# American Institute of Mathematical Sciences

August  2021, 26(8): 4359-4373. doi: 10.3934/dcdsb.2020291

## Density function analysis for a stochastic SEIS epidemic model with non-degenerate diffusion

 1 School of Mathematics and Statistics, Key Laboratory of Applied Statistics of MOE, Northeast Normal University, Changchun 130024, Jilin Province, China 2 School of Continuing Education, Northeast Normal University, Changchun 130024, Jilin Province, China

* Correspondence should be addressed to Qingmei Chen, E-mail: chenqingmei.2007@163.com, Tel.:+8613617755207; fax:+8613617755207

Received  April 2020 Revised  July 2020 Published  October 2020

Fund Project: The authors were supported by the National Natural Science Foundation of China (No.12001090) and the Fundamental Research Funds for the Central Universities of China (No.2412020QD024)

In this paper, we construct a stochastic SEIS epidemic model that incorporates constant recruitment, non-degenerate diffusion and infectious force in the latent period and infected period. By solving the corresponding Fokker-Planck equation, we obtain the exact expression of the density function around the endemic equilibrium of the deterministic system provided that the basic reproduction number is greater than one. Our work greatly improves the result of Chen [A new idea on density function and covariance matrix analysis of a stochastic SEIS epidemic model with degenerate diffusion, Appl. Math. Lett., 2020, 106200].

Citation: Qun Liu, Qingmei Chen. Density function analysis for a stochastic SEIS epidemic model with non-degenerate diffusion. Discrete & Continuous Dynamical Systems - B, 2021, 26 (8) : 4359-4373. doi: 10.3934/dcdsb.2020291
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