Dynamics of a reaction-diffusion SVIR model in a spatial heterogeneous environment

In this paper, a reaction-diffusion SVIR epidemic model in a spatial heterogeneous environment is proposed. We defined the basic reproduction number 910 and showed that it is a threshold parameter, which determines the disease extinction or persistence in the case of a bounded domain. The global attractiveness of the constant positive steady state and the explicit formula of 910 are obtained when the space is homogeneous. Simulation results reveal that the spatial heterogeneity can enhance the spread risk of the disease. It is found that the distribution of infected individuals is affected by different diffusion rate and its prevalence becomes higher when a larger diffusion rate is used. The relationship among the basic reproduction number, the vaccination rate and recovery rate of vaccinated individuals and infected individuals are also addressed. If the recovery rates of vaccinated individuals and infected individuals are sufficiently large, disease can be eradicated by conducting suitable vaccination strategy, which reveals that increasing the recovery rates of vaccinated individuals and infected individuals seems more important than increasing vaccination rate. (C) 2019 Elsevier B.V. All rights reserved.