Resumen de Dynamical Analysis for a Malaria Transmission Model
Zhihong Zhao, Shaochun Li, Zhaosheng Feng
In this paper, we present a malaria transmission model with climatic factors to study the climatic transmission dynamics of malaria with the effect of the Serratia AS1 bacterium. It has been shown in controlled laboratory experiments that Serratia AS1 bacterium can rapidly disseminate throughout mosquito populations and efficiently inhibit development of malaria parasites in mosquitoes. We derive the basic reproduction ratio R0. We introduce the basic reproduction ratio R0 which can be used as a threshold parameter in the global dynamical model. When R0 ≤ 1, the disease-free periodic solution of this model is globally asymptotically stable; and when R0 > 1, the disease remains persistent. We analyze the sensitivity of R0 in terms of the vertical and horizontal transmission rates of Serratia AS1, and find that R0 can be small when the vertical transmission rate of Serratia AS1 tends to 1 and the influence of the horizontal transmission rate performs inversely proportional to R0 when the vertical transmission rate is less than 1. Based on the data of Luanda, we perform numerical simulations to illustrate our theoretical results, which indicate that treatment of Serratia AS1 provides us an effective measure in controlling malaria.
