Asymptotic stability of a viral dynamics model with diffusion and B-D functional responses.

*(Chinese. English summary)*Zbl 1313.35181Summary: A viral dynamics model with diffusion and B-D functional response under homogeneous Neumann boundary conditions is investigated in this paper, in which the stabilities of equilibria are analyzed. An a priori estimate is proved by the maximum principle of the coupled parabolic inequalities. Based on the Hurwitz theorem, it is proved that the endemic equilibrium is locally stable when the basic reproductive number is greater than one and the disease-free equilibrium is locally stable when it is less than one. Furthermore, through constructing upper and lower solutions to the problem and establishing its associated monotone iterative sequences, we prove the global stability of the disease-free solution. The result shows that if the recruitment rate or the contact rate of the susceptible population or the resolution ratio of the infected compartment is small enough, the disease-free solution is globally stable.