Open AccessDynamics of a stochastic HBV infection model with cell-to-cell transmission and immune response
Author(s) -
Xiaoqin Wang,
Yiping Tan,
Yongli Cai,
Kaifa Wang,
Weiming Wang
Publication year - 2021
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.2021034
Subject(s) - transmission (telecommunications) , stochastic modelling , basic reproduction number , statistical physics , dynamics (music) , hepatitis b virus , stochastic dynamics , stochastic differential equation , mathematics , computer science , physics , virology , biology , virus , statistics , medicine , telecommunications , population , acoustics , environmental health
In this paper, considering the proven role of exosomes and the inevitable randomization within-host, we establish a hepatitis B virus (HBV) model with cell-to-cell transmission and CTL immune response from a deterministic framework to a stochastic differential equation (SDE). By introducing the reproduction number $ R_0 $, we prove that $ R_0 $ can be used to govern the stochastic dynamics of the SDE HBV model. Under certain assumptions, if $ R_{0}\leq1 $, the solution of the SDE model always fluctuates around the infection-free equilibrium of the deterministic model, which indicates that the HBV will eventually disappear almost surely; if $ R_{0} > 1 $, under extra conditions, the solution of the SDE model fluctuates around endemic equilibrium of the corresponding deterministic model, which leads to the stochastic persistence of the HBV with probability one. One of the most interesting findings is that the fluctuation amplitude is positively related to the intensity of the white noise, which can provide us some useful control strategies to regulate HBV infection dynamics.