The potential elimination of Plasmodium vivax malaria by relapse treatment: insights from a transmission model and surveillance data from NW India

Abstract

Background: With over a hundred million annual infections and rising morbidity and mortality, Plasmodium vivax malaria remains largely a neglected disease. In particular, the dependence of this malaria species on relapses and the potential significance of the dormant stage as a therapeutic target, are poorly understood.

Methodology/principal findings: To quantify relapse parameters and assess the population-wide consequences of anti-relapse treatment, we formulated a transmission model for P. vivax suitable for parameter inference with a recently developed statistical method based on routine surveillance data. A low-endemic region in NW India, whose strong seasonality demarcates the transmission season, provides an opportunity to apply this modeling approach. Our model gives maximum likelihood estimates of 7.1 months for the mean latency and 31% for the relapse rate, in close agreement with regression estimates and clinical evaluation studies in the area. With a baseline of prevailing treatment practices, the model predicts that an effective anti-relapse treatment of 65% of those infected would result in elimination within a decade, and that periodic mass treatment would dramatically reduce the burden of the disease in a few years.

Conclusion/significance: The striking dependence of P. vivax on relapses for survival reinforces the urgency to develop more effective anti-relapse treatments to replace Primaquine (PQ), the only available drug for the last fifty years. Our methods can provide alternative and simple means to estimate latency times and relapse frequency using routine epidemiological data, and to evaluate the population-wide impact of relapse treatment in areas similar to our study area.

Figure 1. P. vivax transmission models.

Human classes are represented as squares, and mosquito class λ as a circle, with arrows indicating the direction of transition between classes. The per-capita rate of transition is included next to each arrow (see supplement for model equations and description). A. The general model SEIHⁿQS with n H classes and the relapsing loop I-to-H_1…n-to-I (in red). The multiple H classes effectively implement a realistic Gamma-distributed latency period , and may also represent possible intermediate stages of hypnozoites during its long stay in the liver (see supplement for more details). The class Q provides a simple representation of partial, temporary, immunity that confers protection against clinical infection but not infectiousness . Prompt clinical intervention prevents some patients from developing immunity , which is captured in the I-to-S transition. B. The non-relapse model SEIQS, without the relapse loop but otherwise identical to SEIHnQS. C. The non-relapse model SEIRS, where the completely immune class R (no blood-stage parasitemia) replaces the Q class, and the I-to-S transition is no longer present. (This model is same as the VSEIRS model previously used for the population dynamics of P. falciparum malaria in Kutch [23]).

Figure 2. Malaria time series and regression estimates of relapse frequency and latency.

A. The monthly P. vivax (red) and P. falciparum (black) cases between January 1987 and August 2010 are overlaid. B. The power spectrum of P. vivax data (red) shows a strong yearly cycle as well as different dominant periods longer than one year (i.e. interannual cycles) (The power spectrum describes how the variance of the data is distributed among different periods). The interannual cycles of period less than 6 years are also present in the rainfall spectrum (dashed black). C. The comparison of the observed seasonal patterns of P. vivax (red) and P. falciparum (solid black) shows significant relapses in P. vivax during January–June when rainfall is minimal (dotted black) – these are called “relapse cases” in the text. The majority of P. vivax cases due to transmission arise between August and November, and are likewise referred to as “transmission cases”. D. The autocorrelation values of P. vivax cases in each of the four transmission months - August (red), September (blue), October (light blue) and November (yellow) - and the cases in the subsequent twelve months show large correlation peaks between January and June, giving latency periods ranging between 5 and 8 months. E. A linear regression of aggregated transmission and relapse cases gives a slope of 0.31, suggesting a 31% average relapse rate. In the driest months of May–June, when entomological conditions exclude transmission, the regression gives a much tighter relation (not shown). F. The average of these autocorrelation curves suggests a relapse latency of 7 months.

Figure 3. Comparison of model simulations with malaria data and regression estimates.

The data and the regression estimates for relapse latency and frequency from figure 2 are plotted in red, the median of 1000 model simulations is plotted in blue, and the 10–90 percentile range shaded in light blue (all simulations use the maximum-likelihood-estimates of the parameters, see suppl Table S1). A. The peaks and troughs of the monthly simulated cases track the data well, except for the underestimation and overestimation of large outbreaks before and after 2007 respectively (see text). B. The power spectrum of the median cases from the simulated time series reproduces the yearly and the two longer interannual cycles observed in the data (and also present in the rainfall covariate, see Fig. 2B). C. The seasonal patterns in the data and simulations show good agreement. D. A linear regression of aggregated transmission and relapse cases in each of the 1000 simulation time series gives the same 31% relapse rate as in the data. E. The average autocorrelation curve of the simulated cases reproduces the observed 7-month mean latency period. F. The gamma-shaped latency distribution is plotted using the shape parameter values taken from supplement Table S1, which predicts median and mean latency periods of 6.4 and 7.1 months respectively.

Figure 4. Model simulations with an effective anti-relapse treatment.

For a given treated fraction a, the model is driven by a surrogate rainfall series (reproducing main features of the observed rainfall data) and simulated 25 yrs ahead, with 1000 independent runs per surrogate and 1000 surrogate series in all (see Methods, Supplementary Material). The error bars denote standard errors over surrogates. A. The median seasonal patterns are compared among control (red), 10% treatment (blue) and 30% treatment (light blue), showing a drop of 45% and 90% in transmission cases (aggregated over Aug–Nov) relative to control for these two treatment levels. B. Treatment effect, defined as the relative drop in transmission cases, as a function of a. C. In the alternative annual mass treatment scenario, with 90% of the population successfully covered at the beginning of the year for 5 consecutive years from year 6-to-10 (equivalent to a = 0.9 between January of year 6 and December of year 10, and a = 0 at other times), the P. vivax burden is substantially reduced on average, ranging from a 50% drop after one annual intervention, to 95% at the end of the treatment period (the median of the surrogate runs is plotted in red, and the 10–90 percentile range shaded in light blue; the inset shows the cumulative % reduction in the P. vivax burden after mass treatment). Without further prevention of relapses the parasite will gradually recover over several decades, highlighting the need to use such an intervention in conjunction with effective treatment of clinical cases.