Dynamics of a dengue fever model with vertical transmission and time periodic in spatially heterogeneous environments

Abstract

To reflect the impacts of vertical transmission in human and mosquitoes on the transmission of dengue fever, we propose an SIS‐SI dengue fever model with time periodic in spatially heterogeneous environments. Firstly, we obtain the properties of the basic reproduction number R0 for the dengue model by the eigenvalue problem and the spectral radius of next infection operator. Secondly, we investigate the existence and attractivity of the positive ω‐periodic solution for the dengue fever model. We also investigate the stability of ω‐periodic solution. The theoretical results indicate that vertical transmission can enhance the persistence of dengue virus in spatially heterogeneous environments with time periodic when R0 > 1. We perform numerical simulations to illustrate theoretical results of dengue fever model and give some epidemiological explanations. Finally, we combine medical advice to seek some effective prevention and control measures for vertical transmission.