Speaker
Description
Mathematical models with time delays are useful for describing the effects of temporary immunity and delayed epidemiological processes. In this work, we consider a delayed epidemic reaction-diffusion model that incorporates two classes of individuals with different levels of disease awareness. We introduce a time delay to account for the temporary immunity period of recovered individuals, and we include diffusion terms to describe the population's spatial movement.
We first investigate the dynamical properties of the model and establish conditions for the stability of the disease-free equilibrium. We then analyze the influence of the time delay on the system's stability. Furthermore, by incorporating diffusion, we investigate the possibility of diffusion-driven instability and the emergence of spatial patterns. In particular, sufficient conditions for Turing instability are derived, showing how the interaction between epidemic dynamics, awareness heterogeneity, time delay, and spatial diffusion can lead to pattern formation. Numerical simulations are provided to illustrate the theoretical results and demonstrate the development of spatial epidemic patterns under appropriate parameter conditions.