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Stationary distribution, density function and extinction of a stochastic SIQR epidemic model with Ornstein–Uhlenbeck process

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  • Yang, Ying
  • Zhang, Jingwen
  • Wang, Kaiyuan
  • Zhang, Guofang

Abstract

In this paper, an analysis of a stochastic SIQR epidemic model under the Ornstein–Uhlenbeck process is provided. The local asymptotic stability of the endemic equilibrium for the deterministic system is discussed, followed by a proof of the existence and uniqueness of the global positive solution for the stochastic system. Subsequently, a stochastic threshold R0e is established to ensure disease extinction. The study further investigates the persistence and stationary distribution of the stochastic SIQR epidemic model, and calculates the probability density function near the quasi-endemic equilibrium. Finally, numerical simulations are presented to corroborate the theoretical findings.

Suggested Citation

  • Yang, Ying & Zhang, Jingwen & Wang, Kaiyuan & Zhang, Guofang, 2024. "Stationary distribution, density function and extinction of a stochastic SIQR epidemic model with Ornstein–Uhlenbeck process," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:chsofr:v:184:y:2024:i:c:s0960077924005241
    DOI: 10.1016/j.chaos.2024.114972
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