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

TL;DR

This paper develops a comprehensive within-host malaria model with multiple age classes and parasite strains, analyzing its global stability and competitive dynamics based on the basic reproduction number R0.

Contribution

It introduces a novel multi-strain, age-structured malaria model and provides a rigorous global analysis of its stability and competitive exclusion principles.

Findings

If R0 ≤ 1, the disease-free state is globally stable.

If R0 > 1, a unique endemic equilibrium exists with the dominant strain stabilizing.

The endemic equilibrium is globally stable under mild conditions.

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 R0, the basic reproduction number, satisfies R0 </- 1, then the disease-free equilibrium is globally asymptotically stable. On the contrary if R0 > 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.