Open AccessStationary distribution and extinction of a stochastic SEIQ epidemic model with a general incidence function and temporary immunity
Author(s) -
Yuhuai Zhang,
Xiaotong Ma,
Anwarud Din
Publication year - 2021
Publication title -
aims mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.329
H-Index - 15
ISSN - 2473-6988
DOI - 10.3934/math.2021715
Subject(s) - epidemic model , uniqueness , stationary distribution , ergodic theory , lyapunov function , extinction (optical mineralogy) , mathematics , incidence (geometry) , distribution (mathematics) , statistical physics , mathematical analysis , physics , statistics , medicine , markov chain , population , nonlinear system , geometry , quantum mechanics , optics , environmental health
In this paper, we propose a novel stochastic SEIQ model of a disease with the general incidence rate and temporary immunity. We first investigate the existence and uniqueness of a global positive solution for the model by constructing a suitable Lyapunov function. Then, we discuss the extinction of the SEIQ epidemic model. Furthermore, a stationary distribution for the model is obtained and the ergodic holds by using the method of Khasminskii. Finally, the theoretical results are verified by some numerical simulations. The simulation results show that the noise intensity has a strong influence on the epidemic spreading.