Dynamics of a stochastic HBV infection model with drug therapy and immune response

Abstract

<abstract><p>Hepatitis B is a disease that damages the liver, and its control has become a public health problem that needs to be solved urgently. In this paper, we investigate analytically and numerically the dynamics of a new stochastic HBV infection model with antiviral therapies and immune response represented by CTL cells. Through using the theory of stochastic differential equations, constructing appropriate Lyapunov functions and applying Itô's formula, we prove that the disease-free equilibrium of the stochastic HBV model is stochastically asymptotically stable in the large, which reveals that the HBV infection will be eradicated with probability one. Moreover, the asymptotic behavior of globally positive solution of the stochastic model near the endemic equilibrium of the corresponding deterministic HBV model is studied. By using the Milstein's method, we provide the numerical simulations to support the analysis results, which shows that sufficiently small noise will not change the dynamic behavior, while large noise can induce the disappearance of the infection. In addition, the effect of inhibiting virus production is more significant than that of blocking new infection to some extent, and the combination of two treatment methods may be the better way to reduce HBV infection and the concentration of free virus.</p></abstract>

Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by Ornstein-Uhlenbeck process

“…Let W(t) = (u 1 (x, t), u 2 (x, t), u 3 (x, t)) T , together with ( 9) and (10), system (8) has been rewritten as the following abstract Cauchy problem…”

“…Meanwhile, much work can be found on the dynamic behavior of HBV infection model [1][2][3][4][5][6][7][8][9][10]. For example, Din and Li [4] built stochastic HBV model with Markov switching and white noise, and verified the results of the theorem using runge Kutta method.…”

Stationary distribution of a reaction-diffusion hepatitis B virus infection model driven by the Ornstein-Uhlenbeck process

“…Mathematical models are regarded as an efficient method when it comes to comprehending how HBV is transmitted. In the meantime, much research has been done on the HBV infection model's dynamic behavior [3][4][5][6][7][8][9][10][11][12]. For example, Din and Li [6] built a stochastic HBV model with Markov switching and white noise, and verified the theorem results using Runge-Kutta method.…”