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Ingegneria Sismica
  • Research article

Ingegneria Sismica

Ingegneria Sismica - Cover

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

Author(s): Liqin Zheng1, Dongrui Qing2, Yan Zhang1
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
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.

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.

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