Threshold Dynamics of a Degenerate Diffusive HBV Infection Model with DNA-Containing Capsids in Heterogeneous Environment

This paper is concerned with threshold dynamics of a degenerate diffusive HBV infection model with DNA-containing capsids in heterogeneous environment. We firstly address the existence of global solutions, uniform and ultimate boundedness of solutions, asymptotic smoothness of semiflows and existence of a connected global attractor for the diffusive model. Then, we identify the basic reproduction number \({\mathcal {R}}_0\) ${\mathcal{R}}_0$ and establish a threshold-type result for the disease eradication or uniform persistence when \({\mathcal {R}}_0\le 1\) ${\mathcal{R}}_0\le 1$ or \({\mathcal {R}}_0>1\) ${\mathcal{R}}_0>1$ , respectively. Especially, when \({\mathcal {R}}_0>1\) ${\mathcal{R}}_0>1$ and the diffusion rate of capsids or the diffusion rate of virions is zero, we further show that the model admits a unique infection steady state which is globally attractive. Our results indicate that the pathogen can be eliminated by limiting the mobility of the capsids or virions.