Ergodic Properties and Probability Distribution Dynamics of a Stochastic SEIR Model with Recovery Rate

Zheng, Liqin; Qing, Dongrui; Zhang, Yan

doi:10.65102/is20261167

Research article

Ingegneria Sismica

Volume 43 Issue 3
Pages: 1
-28

Ergodic Properties and Probability Distribution Dynamics of a Stochastic SEIR Model with Recovery Rate

Author(s): ^¹, ^², ^¹

¹School of Mathematics and Statistics, Shaan Xi Xue Qian Normal University Xi’an 710100, P.R.China

²School of Marxism, Xi’an University of Finance and Economics Xi’an 710100, P.R.China

Published: 10/06/2026

Cite

Zheng, Liqin ., Qing, Dongrui ., and Zhang, Yan . “Ergodic Properties and Probability Distribution Dynamics of a Stochastic SEIR Model with Recovery Rate.” Ingegneria Sismica Volume 43 Issue 3: 1-28, doi:10.65102/is20261167.

https://doi.org/10.65102/is20261167

Abstract

This paper examines the dynamics of a stochastic SEIR model, proving the existence of a unique global positive solution. Conditions for an ergodic stationary distribution are determined using Lyapunov functions. An exact expression for the probability density function is derived. The threshold for persistence versus extinction is identified, and numerical simulations confirm the analysis.

Keywords
SEIR model; ergodic stationary distribution; probability density function.