Using Mathematics to Understand Malaria Infection During Erythrocytic Stages

Abstract

We review the basic intra-host model of malaria, without immunity. The model describes the Erythrocytic stage in a malaria-infected human, which involves the interaction between malaria parasites and red blood cells. These two populations interact on a dynamic landscape, in which a population of replicating parasites depletes a population of replenishing red blood cells. This paper shows how concepts from nonlinear dynamics can be used to unravel the underlying dynamical features of the model. The intra-host basic reproductive number R0, crucial to calculations concerning control of the infection is calculated. Using mathematical analysis of stability, conditions necessary for reducing and/or clearing parasites in the host are determined. Numerical simulations are also performed to verify analytic results and illustrate the possible behaviour of the model.