A mathematical model for malaria treating both sensitive and resistant strains in a multigroup population

Abstract

The emergence of drug-resistant malaria parasites in recent years has become a significant public health problem. Drawing from our ealier models [2], which deal with a single population group, a multigroup model is hereby introduced. Human population is assumed fixed in all considerations while that of vectors varry. All the models are nonlinear ordinary differential equations models. The models describe accurately, the current trend in malaria infection in a malaria endemic region. Our focus in analysing the models is on the possibility of establishing some positive asymptotic equilibria. It is shown that (under suitable conditions) the equilibrium points are (globally) asymptotically stable. As a function of some interplay between the various parameters, the equilibrium can lead to endemic infection with sensitive infection only, resistant infection only, or both, or to elimination of both infections. The biological significance of these equilibrium points, namely, their usefulness to practical health officials, also emerges as a byproduct.