Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process

Zhiming Ni ^[1] ; Daqing Jiang ^[1] ; Zhongwei Cao ^[2] ; Xiaojie Mu ^[1]
1. [1] China University of Petroleum
  
  China University of Petroleum
  
  China
2. [2] Jilin University of Finance and Economics
  
  Jilin University of Finance and Economics
  
  China
Localización: Qualitative theory of dynamical systems, ISSN 1575-5460, Vol. 22, Nº 3, 2023
Idioma: inglés
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Resumen
- In this paper, we analyze a stochastic SIRC model with Ornstein–Uhlenbeck process.
  
  Firstly, we give the existence and uniqueness of global solution of stochastic SIRC model and prove it. In addition, the existence of ergodic stationary distributions for stochastic SIRC system is proved by constructing a suitable series of Lyapunov functions. A quasi-endemic equilibrium related to endemic equilibrium of deterministic systems is defined by considering randomness. And we obtain the probability density function of the linearized system near the equilibrium point. After the proof of probability density function, the sufficient condition of disease extinction is given and proved. We prove the theoretical results in the paper by numerical simulation at the end of the paper.