This paper presents a deterministic SIS model for the transmission dynamics of malaria, a life-threatening disease transmitted by mosquitos. Four species of the parasite genus Plasmodium are known to cause human malaria. Some species of the parasite have evolved into strains that are resistant to treatment. Although proportions of Plasmodium species vary considerably between geographic regions, multiple species and strains do coexist within some communities. The mathematical model derived here includes all available species and strains for a given community. The model has a disease-free equilibrium, which is a global attractor when the reproduction number of each species or strain is less than one. The model possesses quasiendemic equilibria; local asymptotic stability is established for two species, and numerical simulations suggest that the species or strain with the highest reproduction number exhibits competitive exclusion.

This paper presents a deterministic SIS model for the transmission dynamics of malaria, a life-threatening disease transmitted by mosquitos. Four species of the parasite genus Plasmodium are known to cause human malaria. Some species of the parasite have evolved into strains that are resistant to treatment. Although proportions of Plasmodium species vary considerably between geographic regions, multiple species and strains do coexist within some communities. The mathematical model derived here includes all available species and strains for a given community. The model has a disease-free equilibrium, which is a global attractor when the reproduction number of each species or strain is less than one. The model possesses quasiendemic equilibria; local asymptotic stability is established for two species, and numerical simulations suggest that the species or strain with the highest reproduction number exhibits competitive exclusion. ARTICLE HISTORY

We present a mathematical model of the transmission dynamics of two species of malaria with time lags. The model is equally applicable to two strains of a malaria species. The reproduction numbers of the two species are obtained and used as threshold parameters to study the stability and bifurcations of the equilibria of the model. We find that the model has a disease free equilibrium, which is a global attractor when the reproduction number of each species is less than one. Further, we observe that the non-disease free equilibrium of the model contains stability switches and Hopf bifurcations take place when the delays exceed the critical values.

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