Open AccessA model of HBV infection with intervention strategies: dynamics analysis and numerical simulations
Author(s) -
Kang Bo Bao,
Qi Min Zhang,
Xi Ning Li
Publication year - 2019
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2019129
Subject(s) - basic reproduction number , extinction (optical mineralogy) , noise (video) , stationary distribution , transmission (telecommunications) , intervention (counseling) , stochastic modelling , outbreak , hepatitis b virus , disease , mathematics , markov chain , statistical physics , persistence (discontinuity) , computer science , virology , statistics , medicine , biology , virus , environmental health , artificial intelligence , physics , engineering , population , telecommunications , psychiatry , image (mathematics) , pathology , paleontology , geotechnical engineering
In this paper, we analyze the effect 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.