Lihong Huang,Zhibei Jiang,Yixiang Wu,Zhaohui Yuan. Analysis of a diffusive epidemic model with a zero-infection zone. Journal of Mathematical Analysis and Applications
In this paper, we propose and analyze a diffusive epidemic model with a zero-infection zone for the susceptible population. A distinct feature of the model is that the infected people are assumed to not able to cross the boundary of the zero-infection zone while the susceptible people cross the boundary at a prescribed rate. We investigate the global existence and boundedness of the solutions of the model and the existence and uniqueness of the disease-free equilibrium. We define the basic reproduction number and show that it is a threshold parameter for the disease dynamics. Moreover, we study the impact of the population transfer rate at the zero-infection zone boundary on the magnitude of the basic reproduction number. Finally, numerical simulations are performed as a supplement to our theoretical results.
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