title: A MULTI-PATCH MALARIA MODEL WITH LOGISTIC GROWTH POPULATIONS.
abstract: 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.
authors.affiliation: Department of Mathematics, University of Miami, Coral Gables, FL 33124-4250, USA ( dzgao@math.miami.edu , ruan@math.miami.edu ).
authors.forename: Daozhou
authors.initials: D
authors.lastname: Gao
authors.forename: Shigui
authors.initials: S
authors.lastname: Ruan
keywords: basic reproduction number; disease-free equilibrium; human movement; malaria; monotonicity; patch model; travel rate