Abstract
Abstract We develop and analyse a deterministic population-based ordinary differential equation of malaria transmission to consider the impact of three common assumptions of malaria models: (1) malaria infection does not change the attractiveness of humans to mosquitoes; (2) exposed mosquitoes (infected with malaria but not yet infectious to humans) have the same biting rate as susceptible mosquitoes; and (3) mosquitoes infectious to humans have the same biting rate as susceptible mosquitoes. We calculate the basic reproductive number, $$R_0$$ R 0 , for this model and show the existence of a transcritical bifurcation at $$R_0=1$$ R 0 = 1 , in common with most epidemiological models. We further show that for some sets of parameter values, this bifurcation can be backward (subcritical). We show with numerical simulations that increasing the relative attractiveness of infectious humans, increases $$R_0$$ R 0 but reduces the equilibrium prevalence of infectious humans; decreasing the biting rate of exposed mosquitoes increases $$R_0$$ R 0 and the equilibrium prevalence of infectious humans and mosquitoes; and increasing the biting rate of infectious mosquitoes has no impact on $$R_0$$ R 0 or the equilibrium prevalence of infectious humans, but decreases the infectious prevalence of infectious mosquitoes. These analyses of a simple malaria model show that common assumptions around the relative attractiveness of infectious humans and the relative biting rates of exposed and infectious mosquitoes can have substantial and counter-intuitive effects on malaria transmission dynamics.
Highlights
Malaria is an infectious disease of humans, usually transmitted through the bites of Anopheline mosquitoes
In order to account for the effects of malaria parasites on the mosquito’s host-seeking behaviour [1,19,20], we introduce two positive constants, φE, and φI, to represent the biting rate of exposed and infectious mosquitoes relative to susceptible mosquitoes, with φE < 1 and φI > 1
We developed and analysed a simple malaria model to investigate the impact of relaxing three assumptions that mathematical models of malaria commonly make
Summary
Malaria is an infectious disease of humans, usually transmitted through the bites of Anopheline mosquitoes. Mosquitoes with oocysts (who are infected but not yet infectious) tend to be less mobile and spend more time resting They have longer feeding cycles and experience a lower mortality rate than uninfected mosquitoes. Mosquitoes with sporozoites tend to be more restless and are likely to take multiple blood meals in a single feeding cycle (that is, they bite multiple hosts before resting). They experience a higher mortality rate than uninfected mosquitoes, they feed more frequently and thereby infect humans more often than they would if their feeding rate was unchanged. We perform some numerical simulations that illustrate the effects of varying the infection-state dependent mosquito biting frequency and the relative attractiveness of infectious humans
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