Transmission Dynamics For A Multipatch Malaria Model

In this paper, we propose a multipatch model to study the effects of population dispersal and disease latencies in both host and vectors on the spatial spread of malaria between patchs. The main result is divided into three parts.Firstly, we describe the background of the model, and give a brief introduction to the problem of this paper.Secondly, we formulate an SLIR model for humans and an SLI model for mosquitoes. Thus, we get a system of delay differential equations and use the theory of the next generation operator to define the basic reproduction number R0 for our model. It is shown that the disease-free equilibrium is asymptotically stable if Ro< 1 and unstable if Ro> 1. A sufficient condition for the existence of an endemic equilibrium when R0> 1 is obtained. In the chapter, due to the complexity of the model, we can not give the expression of R0.Lastly, we discuss the special case of a two-patch epidemic model, and investigate the dependence of R0 on the movement of susceptible, infectious, recovered humans and mosquitoes between the two patches. We point out that unbalanced dispersions of sus-ceptible hosts will increase the global basic reproduction number. It is possible that unbalanced dispersions of latent class will increase the GBRN and also will decrease the GBRN. In addition, we get that when mosquitoes begin disperse, the GBRN will also increase.