Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China

Jiying Ma; Shasha Ma; Jiying Ma; Shasha Ma

doi:10.3934/mbe.2023145

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 2: 3070-3098. doi: 10.3934/mbe.2023145

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Research article

Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China

Jiying Ma ^,,
Shasha Ma

College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Academic editor: Hao Wang

Received: 19 September 2022 Revised: 03 November 2022 Accepted: 08 November 2022 Published: 01 December 2022

Hepatitis B virus (HBV) infection is a global public health problem and there are $ 257 $ million people living with chronic HBV infection throughout the world. In this paper, we investigate the dynamics of a stochastic HBV transmission model with media coverage and saturated incidence rate. Firstly, we prove the existence and uniqueness of positive solution for the stochastic model. Then the condition on the extinction of HBV infection is obtained, which implies that media coverage helps to control the disease spread and the noise intensities on the acute and chronic HBV infection play a key role in disease eradication. Furthermore, we verify that the system has a unique stationary distribution under certain conditions, and the disease will prevail from the biological perspective. Numerical simulations are conducted to illustrate our theoretical results intuitively. As a case study, we fit our model to the available hepatitis B data of mainland China from 2005 to 2021.
- hepatitis B virus,
- media coverage,
- extinction,
- stationary distribution,
- numerical simulation
Citation: Jiying Ma, Shasha Ma. Dynamics of a stochastic hepatitis B virus transmission model with media coverage and a case study of China[J]. Mathematical Biosciences and Engineering, 2023, 20(2): 3070-3098. doi: 10.3934/mbe.2023145

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Abstract

Hepatitis B virus (HBV) infection is a global public health problem and there are $ 257 $ million people living with chronic HBV infection throughout the world. In this paper, we investigate the dynamics of a stochastic HBV transmission model with media coverage and saturated incidence rate. Firstly, we prove the existence and uniqueness of positive solution for the stochastic model. Then the condition on the extinction of HBV infection is obtained, which implies that media coverage helps to control the disease spread and the noise intensities on the acute and chronic HBV infection play a key role in disease eradication. Furthermore, we verify that the system has a unique stationary distribution under certain conditions, and the disease will prevail from the biological perspective. Numerical simulations are conducted to illustrate our theoretical results intuitively. As a case study, we fit our model to the available hepatitis B data of mainland China from 2005 to 2021.

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