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].

中文翻译：

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具有非退化扩散的随机SEIS流行病模型的密度函数分析

在本文中，我们构建了一个随机SEIS流行病模型，该模型在潜伏期和感染期将持续招募，非退化扩散和传染力结合起来。通过求解相应的Fokker-Planck方程，只要基本复制数大于1，我们就可以得出确定性系统地方均衡周围密度函数的精确表达式。我们的工作极大地改善了Chen的结果[关于退化扩散的随机SEIS流行病模型的密度函数和协方差矩阵分析的新思路，Appl。数学。Lett。，2020，106200]。