The spreading frontiers in partially degenerate reaction–diffusion systems

In this paper, we study the spreading frontiers in the partially degenerate reaction–diffusion systems with a mobile and a stationary component, which are described by a class free boundary condition. The center of our investigation is to understand the effect of the dispersal rate DD of the mobile component, the expansion capacity μμ (the ratio of the expansion speed of the free boundary and the gradient of the mobile component at the spreading frontiers) and the initial numbers u0u0 and v0v0 on the long-run dynamics of the spreading frontiers. It is shown that a spreading–vanishing dichotomy holds, and the sharp criteria for the spreading and vanishing by choosing DD, μμ, u0u0 and v0v0 as variable factors are also obtained. In particular, our results still reveal that slow dispersal rate unconditionally favors the frontiers to spread, but the fast one, however, leads to a conditional vanishing of the frontiers. Moreover, as applications, we consider a man–environment–man epidemic model in physiology and a reaction–diffusion model with a quiescent stage in population dynamics.