Spreading Speed in an Asymptotic Autonomous System with Application to a Diffusive Stage-Structured SLIRM Model

This article studies the spreading properties in an asymptotic autonomous non-cooperative system that can be regarded as an epidemic model or a predator–prey system. In particular, due to the effect of nonlocal delay, it is possible that the system does not satisfy the comparison principle for mixed quasimonotone systems. When the initial value has proper decaying behavior, we obtain a constant spreading speed of solutions. Finally, the main result is applied to a stage-structured susceptible-latent-infected-recovered-matured epidemic model to show its spreading feature by presenting the spreading speed about the susceptible and the infected.