Stationary distribution and extinction of a stochastic influenza virus model with disease resistance

Ming-Zhen Xin; Bin-Guo Wang; Yashi Wang; Ming-Zhen Xin; Bin-Guo Wang; Yashi Wang

doi:10.3934/mbe.2022424

Mathematical Biosciences and Engineering

2022, Volume 19, Issue 9: 9125-9146. doi: 10.3934/mbe.2022424

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Research article Special Issues

Stationary distribution and extinction of a stochastic influenza virus model with disease resistance

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
2.
Department of Science and Technology, China University of Political Science and Law, Beijing 100027, China

Academic Editor: Jesús Martín Vaquero

Received: 09 March 2022 Revised: 07 May 2022 Accepted: 16 May 2022 Published: 22 June 2022

Influenza is a respiratory infection caused influenza virus. To evaluate the effect of environment noise on the transmission of influenza, our study focuses on a stochastic influenza virus model with disease resistance. We first prove the existence and uniqueness of the global solution to the model. Then we obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Moreover, certain sufficient conditions are provided for the extinction of the influenza virus flu. Finally, several numerical simulations are revealed to illustrate our theoretical results. Conclusively, according to the results of numerical models, increasing disease resistance is favorable to disease control. Furthermore, a simple example demonstrates that white noise is favorable to the disease's extinction.
- stochastic influenza virus model,
- disease resistance,
- stationary distribution,
- extinction,
- ergodic property
Citation: Ming-Zhen Xin, Bin-Guo Wang, Yashi Wang. Stationary distribution and extinction of a stochastic influenza virus model with disease resistance[J]. Mathematical Biosciences and Engineering, 2022, 19(9): 9125-9146. doi: 10.3934/mbe.2022424

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Abstract

Influenza is a respiratory infection caused influenza virus. To evaluate the effect of environment noise on the transmission of influenza, our study focuses on a stochastic influenza virus model with disease resistance. We first prove the existence and uniqueness of the global solution to the model. Then we obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Moreover, certain sufficient conditions are provided for the extinction of the influenza virus flu. Finally, several numerical simulations are revealed to illustrate our theoretical results. Conclusively, according to the results of numerical models, increasing disease resistance is favorable to disease control. Furthermore, a simple example demonstrates that white noise is favorable to the disease's extinction.

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