title: A PERIODIC ROSS-MACDONALD MODEL IN A PATCHY ENVIRONMENT.
abstract: Based on the classical Ross-Macdonald model, in this paper we propose a periodic malaria model to incorporate the effects of temporal and spatial heterogeneity on disease transmission. The temporal heterogeneity is described by assuming that some model coefficients are time-periodic, while the spatial heterogeneity is modeled by using a multi-patch structure and assuming that individuals travel among patches. We calculate the basic reproduction number [Formula: see text] and show that either the disease-free periodic solution is globally asymptotically stable if [Formula: see text] or the positive periodic solution is globally asymptotically stable if [Formula: see text]. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.
authors.affiliation: Francis I. Proctor Foundation for Research in Ophthalmology University of California, San Francisco San Francisco, CA 94143, USA.
authors.forename: Daozhou
authors.initials: D
authors.lastname: Gao
authors.affiliation: Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom, Kowloon, Hong Kong, China.
authors.forename: Yijun
authors.initials: Y
authors.lastname: Lou
authors.affiliation: Department of Mathematics University of Miami Coral Gables, FL 33124, USA.
authors.forename: Shigui
authors.initials: S
authors.lastname: Ruan
keywords: Malaria; basic reproduction number; patch model; seasonality; threshold dynamics