Mathematical analysis of an age-structured model for malaria transmission dynamics

Abstract

A new deterministic model for assessing the role of age-structure on the transmission dynamics of malaria in a community is designed. Rigorous qualitative analysis of the model reveals that it undergoes the phenomenon of backward bifurcation, where the stable disease-free equilibrium of the model co-exists with a stable endemic equilibrium when the associated reproduction number (denoted by R0) is less than unity. It is shown that the backward bifurcation phenomenon is caused by the malaria-induced mortality in humans. A special case of the model is shown to have a unique endemic equilibrium whenever the associated reproduction threshold exceeds unity. Further analyses reveal that adding age-structure to a basic model for malaria transmission in a community does not alter the qualitative dynamics of the basic model, with respect to the existence and asymptotic stability of the associated equilibria and the backward bifurcation property of the model. Numerical simulations of the model show that the cumulative number of new cases of infection and malaria-induced mortality increase with increasing average lifespan and birth rate of mosquitoes.