Complex dynamics and pattern formation in a diffusive epidemic model with an infection-dependent recovery rate

Abstract: A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifur cation analysis of the reaction kinetics. It is shown that the model exhibits diffusion-driven instability, where the infected population acts as an activator and the susceptible population functions as an in hibitor. The faster movement of the susceptible class will induce the spatial and spatiotemporal patterns, which are characterized by k-mode Turing instability and (k1,k2)-mode Turing-Hopf bifurcation. The transient dynamics from a purely temporal oscillatory regime to a spatial periodic pattern are discov ered. The model reveals key transmission dynamics, including asynchronous disease recurrence, spa tially patterned waves, and the formation of localized hotspots. The study suggests that spatially targeted strategies are necessary to contain disease waves that vary regionally and cyclically.