Dynamics in a reaction-diffusion epidemic model via environmental driven infection in heterogenous space

• Main Authors: Ning Wang, Long Zhang, Zhidong Teng
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2021-03-01
• Series: Journal of Biological Dynamics
• Subjects: sir epidemic model; environmental driven infection; spatial heterogeneity; basic reproduction number; global stability
• Online Access: http://dx.doi.org/10.1080/17513758.2021.1900428

In this paper, a reaction-diffusion SIR epidemic model via environmental driven infection in heterogeneous space is proposed. To reflect the prevention and control measures of disease in allusion to the susceptible in the model, the nonlinear incidence function $ Ef(S) $ is applied to describe the protective measures of susceptible. In the general spatially heterogeneous case of the model, the well-posedness of solutions is obtained. The basic reproduction number $ R_{0} $ is calculated. When $ R_{0}\leq 1 $ the global asymptotical stability of the disease-free equilibrium is obtained, while when $ R_{0} \gt 1 $ the model is uniformly persistent. Furthermore, in the spatially homogeneous case of the model, when $ R_{0} \gt 1 $ the global asymptotic stability of the endemic equilibrium is obtained. Lastly, the numerical examples are enrolled to verify the open problems.