A diffusive viral propagation model with nonlinear infection rate and free boundaries

This paper concerns with the dynamical properties of a diffusive viral model with free boundaries, which describes the spread of viruses in space. Unlike the paper (Li et al. in Sci China Math 64:1971–1992, 2021), free boundaries at both ends will extend to infinity, i.e., the habitat eventually expands to the entire space. Moreover, the virus will eventually die out when the Basic Reproduction Number \({{\mathcal {R}}}_0\le 1\) ${\mathcal{R}}_0\le 1$ , while the virus will stabilize in a positive equilibrium when \({{\mathcal {R}}}_0>1\) ${\mathcal{R}}_0>1$ and some further assumptions (Theorem 3.2).