TY - JOUR
T1 - Dynamics of a Deterministic and Stochastic Susceptible-Exposed-Infectious-Recovered Epidemic Model
AU - Wang , Xinghao
AU - Zhang , Liang
AU - Guo , Jiajun
JO - Journal of Nonlinear Modeling and Analysis
VL - 1
SP - 24
EP - 53
PY - 2023
DA - 2023/08
SN - 5
DO - http://doi.org/10.12150/jnma.2023.24
UR - https://global-sci.org/intro/article_detail/jnma/21915.html
KW - Asymptomatic infective individual, Extinction, Persistence, Stationary distribution.
AB - <p style="text-align: justify;">We investigate a susceptible-exposed-infectious-recovered (SEIR)
epidemic model with asymptomatic infective individuals. First, we formulate
a deterministic model, and give the basic reproduction number $R_0.$ We show
that the disease is persistent, if $R_0 &gt; 1,$ and it is extinct, if $R_0 &lt; 1.$ Then,
we formulate a stochastic version of the deterministic model. By constructing
suitable stochastic Lyapunov functions, we establish sufficient criteria for the
extinction and the existence of ergodic stationary distribution to the model.
As a case, we study the COVID-19 transmission in Wuhan, China, and perform some sensitivity analysis. Our numerical simulations are carried out to
illustrate the analytic results.</p>