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| Dynamics of a Deterministic and Stochastic Susceptible-exposed-infectious-recovered Epidemic Model |
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| KeyWord:Asymptomatic infective individual Extinction Persistence Stationary distribution |
| Author Name | Affiliation | | Xinghao Wang | College of Science, Northwest Northwest Agriculture and Forestry University (A\&F) University, Yangling, Shaanxi 712100, China | | Liang Zhang | College of Science, Northwest Northwest Agriculture and Forestry University (A\&F) University, Yangling, Shaanxi 712100, China | | Jiajun Guo | College of Science, Northwest Northwest Agriculture and Forestry University (A\&F) University, Yangling, Shaanxi 712100, China |
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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 $\mathcal{R}_{0}$. We show that the disease is persistent, if $\mathcal{R}_{0}>1$, and it is extinct, if $\mathcal{R}_{0}<1$. 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. |
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