Global Analysis of New Malaria Intrahost Models with a Competitive Exclusion Principle

Source abstract

In this paper we propose a malaria within‐host model with k classes of age for the parasitized red blood cells and n strains for the parasite. We provide a global analysis for this model. A competitive exclusion principle holds. If $\mathcal R_0$, the basic reproduction number, satisfies $\mathcal R_0 \leq 1$, then the disease‐free equilibrium is globally asymptotically stable. On the contrary if $\mathcal R_0 >1$, then generically there is a unique endemic equilibrium which corresponds to the endemic stabilization of the most virulent parasite strain and to the extinction of all the other parasites strains. We prove that this equilibrium is globally asymptotically stable on the positive orthant if a mild sufficient condition is satisfied.