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 [Formula: see text] is greater than one or less than one. At last, numerical simulations are carried out to illustrate our mathematical results.
Keywords: 37N25; 37N30; 65L12; 65U05; Uniform persistence; basic reproduction ratio; immunity; periodic solution; stability.