Stationary distribution for a three-dimensional stochastic viral infection model with general distributed delay

Ying He; Junlong Tao; Bo Bi; Ying He; Junlong Tao; Bo Bi

doi:10.3934/mbe.2023800

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 10: 18018-18029. doi: 10.3934/mbe.2023800

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Research article

Stationary distribution for a three-dimensional stochastic viral infection model with general distributed delay

Ying He ¹,
Junlong Tao ²,
Bo Bi ^{2
,
,}

1.
School of Mathematics and Statistics, Northeast Petroleum University, Daqing 163318, China
2.
International School of Public Health and One Health, Hainan Medical University, Haikou 571199, China

Received: 08 July 2023 Revised: 27 August 2023 Accepted: 03 September 2023 Published: 19 September 2023

This work examines a stochastic viral infection model with a general distributed delay. We transform the model with weak kernel case into an equivalent system through the linear chain technique. First, we establish that a global positive solution to the stochastic system exists and is unique. We establish the existence of a stationary distribution of a positive solution under the stochastic condition $ R^s > 0 $, also referred to as a stationary solution, by building appropriate Lyapunov functions. Finally, numerical simulation is proved to verify our analytical result and reveals the impact of stochastic perturbations on disease transmission.
- stochastic viral infection model,
- distributed delay,
- stationary distribution,
Citation: Ying He, Junlong Tao, Bo Bi. Stationary distribution for a three-dimensional stochastic viral infection model with general distributed delay[J]. Mathematical Biosciences and Engineering, 2023, 20(10): 18018-18029. doi: 10.3934/mbe.2023800

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Abstract

This work examines a stochastic viral infection model with a general distributed delay. We transform the model with weak kernel case into an equivalent system through the linear chain technique. First, we establish that a global positive solution to the stochastic system exists and is unique. We establish the existence of a stationary distribution of a positive solution under the stochastic condition $ R^s > 0 $, also referred to as a stationary solution, by building appropriate Lyapunov functions. Finally, numerical simulation is proved to verify our analytical result and reveals the impact of stochastic perturbations on disease transmission.

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