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Volume 5, Issue 1
Dynamics of a Stochastic SIR Epidemic Model with Logistic Growth

Yubo Liu, Jianli Li & Daipeng Kuang

DOI: 10.12150/jnma.2023.73

J. Nonl. Mod. Anal., 5 (2023), pp. 73-94.

Published online: 2023-08

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

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  • Abstract

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.

  • Keywords

Logistic growth, Saturated treatment, Stationary distribution and ergodicity, Non-monotone incidence, Extinction.

  • AMS Subject Headings

37A50, 37H10, 37N25

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-5-73, author = {Liu , YuboLi , Jianli and Kuang , Daipeng}, title = {Dynamics of a Stochastic SIR Epidemic Model with Logistic Growth}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2023}, volume = {5}, number = {1}, pages = {73--94}, abstract = {

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.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2023.73}, url = {http://global-sci.org/intro/article_detail/jnma/21917.html} }
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 -

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.

Liu , YuboLi , Jianli and Kuang , Daipeng. (2023). Dynamics of a Stochastic SIR Epidemic Model with Logistic Growth. Journal of Nonlinear Modeling and Analysis. 5 (1). 73-94. doi:10.12150/jnma.2023.73
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