摘要
A type of SEIR epidemic model with media coverage and temporary immunity is investigated in this paper. The existence and uniqueness of the global positive solution with any positive initial value is proved. Under the condition R0s> 1, we prove that the disease is persistent in the mean for a long run. Furthermore, by constructing suitable Lyapunov functions, some sufficient conditions that guarantee the existence of stationary distribution are derived. We also obtain that, if the condition R0e< 1 is satisfied, then the disease is extinct with an exponential rate. As a consequence, some examples and numerical simulation are demonstrated to show the validity and feasibility of the theoretical results.
基金
This work was supported by NSFC under grant 61911530398
Natural Science Foundation of Fujian Province of China under grant 2016J01015.
