A model of HBV infection with intervention strategies: dynamics analysis and numerical simulations

Kangbo Bao; Qimin Zhang; Xining Li; Kangbo Bao; Qimin Zhang; Xining Li

doi:10.3934/mbe.2019129

Mathematical Biosciences and Engineering

2019, Volume 16, Issue 4: 2562-2586. doi: 10.3934/mbe.2019129

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Research article

A model of HBV infection with intervention strategies: dynamics analysis and numerical simulations

School of Mathematics and Statistics, Ningxia University, Yinchuan, 750021, P.R. China

Received: 20 January 2019 Accepted: 08 March 2019 Published: 22 March 2019

In this paper, we analyze the e ect of environment noise on the transmission dynamics of a stochastic hepatitis B virus (HBV) infection model with intervention strategies. By using the Markov semigroups theory, we define the stochastic basic reproduction number and find it can be used to govern disease extinction or persistence. When it is less than one, under a mild extra condition, the stochastic system has a disease-free equilibrium and the disease is predicted to die out with probability one. When it is greater than one, under mild extra conditions, the model admits a stationary distribution which means the persistence of the disease. Thus, we observe that larger intensity of noise (resulting in a smaller stochastic basic reproduction number) can suppress the emergence of hepatitis B outbreak. Numerical simulations are also carried out to investigate the influence of information intervention strategies that may change individual behavior and protect the susceptible from infection. Our analysis shows that the environmental noise can greatly a ect the long-term behavior of the system, highlighting the importance of the role of intervention strategies in the control of hepatitis B.
- stochastic hepatitis B model,
- Markov semigroups,
- stochastic basic reproduction number,
- intervention strategies,
- extinction and persistence
Citation: Kangbo Bao, Qimin Zhang, Xining Li. A model of HBV infection with intervention strategies: dynamics analysis and numerical simulations[J]. Mathematical Biosciences and Engineering, 2019, 16(4): 2562-2586. doi: 10.3934/mbe.2019129

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Abstract

In this paper, we analyze the e ect of environment noise on the transmission dynamics of a stochastic hepatitis B virus (HBV) infection model with intervention strategies. By using the Markov semigroups theory, we define the stochastic basic reproduction number and find it can be used to govern disease extinction or persistence. When it is less than one, under a mild extra condition, the stochastic system has a disease-free equilibrium and the disease is predicted to die out with probability one. When it is greater than one, under mild extra conditions, the model admits a stationary distribution which means the persistence of the disease. Thus, we observe that larger intensity of noise (resulting in a smaller stochastic basic reproduction number) can suppress the emergence of hepatitis B outbreak. Numerical simulations are also carried out to investigate the influence of information intervention strategies that may change individual behavior and protect the susceptible from infection. Our analysis shows that the environmental noise can greatly a ect the long-term behavior of the system, highlighting the importance of the role of intervention strategies in the control of hepatitis B.

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