Turing instability in multiplex epidemics networks with dual delays

This paper investigates Turing instability in multiplex epidemics networks with population growth delay and information transmission delay. By applying linear stability analysis, we derive the threshold conditions for Turing pattern formation induced by the network topology and determine the stability region of the system by examining the relationship between eigenvalues and critical delay. Furthermore, our results reveal how multiplex network topology and dual delays modulate the onset and morphology of diffusion-driven patterns. Especially, increasing the average degree of the susceptible layer amplifies the periodic outbreaks of the infected population, which enhances disease controllability. Numerical simulations validate the theory, and an empirical analysis further supports the findings by using the COVID-19 spatial distribution. These results provide new insights for infectious disease control, regional medical resource allocation, optimization of information-sharing mechanisms and the development of a spatiotemporal early warning system.