A periodic Ross-Macdonald model in a patchy environment

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 ℛ0 and show that either the disease-free periodic solution is globally asymptotically stable if ℛ0 ≤ 1 or the positive periodic solution is globally asymptotically stable if R0 > 1. Numerical simulations are conducted to confirm the analytical results and explore the effect of travel control on the disease prevalence.