Analysis of a diffusive HBV model with logistic proliferation and non-cytopathic antiviral mechanisms

Abstract Non-cytopathic antiviral mechanisms play a vital role in blocking up the HBV infection through the non-cytolytic processes that precede the immune elimination of infected hepatocytes. Due to the fact that the non-cytolytic processes contribute in eliminating at least 90% of the viral DNA from the liver, in this paper, we incorporate non-cytopathic antiviral mechanisms into the classical hepatitis B virus infection model. We consider the situations that: (i) only the movement of virus particles is allowed in the liver, which is modeled by only diffusion term in the virus equation; (ii) the interactions between cells and virus locally occur in the tissue such as lymph nodes, which is modeled by space-dependent parameters; (iii) logistic proliferation terms are considered for both the uninfected and infected liver cells so that even in the absence of pathogen, the liver would regenerate following injury. Through overcoming some difficulties of dynamical behaviors caused by lacks of diffusion terms and space-dependent parameters, the global threshold result governed by the basic reproduction number are obtained. More specifically, infection-free steady state is globally attractive when ℜ 0 1 , while the model is uniformly persistent when ℜ 0 > 1 . Numerical simulations are performed to validate the main results.