Modeling the effects of relapse in the transmission dynamics of malaria parasites

Abstract

Often regarded as "benign," Plasmodium vivax infections lay in the shadows of the much more virulent P. falciparum infections. However, about 1.98 billion people are at risk of both parasites worldwide, stressing the need to understand the epidemiology of Plasmodium vivax, particularly under the scope of decreasing P. falciparum prevalence and ecological interactions between both species. Two epidemiological observations put the dynamics of both species into perspective: (1) ACT campaigns have had a greater impact on P. falciparum prevalence. (2) Complete clinical immunity is attained at younger ages for P. vivax, under similar infection rates. We systematically compared two mathematical models of transmission for both Plasmodium species. Simulations suggest that an ACT therapy combined with a hypnozoite killing drug would eliminate both species. However, P. vivax elimination is predicted to be unstable. Differences in age profiles of clinical malaria can be explained solely by P. vivax's ability to relapse, which accelerates the acquisition of clinical immunity and serves as an immunity boosting mechanism. P. vivax transmission can subsist in areas of low mosquito abundance and is robust to drug administration initiatives due to relapse, making it an inconvenient and cumbersome, yet less lethal alternative to P. falciparum.

Figure 1

Plasmodium transmission dynamics. (a) Illustration of the natural history of infection with the P. vivax parasite. The variables represent a classification of the population at any given age and time into six states: completely susceptible (S); clinical malaria resulting from an infection in a completely susceptible individual (I ₁); recovered with clinical immunity without any hypnozoites (R); mild or asymptomatic infection resulting from exposure of recovered individuals (I ₂); recovered with a certain degree of clinical immunity, carrying hypnozoites (L ₁); recovered with clinical immunity, carrying hypnozoites (L ₂). Description and values for the parameters can be found in Table 1. (b) P. falciparum transmission dynamics. This is a subset of the previous system which is retrieved by making p ₁ = 1.

Figure 2

Expected clinical malaria episodes and parasite prevalence at equilibrium, for both P. vivax and P. falciparum. (a) Bifurcation diagram, showing the influence of β on the equilibrium levels of clinical malaria for P. vivax (blue) and P. falciparum (red). (c) Influence of β on the equilibrium levels of parasite prevalence (I ₁ + I ₂) for P. vivax (blue) and P. falciparum (red). (b) and (d) are similar to (a) and (c), respectively, but use R ₀ as control parameter. For P. vivax, we used p ₁ = p ₂ = 0.25. Dashed lines represent unstable equilibrium solutions, whilst full lines refer to stable endemic equilibria.

Figure 3

Mass drug administration (MDA) strategy applied in regions where P. falciparum (red) and P. vivax (blue) are equally prevalent. The initial parasite prevalence is equal for both P. vivax and P. falciparum as highlighted in Figures 2(c) and 2(d) by V and F, respectively. Asymptomatic infections are treated at a constant rate so they, on average, last as long as a clinical case. The red solid and dashed lines display interventions with durations just below and above the deterministic elimination threshold, respectively, for P. falciparum. For P. vivax, the model indicates no deterministic elimination threshold. The blue solid line represents continuing the intervention for 18 years and then halting, under p ₁ = p ₂ = 0.25. The blue and red dot-dashed lines represent uninterrupted 20-year MDA campaigns.

Figure 4

Age profiles for two transmission settings. Clinical P. vivax malaria age profiles (blue lines) compared with P. falciparum profiles (red lines) for equal risks of infection.