Dynamical Analysis for a Malaria Transmission Model
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.
Zhao, Z., Li, S. & Feng, Z. Dynamical Analysis for a Malaria Transmission Model. Qual. Theory Dyn. Syst. 21, 56 (2022). https://doi.org/10.1007/s12346-022-00589-8
Qualitative Theory of Dynamical Systems