A Multipatch Malaria Model with Logistic Growth Populations

In this paper, we propose a multi-patch model to study the effects of population dispersal on the spatial spread of malaria between patches. The basic reproduction number Formula: see text is derived and it is shown that the disease-free equilibrium is locally asymptotically stable if Formula: see text and unstable if Formula: see text. Bounds on the disease-free equilibrium and Formula: see text are given. A sufficient condition for the existence of an endemic equilibrium when Formula: see text is obtained. For the two-patch submodel, the dependence of Formula: see text on the movement of exposed, infectious, and recovered humans between the two patches is investigated. Numerical simulations indicate that travel can help the disease to become endemic in both patches, even though the disease dies out in each isolated patch. However, if travel rates are continuously increased, the disease may die out again in both patches.