TY - JOUR
T1 - Dynamics of a Stochastic SIR Epidemic Model with Logistic Growth
AU - Liu , Yubo
AU - Li , Jianli
AU - Kuang , Daipeng
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 73
EP - 94
PY - 2023
DA - 2023/08
SN - 5
DO - http://doi.org/10.12150/jnma.2023.73
UR - https://global-sci.org/intro/article_detail/jnma/21917.html
KW - Logistic growth, Saturated treatment, Stationary distribution
and ergodicity, Non-monotone incidence, Extinction.
AB - <p style="text-align: justify;">In this paper, a stochastic SIR epidemic model with saturated
treatment function, non-monotone incidence rate and logistic growth is studied. First, we prove that the stochastic model has a unique global positive
solution. Next, by constructing a suitable Lyapunov function, we can show
that there exists an ergodic stationary distribution in the random SIR model.
Then, we show that a sufficient condition can make the disease tend to extinction. Finally, some numerical simulations are used to prove our analytical
result.</p>