Dynamic modeling and analysis of Hepatitis B epidemic with general incidence

Tingting Xue; Long Zhang; Xiaolin Fan; Tingting Xue; Long Zhang; Xiaolin Fan

doi:10.3934/mbe.2023483

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 6: 10883-10908. doi: 10.3934/mbe.2023483

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Research article Special Issues

Dynamic modeling and analysis of Hepatitis B epidemic with general incidence

School of Mathematics and Physics, Xinjiang Institute of Engineering, Urumqi, Xinjiang, China

Academic Editor: Xiang-Sheng Wang

Received: 20 March 2023 Revised: 08 April 2023 Accepted: 14 April 2023 Published: 20 April 2023

New stochastic and deterministic Hepatitis B epidemic models with general incidence are established to study the dynamics of Hepatitis B virus (HBV) epidemic transmission. Optimal control strategies are developed to control the spread of HBV in the population. In this regard, we first calculate the basic reproduction number and the equilibrium points of the deterministic Hepatitis B model. And then the local asymptotic stability at the equilibrium point is studied. Secondly, the basic reproduction number of the stochastic Hepatitis B model is calculated. Appropriate Lyapunov functions are constructed, and the unique global positive solution of the stochastic model is verified by Itô formula. By applying a series of stochastic inequalities and strong number theorems, the moment exponential stability, the extinction and persistence of HBV at the equilibrium point are obtained. Finally, using the optimal control theory, the optimal control strategy to eliminate the spread of HBV is developed. To reduce Hepatitis B infection rates and to promote vaccination rates, three control variables are used, for instance, isolation of patients, treatment of patients, and vaccine inoculation. For the purpose of verifying the rationality of our main theoretical conclusions, the Runge-Kutta method is applied to numerical simulation.
- stochastic epidemic model,
- Hepatitis B,
- extinction,
- persistence,
- optimal control
Citation: Tingting Xue, Long Zhang, Xiaolin Fan. Dynamic modeling and analysis of Hepatitis B epidemic with general incidence[J]. Mathematical Biosciences and Engineering, 2023, 20(6): 10883-10908. doi: 10.3934/mbe.2023483

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Abstract

New stochastic and deterministic Hepatitis B epidemic models with general incidence are established to study the dynamics of Hepatitis B virus (HBV) epidemic transmission. Optimal control strategies are developed to control the spread of HBV in the population. In this regard, we first calculate the basic reproduction number and the equilibrium points of the deterministic Hepatitis B model. And then the local asymptotic stability at the equilibrium point is studied. Secondly, the basic reproduction number of the stochastic Hepatitis B model is calculated. Appropriate Lyapunov functions are constructed, and the unique global positive solution of the stochastic model is verified by Itô formula. By applying a series of stochastic inequalities and strong number theorems, the moment exponential stability, the extinction and persistence of HBV at the equilibrium point are obtained. Finally, using the optimal control theory, the optimal control strategy to eliminate the spread of HBV is developed. To reduce Hepatitis B infection rates and to promote vaccination rates, three control variables are used, for instance, isolation of patients, treatment of patients, and vaccine inoculation. For the purpose of verifying the rationality of our main theoretical conclusions, the Runge-Kutta method is applied to numerical simulation.

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