A model for malaria treatment evaluation in the presence of multiple species

Abstract

Plasmodium falciparum and P. vivax are the two most common causes of malaria. While the majority of deaths and severe morbidity are due to P. falciparum, P. vivax poses a greater challenge to eliminating malaria outside of Africa due to its ability to form latent liver stage parasites (hypnozoites), which can cause relapsing episodes within an individual patient. In areas where P. falciparum and P. vivax are co-endemic, individuals can carry parasites of both species simultaneously. These mixed infections complicate dynamics in several ways: treatment of mixed infections will simultaneously affect both species, P. falciparum can mask the detection of P. vivax, and it has been hypothesised that clearing P. falciparum may trigger a relapse of dormant P. vivax. When mixed infections are treated for only blood-stage parasites, patients are at risk of relapse infections due to P. vivax hypnozoites. We present a stochastic mathematical model that captures interactions between P. falciparum and P. vivax, and incorporates both standard schizonticidal treatment (which targets blood-stage parasites) and radical cure treatment (which additionally targets liver-stage parasites). We apply this model via a hypothetical simulation study to assess the implications of different treatment coverages of radical cure for mixed and P. vivax infections and a "unified radical cure" treatment strategy where P. falciparum, P. vivax, and mixed infections all receive radical cure after screening glucose-6-phosphate dehydrogenase (G6PD) normal. In addition, we investigated the impact of mass drug administration (MDA) of blood-stage treatment. We find that a unified radical cure strategy leads to a substantially lower incidence of malaria cases and deaths overall. MDA with schizonticidal treatment was found to decrease P. falciparum with little effect on P. vivax. We perform a univariate sensitivity analysis to highlight important model parameters.

Keywords: Malaria; Plasmodium falciparum; Plasmodium vivax; Stochastic modelling; Unified treatment.

Fig. 1

Simplified schematic of the human transmission model for a single parasite species, $x$. The model compartments are $S$ (susceptible), $I$ (clinical infectious), $A$ (asymptomatic infectious), $T$ (undergoing blood-stage treatment), $G$ (undergoing radical cure), $R$ (recovered and partially-immune) and $L$ (latent stage hypnozoites for P. vivax only). Solid lines represent rates, the dashed lines probabilities, and the circles designate where a rate is split by probabilities. The probability parameters are not explicitly shown in the figure as, in many cases, the probability of each outcome depends on the current state (for example, the probability of symptoms upon infection is lower for recovered individuals than susceptible individuals).

Fig. 2

Infections over 10 years for P. falciparum (left panels) and P. vivax (right panels) with clinical treatment only (top row), and mass drug administration (MDA) (bottom row).

Fig. 3

Cumulative infections and deaths over a 10 year period with and without mass drug administration (MDA) for P. falciparum (left panels) and P. vivax (right panels).

Fig. 4

Sensitivities of P. falciparum (top) and P. vivax (bottom) cumulative infections with respect to varying model parameters. These are presented in terms of the mean relative outcome, compared to baseline, when each parameter is scaled by 0.8 and 1.2. Red and blue vertical lines represent the mean outcomes relative to baseline given a parameter scaling of 0.8 and 1.2, respectively. Error bars represent the minimum and maximum relative outcome, compared to baseline. Each minimum, mean and maximum calculated from 50 simulations.