Spreading speeds of a delayed noncooperative system in a shifting environment

Abstract

This article investigates the spreading properties of a noncooperative nonlocal delayed reaction–diffusion system in a shifting environment. It is possible that the system does not satisfy the classical comparison principle for mixed quasimonotone systems. By constructing proper auxiliary equations and utilizing the comparison principle, different spreading speeds are estimated, which depend on the forced speed and the spreading speeds in various limiting equations. These findings are applied to a stage-structured epidemic model, which reveals distinct spreading properties of the susceptible and the infected under different conditions. In particular, the spatial dynamics of the susceptible population, expanding faster than the infected population, generate propagation terraces.