the time scale of the process occurs when the frequency of resistance is very low, hence Eqns (A1.1–A1.4) are good approximations for the rate of evolution (Hastings 1997). Once resistance frequency becomes non-negligible, its effect can be incorporated by tracking frequency of the resistance allele, f, so that f′ the frequency of resistance in the following generation is:

  • image

(where j is a or g as appropriate), which was the approach used to track frequency change over longer time periods shown in Figure 3b.

No account is made of drugs persisting in hosts at concentrations sufficient to prevent sensitive parasites re-establishing an infection (Hastings & Watkins 2006). This is common to all models of antimalarial drug resistance save one (Hastings et al. 2002). The effect can be included simply by scaling the denominator of Eqns (A1.1–A1.4) by (1 - p) where p is the proportion of the host populations with residual drug concentrations sufficient to have a chemoprophylactic effect. This does not affect the qualitative conclusions reached above.

Appendix 2: Gametocytocidal drug combination therapy compared with non-gametocytocidal monotherapy

The selective advantage of the resistant allele under a non-gametocytocidal monotherapy v(mono, a) is, as before,

  • image

If a gametocytocidal drug is added to the first drug to make a combination therapy (CT) a new parameter z is required to represent the probability that an allele resistant to the first drug is killed by the second, gametocytocidal drug. If z = 0 the second drug is completely ineffective and if z = 1 then it is 100% effective, so

  • image((A2.1))

When the infection is successfully treated with CT (with frequency dz) the infection behaves as a sensitive treated with a gametocytocidal drug, and if the infection is treated but survives [with frequency d(1 − z)] then it behaves as a resistant infection treated with a gametocytocidal drug. It is reasonable to ask at what point is the efficacy of the partner so low that its gametocytocidal action outweighs its protective ability? This occurs when

  • image

The algebraic solution for this equation is rather unwieldy but it is simple to solve it numerically using standard algebraic manipulation packages (in this case, Maple v10; Maplesoft, Waterloo, Ontario, Canada); for example the critical value for clinically efficacy is 5 d/(43–35 d) for the values used for the recrudescent model shown on Figure 2. The time periods used in Figures 1 and 2 were used to calculate the critical value of efficacy for varying levels of drug coverage and are shown on Figure 4.

Appendix 3: The impact of gametocytocidal activity and specific aspects of malaria biology, epidemiology and control

The input of new resistant mutations

There are several potential sources of mutations: they may arise spontaneously within sporozoite lineages, be selected from among merozoites emerging from the liver and encountering sub-therapeutic drug levels, or be selected from among the asexual biomass present at the time of drug treatment (Hastings 2004). Gametocytocidal activity has no impact on the first source, which is not initially selected by drugs. It has no impact on the second source, because the drug will have been eliminated by the time the mutant merozoites have developed to the sexual stages. It also has no effect on the third, asexual biomass source because the drug will have been eliminated by the time the mutant asexual parasites recrudesce to form a fully resistant infection with sexual transmission stages. Gametocytocidal activity therefore has no impact on the rate at which mutations arise in the population. Once a resistant mutation has arisen, its chance of survival depends on its selective advantage over the sensitive forms (Hastings 2004). This advantage was quantified above (asv(a) and v(g) in Appendix 1 and v(mono, a) and v(ct, g) in Appendix 2) and shown to increase with gametocytocidal activity so the survival, and hence overall rate of input of new mutations, will be increased by gametocytocidal activity.

The rate of migration of resistance

There are two widely used antimalarial drugs whose molecular basis of resistance is at least partially understood: chloroquine (Wootton et al. 2002) and sulphadoxine-pyrimethamine (SP) (Cortese et al. 2002; Nair et al. 2003; Roper et al. 2003). In both cases, resistance appears to have spread through inter-continental migration of extremely rare mutational events. Standard population genetic analysis shows that the rate of migration of a mutation in an idealised homogenous population is proportional to the square root of its selective advantage (Fisher 1937). This relationship becomes more complex under more realistic ecological conditions but there is still a clear correlation between the size of selective advantage and rate of migration of a mutation (Morjan & Rieseberg 2004). The selective advantage is proportional tov(a) and v(g) in Appendix 1 and v(mono, a) and v(ct, g) in Appendix 2, so gametocytocidal activity, by increasing the selective advantage of resistance, also increases the rate at which resistance mutations migrate through a population.

Repeated drug treatment

In epidemiological settings with poor clinical management, resistant infections may be repeatedly drug-treated while the sensitive infections are, by definition, eradicated and not subject to further treatment. The example outlined on Figure 2 can be used to illustrate and quantify this effect. If the resistant form is treated twice, then a gametocytocidal drug takes two 20-day periods out of the LSI making selection for resistance 46/6 = 7.6 compared with a non-gametocytocidal taking two 10-day periods, making selection for resistance 66/16 = 4.1, so non-gametocytocidal activity remains preferable. Gametocytocidal activity is still deleterious even if the resistant infection is treated three times compared with a single treatment for the sensitive infection (26/6 = 4.3 compared with 56/16 = 3.5 in the above example), although the disadvantage of gametocytocidal activity is further diminished.

Infectivity gradually declines following drug treatment

The number of circulating mature gametocytes starts to decline with a half-life of approximately 2.4 days (Smalley & Sinden 1977) after the supply of gametocytes is eliminated. This contrasts with the all-or-nothing infectivity used in the calculations and illustrated on Figures 1 and 2. It is possible to incorporate this gradual decline mathematically to calculate the equivalent number of infective days. For example, if infectivity declines by 10% per day after drug treatment has eliminated the supply of gametocytes, total host infectivity following drug treatment would be inline image, which is still in units of infective days. The decline in infectivity is likely to be more complicated because two gametocytes are required for fertilisation but the details are immaterial for this argument: provided the same number of infective days is subtracted from both the resistant and sensitive infective lifespans then it still has a greater impact on the sensitive forms thereby favouring the evolution of resistance.

Primary and recrudescent infections may differ in their levels of infectivity

Recrudescent infections may be less infective, or conversely may be more infective, than the primary infections present before drug treatment (both assertions are made in the literature). It is mathematically simple to investigate this by giving greater or lesser weighting to recrudescent infections and to show it has no qualitative effect. As a specific example, the timescale used on Figure 2 results in 60 days of infective recrudescence. Doubling infectivity during this period can be incorporated by adding 60 to the numerators of the LSI ratios presented in that figure. The ratio in the presence of non-gametocytocidal drugs is therefore 136/16 = 8.5 compared with 126/6 = 21 for gametocytocidal drugs, gametocytocidal activity therefore causing a 2.5-fold increase. Even quadrupling infectivity does not nullify the effect. Adding 180 to the numerators leads to selective advantages of 256/16 = 16 and 246/6 = 41 for non-gametocytocidal and gametocytocidal drugs respectively, still a 2.5-fold increase in the advantage of resistance because of gametocytocidal activity. The important qualitative point is that altered infectivity during recrudescence does not alter the conclusion that gametocytocidal activity enhances the spread of resistance.

Antimalarial drugs may increase infectivity

Chloroquine and/or SP may be gametocytostimulatory, i.e. stimulate the commitment of asexual parasites into sexual development (Butcher 1997; Hogh et al. 1998). Gametocytocidal drugs promote resistance, so it is reasonable to consider whether the converse is true, i.e. whether gametocytostimulatory drugs slow the spread of resistance. The increase in infectivity because of gametocytostimulation can be incorporated by adding a constant to both numerator and denominator of Eqns (A1.1 and A1.3) (Appendix 1). This shows that gametocytostimulatory activity does slow the spread of resistance for a reason that is easily grasped intuitively: adding a constant arithmetic amount to the infective lifespan of both resistant and sensitive parasites reduces the ratio of their LSI, inhibiting the evolution of resistance. Once again, conventional views on this effect appear erroneous, Hogh et al. (1998) for example, stating that ‘the observed enhancement in infectivity induced by the use of chloroquine… may in part explain the rapid spread of chloroquine resistance’. In principle, gametocytostimulation could favour evolution of resistance if only the resistant forms can respond by additional sexual stage production but this appears unlikely because the vast majority of ‘resistant’ parasites, at least in the early stages of the evolution of resistance, are killed by therapy (only a small number survive to recrudesce later).

Drugs target different stages of gametocyte development

Developing gametocytes pass through several distinct morphological and metabolic stages (Carter & Graves 1988). Artesunate and the 4-aminoquinilines such as chloroquine appear to affect only the early stages of gametocyte development (probably during the first six of the 10 days required for gametocytes to reach maturity), and appear ineffective against mature gametocytes (Butcher 1997). Chloroquine and artesunate are therefore more like purely schizontocidal drugs such as the antifolates because all eliminate the supply of gametocyte precursors rather than directly killing mature infective gametocytes. The general principles described above make it obvious that chloroquine and artesunate's ability to kill early gametocytes increases the rate at which resistance evolves. At best, the drug will kill all early gametocytes irrespective of whether they carry a resistant or sensitive allele (the recrudescence model illustrated on Figure 2) taking approximately 6 days from each of their infective lifespan. At worst, early gametocytes carrying resistance alleles survive while those carrying sensitive alleles die (Figure 1); this further increases the relative impact on sensitive forms thereby increasing selection for resistance.

Some antifolates are sporontocidal

Drugs such as pyrimethamine and proguanil do not affect gametocytes, but their presence in ingested human blood allows them to affect developing ookinetes in the mosquito midgut (Butcher 1997). This activity is called sporontocidal and is analogous to gametocytocidal activity, both logically and mathematically. Gametocytocidal drugs reduced infectivity by killing gametocytes while sporontocidal drugs reduced infectivity by killing ookinetes. The consequences are the same in both cases: a constant amount is removed from the infective lifespan of both resistant and sensitive forms so both gametocytocidal and sporontocidal drugs favour the evolution of resistance. The rapid selection of resistance to SP has been explained as a consequence of its long elimination half-life (Watkins & Mosobo 1993; Nzila et al. 2000; Hastings et al. 2002) but it is interesting to note that the sporontocidal activity of the pyrimethamine component may plausibly have contributed to its rapid evolution, albeit at an unknown rate.

Transmission-blocking immunity

The human immune system may recognise sexual transmission stages, making the human host non-infective to mosquitoes even though s/he may harbour significant numbers of asexual parasites. The life history shown in Figures 1 and 2 may therefore be atypical in areas of high transmission where transmission-blocking immunity (TBI) makes the infection non-infective to the mosquito vectors long before it is eliminated by host immunity. Provided TBI acts after drug treatment (else drug treatment has no evolutionary effect because the infection cannot be transmitted) it is easy to incorporate TBI into the equations in Appendix 1: redefine ni to be the average time until an infection is made sterile by TBI and remove a factor tp from the numerator of each of Eqns (A1.1–A1.4); this shows that the basic qualitative conclusions are unaffected by TBI.

The impact of other interventions

There is one important public policy point that needs to be stressed: a general decrease in background levels of transmission caused by interventions such as provision of bednets or transmission-blocking vaccines will not favour the evolution of resistance in the manner described above for gametocytocidal drugs (although both obviously reduce transmission). The reason is that gametocytocidal activity has a differential impact on sensitive and resistant parasites. In contrast, changes in the intensity of transmission caused by vaccines, bednets, etc, has the same impact on both resistant and sensitive forms and is included in the factor ‘k’ which describes background epidemiology; this factor immediately cancels out of the calculations, so changes in transmission have no impact on the above calculations.