Variation in relapse frequency and the transmission potential of Plasmodium vivax malaria

Abstract

There is substantial variation in the relapse frequency of Plasmodium vivax malaria, with fast-relapsing strains in tropical areas, and slow-relapsing strains in temperate areas with seasonal transmission. We hypothesize that much of the phenotypic diversity in P. vivax relapses arises from selection of relapse frequency to optimize transmission potential in a given environment, in a process similar to the virulence trade-off hypothesis. We develop mathematical models of P. vivax transmission and calculate the basic reproduction number R0 to investigate how transmission potential varies with relapse frequency and seasonality. In tropical zones with year-round transmission, transmission potential is optimized at intermediate relapse frequencies of two to three months: slower-relapsing strains increase the opportunity for onward transmission to mosquitoes, but also increase the risk of being outcompeted by faster-relapsing strains. Seasonality is an important driver of relapse frequency for temperate strains, with the time to first relapse predicted to be six to nine months, coinciding with the duration between seasonal transmission peaks. We predict that there is a threshold degree of seasonality, below which fast-relapsing tropical strains are selected for, and above which slow-relapsing temperate strains dominate, providing an explanation for the observed global distribution of relapse phenotypes.

Keywords: Plasmodium vivax malaria; mathematical model; relapse; seasonality; transmission potential.

Figure 1.

Schematic diagrams of malaria transmission models. The force of infection owing to new mosquito bites is λ = mabI_M. Parameter definitions and values are provided in table 1. Model 1: non-relapsing P. falciparum malaria. Model 2: relapsing P. vivax malaria of a tropical phenotype. Model 3: relapsing P. vivax malaria of a temperate phenotype. Dashed boxes denote states where an individual is harbouring dormant hypnozoites. The models are built up by sequentially adding compartments for latent hypnozoite stages, and compartments for dormant hypnozoite stages. Mosquito compartments are not shown.

Figure 2.

(a) Tropical and (b) temperate relapse phenotypes. Comparison between model predicted survival time until nth relapse and data from six cohorts. After primary infection, participants in each cohort were followed longitudinally for the detection of relapses. Up to five relapses were detected per participant with treatment administered following each detected relapse. Data are presented using survival analysis to show the proportion of individuals with at least n relapses (circles) and 95% confidence intervals (vertical lines). The duration of dormancy for the temperate relapse phenotype is described by a gamma distribution. The solid curves shows the best-fit prediction from the within-host model (number of hypnozoites accounted for) and the dashed curves denote the prediction from the binary model (hypnozoite infection regarded as a binary state). The close agreement between the solid and dashed curves suggests that the within-host biology of hypnozoites and subsequent relapses can be approximated by simpler binary models. All parameter values are provided in the electronic supplementary material.

Figure 3.

The optimal transmission potential of P. vivax in non-seasonal settings. (a) Slower hypnozoite activation rates reduce the number of relapsing hypnozoites. This is because spending more time in the liver increases the probability of hypnozoite death. (b) Slower hypnozoite activation rates increase the expected duration of time spent by hypnozoites in the liver. In particular, very fast relapse rates lead to hypnozoites being flushed out of the liver and short durations of hypnozoite carriage. (c) Transmission potential (as measured by R₀) is optimized at intermediate values of relapse frequency, here predicted to be α = 1/206 days for tropical strains. Relapse too quickly and all relapses coincide with the primary infection; relapse too slowly and hypnozoites risk death in the liver.

Figure 4.

Effect of seasonality on the transmission potential of P. vivax. (a) For non-relapsing P. falciparum, R₀ decreases with increasing seasonality. For tropical strains of P. vivax, there is a modest reduction in R₀ with increasing seasonality. By contrast, for temperate strains of P. vivax, R₀ increases with seasonality. In the simulations presented here, the difference between R₀ for P. falciparum and P. vivax is owing to relapses. (b) The transmission potential of temperate strains of P. vivax will depend on the duration of dormancy, with R₀ optimized at longer durations in more seasonal settings. (c) For a given seasonal profile, the time to first relapse (dormancy plus latency in the liver) can be estimated by maximizing R₀. The time to first relapse (solid line) is predicted to increase with seasonality. Notably when seasonality crosses a threshold of ≈50% of transmission in the peak three months, the time to first relapse switches from 3–4 months characteristic of tropical phenotypes [24,38,39] to 6–9 months characteristic of temperate phenotypes [27,40].

Figure 5.

The effect of time to next relapse on equilibrium parasite prevalence of tropical P. vivax. Transmission intensity was varied by changing the number of mosquitoes per human m. At higher transmission intensities, the time to next relapse that maximizes P. vivax prevalence (PvPR) decreases. Faster relapses are favoured at high prevalence because if hypnozoites wait for the primary infection to clear, another primary infection will occur. Slower relapses are favoured at lower prevalence because hypnozoites can safely wait for the primary infection to clear before relapsing. The vertical dashed line corresponds to the time to first relapse (f = 66 days) that optimizes R₀.

Figure 6.

Competition between temperate strains of P. vivax with varying time to first relapse. The time to first relapse was varied by changing the duration of dormancy d while keeping the average time in the latent stage fixed (1/f). Simulations were initialized with the distribution of strain phenotype assumed to follow a normal distribution. In a low seasonality setting, the mean time to first relapse converges on approximately four months. In a high-seasonality setting, the mean time to first relapse converges on six to nine months.