Threshold dynamics of a HBV infection model with degenerate diffusion, DNA-containing capsids and time-delays in heterogeneous environment.

In this paper, we consider the global dynamics of a HBV infection model with degenerate diffusion, DNA-containing capsids and time-delays in heterogeneous environment. Since only the free virus equation contains a diffusion term, the model is partially degenerate, which makes that the solution semiflow lacks compactness. In addition, different to early works, the consideration of time-delay effect increases the difficulty in studying the dynamics of the model. To overcome these difficulties, we regard the model as a one-periodic system. Then, apply the method of Kuratowski's measure of non-compactness, we establish the global threshold dynamics of the system, which can be characterized by the value of basic reproduction number $R_0$ . In addition, we establish the global asymptotic stability of infection-free steady state when $R_0=1$ , and find that $R_0$ is decreasing with respect to the three time delay terms. We further provide some examples to support our theoretical results.