### Mathematical Biosciences and Engineering

2020, Issue 5: 5341-5368. doi: 10.3934/mbe.2020289
Research article Special Issues

# Asymptotic behavior of a stochastic delayed avian influenza model with saturated incidence rate

• Received: 18 May 2020 Accepted: 03 August 2020 Published: 11 August 2020
• In this paper, we establish a stochastic delayed avian influenza model with saturated incidence rate. Firstly, we prove the existence and uniqueness of the global positive solution with any positive initial value. Then, we study the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium by constructing some suitable Lyapunov functions and applying the Young's inequality and H?lder's inequality. If $\mathscr{R}_0 < 1$, then the solution of stochastic system is going around disease-free equilibrium while the solution of stochastic system is going around endemic equilibrium as $\mathscr{R}_0 >1$. Finally, some numerical examples are carried out to illustrate the accuracy of the theoretical results.

Citation: Yanyan Du, Ting Kang, Qimin Zhang. Asymptotic behavior of a stochastic delayed avian influenza model with saturated incidence rate[J]. Mathematical Biosciences and Engineering, 2020, 17(5): 5341-5368. doi: 10.3934/mbe.2020289

### Related Papers:

• In this paper, we establish a stochastic delayed avian influenza model with saturated incidence rate. Firstly, we prove the existence and uniqueness of the global positive solution with any positive initial value. Then, we study the asymptotic behaviors of the disease-free equilibrium and the endemic equilibrium by constructing some suitable Lyapunov functions and applying the Young's inequality and H?lder's inequality. If $\mathscr{R}_0 < 1$, then the solution of stochastic system is going around disease-free equilibrium while the solution of stochastic system is going around endemic equilibrium as $\mathscr{R}_0 >1$. Finally, some numerical examples are carried out to illustrate the accuracy of the theoretical results.

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沈阳化工大学材料科学与工程学院 沈阳 110142

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