A Periodic Vector-Bias Malaria Model with Incubation Period

Abstract

In this paper, we propose a malaria model which takes into account the climate factors, the extrinsic incubation period (EIP), and the vector-bias effect. We first introduce the basic reproduction ratio $R_0$ and then prove that $R_0$ serves as a threshold parameter in determining the global dynamics of the model, that is, the disease-free periodic solution is globally attractive if $R_0\le1$, and the system admits a unique positive periodic solution which is globally attractive if $R_0>1$. Numerically, we study the malaria transmission case in Maputo Province, Mozambique. Our numerical simulation results are consistent with the obtained analytic results. In addition, we observe that prolonging the length of the EIP is helpful for the control of the disease.