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Volume 5, Issue 1
Dynamics of a Deterministic and Stochastic Susceptible-Exposed-Infectious-Recovered Epidemic Model

Xinghao Wang, Liang Zhang & Jiajun Guo

DOI: 10.12150/jnma.2023.24

J. Nonl. Mod. Anal., 5 (2023), pp. 24-53.

Published online: 2023-08

[An open-access article; the PDF is free to any online user.]

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  • Abstract

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 $R_0 > 1,$ and it is extinct, if $R_0 < 1.$ 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.

  • Keywords

Asymptomatic infective individual, Extinction, Persistence, Stationary distribution.

  • AMS Subject Headings

92D30, 34D05, 60H10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-24, author = {Wang , XinghaoZhang , Liang and Guo , Jiajun}, title = {Dynamics of a Deterministic and Stochastic Susceptible-Exposed-Infectious-Recovered Epidemic Model}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {1}, pages = {24--53}, abstract = {

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 $R_0 > 1,$ and it is extinct, if $R_0 < 1.$ 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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.24}, url = {http://global-sci.org/intro/article_detail/jnma/21915.html} }
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 -

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 $R_0 > 1,$ and it is extinct, if $R_0 < 1.$ 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.

Xinghao Wang, Liang Zhang & Jiajun Guo. (2023). Dynamics of a Deterministic and Stochastic Susceptible-Exposed-Infectious-Recovered Epidemic Model. Journal of Nonlinear Modeling and Analysis. 5 (1). 24-53. doi:10.12150/jnma.2023.24
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