^{1}

^{*}

^{1}

^{2}

^{3}

^{2}

^{3}

^{4}

^{1}

The authors have declared that no competing interests exist.

Conceived and designed the experiments: AS HPD ME. Performed the experiments: AS. Analyzed the data: AS HPD. Contributed reagents/materials/analysis tools: JCD MV SS. Wrote the paper: AS HPD ME. Contextualized the model analyses and contributed to the writing of the paper: JCD MV SS.

Pentavalent antimonials have been the mainstay of antileishmanial therapy for decades, but increasing failure rates under antimonial treatment have challenged further use of these drugs in the Indian subcontinent. Experimental evidence has suggested that parasites which are resistant against antimonials have superior survival skills than sensitive ones even in the absence of antimonial treatment.

We use simulation studies based on a mathematical

Both hypotheses can potentially explain the Bihar observations. However, increased transmissibility as an explanation appears more plausible because it can occur in the background of asymptomatically transmitted infection whereas disease-related factors would most probably be observable. Irrespective of the cause of fitness, parasites with a higher fitness will finally replace sensitive parasites, even if antimonials are replaced by another drug.

The protozoan flagellate

Visceral leishmaniasis (VL), also known as Kala-azar (KA), causes each year about 200,000 to 400,000 cases with about 20,000 to 40,000 deaths worldwide. About 70% of the VL burden occurs in the Indian subcontinent, mostly in the state of Bihar

Pentavalent antimonials were introduced in 1922 as therapeutic drug for leishmaniasis

In 2005, the governments of India, Nepal, and Bangladesh agreed to participate in a regional ‘VL elimination program’ to reduce the annual incidence of VL from about 22 cases per 10,000 inhabitants to only one case per 10,000 inhabitants by 2015. This programme was based among others on the replacement of antimonials as first-line treatment by the oral drug miltefosine. So far, the treatment success rate of this drug does not seem to be affected by antimony-resistance.

The action mechanism of antimonials is still poorly understood

The aim of this study is to investigate the dynamics of the emergence and spread of antimony-resistant

The first mathematical study of the dynamics of VL used a deterministic model to explain the observed inter-epidemic periods between 1875 and 1950 in Assam, India

Based on data from Morocco, a mathematical model for cutaneous leishmaniasis was developed

Data on the TFR of antimonial treatment originate from a review of clinical trials in Bihar between 1980 and 2004. Although treatment dosage and duration differed between studies over the study period of two decades the data support the finding of a substantially declining efficacy of antimonial treatment over time

Twenty treatment groups taken from 12 clinical studies involving antimonial treatment in Bihar, India, between 1980 and 1997

We extend an existing mathematical model

We vary parameters controlling the longitudinal evolution of the TFR and select all those parameter combinations for which the simulated TFR curves pass through the confidence intervals in _{H}_{FS}_{FA}_{FH}_{HF}

Simulations start in the endemic equilibrium with only sensitive parasites, using a population of 104 millions inhabitants (population size of Bihar). The mathematical model is considered to be in the endemic equilibrium when there is no change in the variables over a period of at least 100 years within an accuracy of five digits after the decimal (see

Parameter _{res}_{sens}_{res}_{sens}_{sens}_{res}

We consider five scenarios with modified fitness of resistant parasites:

Resistant parasites increase the probability that infected humans become sick. This increases the transmission probability of the parasites because of the long infectious duration and the high transmissibility of patients. The proportions 0.28% and 0.01% who develop KA or post-kala-azar dermal leishmaniasis (PKDL), respectively, when infected with sensitive parasites (see parameters _{HS}_{HL}_{H}_{H}_{H}

Resistant parasites increase the parasite load in patients due to a higher virulence. This increases the probability that sand flies become infected when feeding on patients. The probability of 10% that they become infected when feeding on a patient with sensitive parasites (see parameters _{F3}_{F4}_{FS}_{FS}_{FS}

Resistant parasites increase the probability that sand flies become infected when feeding on asymptomatically infected hosts. The probabilities 2.2% and 4.4% that they become infected when feeding on a host with sensitive parasites who is in the early or late infected stage, respectively, (see parameters _{F1}_{F2}_{FA}_{FA}_{FA}

Resistant parasites increase the probability that sand flies become infected when feeding on symptomatic or asymptomatic hosts. The probabilities that they become infected when feeding on a host with sensitive parasites (parameters _{F1}_{F2}_{F3}_{F4}_{FH}_{FH}_{FH}

Resistant parasites increase the probability that humans become infected when being bitten by infected sand flies. The probability of 10% that a human becomes infected with the sensitive parasite (see parameters _{H}_{HF}_{HF}_{HF}

We numerically solve the differential equation model for 700,000 sets of parameter values and calculate how the TFR changes over time because of the spread of resistant parasites. Apart from using the standard parameter values given in _{res}_{H}_{FS}_{FA}_{FH}_{HF}

Among 700,000 parameter combinations, the TFR curves of 1,605 combinations pass through the confidence intervals shown in

Two hypotheses on increased fitness in resistant parasites are compared in three panels A, B, C. Panel A) the distributions of and correlations between _{res}_{FS}_{FA}

The TFR of cases infected with resistant parasites (_{res}_{res}_{res}_{res}

Resistant pathogens have a higher fitness because they lead to more clinical cases (scenario 1: pathogenicity factor _{H}_{FS}_{H}_{FS}_{FS}

Resistant pathogens have a higher fitness because they have a higher transmissibility in asymptomatic carriers (scenario 3: _{FA}_{FH}_{HF}_{FA}_{FH}_{HF}_{FA}

In summary, the explanation of the Bihar data requires the assumptions that the TFR of patients infected with resistant parasites is high and that resistant parasites have an increased fitness. Both hypotheses on additional fitness offer the potential to explain these data.

Using a mathematical model for _{res}_{res}

Two hypotheses on increased fitness can explain the Bihar observations.

Hypothesis 1: a disease-related fitness with _{H}_{FS}

Hypothesis 2: a transmission-related fitness with _{FA}_{FH}_{HF}

To demonstrate the effects of the increase in disease-related fitness parameters (Hypothesis 1 in _{res}_{H}_{FS}_{FA}_{FH}_{HF}

In case of higher virulence, the strongly increased infectiousness of symptomatic cases infected with resistant parasites might be confirmed by xenodiagnosis or by quantitative PCR of blood or skin tissue of the patients.

We investigated disease- and transmission-related fitness parameters separately to quantify the effect of each parameter although combinations of several fitness parameters seem rather realistic as their biological origins are closely inter-linked.

Simulations of both hypotheses suggest that sensitive parasites are replaced almost completely by resistant ones already 20 to 40 years after the first noticeable decline in treatment efficacy (

Issues on selection pressure in the context of antimony resistance are complex. Poor treatment compliance is suspected to have caused the development of resistance in Bihar

An emergence of resistant parasites before 1960 seems rather unlikely: VL had almost been eliminated at that time as a consequence of the National Malaria Eradication program

Further data and model related limitations of these modelling analyses are pointed out in the following. To investigate the spread of antimony-resistant parasites we used a previously published mathematical model

The main data related uncertainty originates from the assumption that cellular immunity can be represented by Leishmanin skin test (LST) measurements. Under the assumption of a life-long cellular immunity the model showed that the prevalence of LST-positive individuals in the population would be higher than 50% as had been observed (for further detail see

Model related uncertainties originate from assumptions underlying the deterministic modelling approach as, for instance, homogeneous mixing within and between human and fly populations, an infinitely large population size, age structure of the human population, heterogeneities in living conditions, or seasonal transmission patterns. Such factors can influence short term predictions and would demand a stochastic modelling approach. As, however, this investigation addresses development of resistance over several decades we believe that stochastic influences are of minor relevance and that the deterministic model is adequate to describe a trend over decades.At least partially, antimonial treatment has been replaced in Bihar around the year 2000 by drugs like amphotericin B, miltefosin and paromomycin, which are assumed to be not affected by antimonial-related resistance. This leads to the question whether this will stop or even reverse the process of strain replacement, a question which might be of relevance if a return to antimonials in therapeutic schemes, including combination schemes, would be considered in the future. Thus, in addition to the model predictions in

Our analyses suggest that antimony-resistance alone cannot explain why the TFR observed in Bihar increased up to 65% between 1980 and 1997. Most infections do not lead to symptomatic disease and thus, only a minority of parasites is exposed to antimonial treatment. This minor proportion of parasites cannot increase the TFR as quickly as it has been observed in Bihar.

Following recent experimental findings on increased fitness of resistant parasites, we examined two hypotheses for an additional fitness benefit: disease-related or transmission-related fitness increase. At the current stage of knowledge, we cannot favour one fitness hypothesis over the other; both offer the potential to explain the data. Disease-related fitness, however, requires increasing the proportion of clinical cases among all infections or the infectiousness of symptomatic cases by at least 550%, which most probably would have been observable.

Transmission-related fitness, on the other hand, requires increasing the infectiousness in sand flies, in asymptomatically infected humans, or in all infected humans by at least 5%. Such a minor increase can occur in the background of asymptomatic transmission without being apparently recognized under field conditions. After a parasite with higher fitness independent of a treatment-based selection pressure has emerged, it will finally replace the sensitive one, even in complete absence of antimonial treatment.

This modelling study suggests that entomological studies are urgently required to gain better data on sand flies abundance, biting rates and infectiousness. Furthermore, research on the fitness of the parasites should also be conducted in the context of the natural vector

(DOC)

(TIF)

(DOC)

(DOC)

(DOC)

(DOC)

(DOC)

(DOC)

(DOC)

We thank Helmut Pitters for assistance in programming with Matlab.