A mathematical model of malaria transmission in a periodic environment

Abstract

In this paper, we present a mathematical model of malaria transmission dynamics with age structure for the vector population and a periodic biting rate of female anopheles mosquitoes. The human population is divided into two major categories: the most vulnerable called non-immune and the least vulnerable called semi-immune. By applying the theory of uniform persistence and the Floquet theory with comparison principle, we analyse the stability of the disease-free equilibrium and the behaviour of the model when the basic reproduction ratio $ \mathcal {R}_0 $ is greater than one or less than one. At last, numerical simulations are carried out to illustrate our mathematical results.

Keywords

• uniform persistence
• basic reproduction ratio
• stability
• periodic solution
• immunity