Turing instability on multiplex simplicial epidemic networks with cross-diffusion and behavioral delay.

Publication date: Dec 16, 2025

Modern epidemics are characterized by the emergence of spatial hotspots and periodic outbreaks. This paper reveals that such complex spatiotemporal patterns are driven by a combination of many-body transmission pathways and delayed behavioral responses. We propose a reaction-diffusion epidemic model defined on a multiplex simplicial complex and introduce the behavioral response delay. Through linear stability analysis, we derive the conditions for Turing instability and delay-induced Hopf bifurcation. The analysis reveals that higher-order topological structures and cross-diffusion expand the instability domain and promote the formation of spatial patterns. The higher-order aggregation of susceptible individuals is a key factor in triggering Turing instability, while the higher-order structure of the infected layer primarily modulates its extent. Furthermore, the behavioral response delay acts as a bifurcation parameter, inducing temporal oscillations when it exceeds a critical threshold. Numerical simulations corroborate our theoretical findings, reproducing clustered and periodic oscillation phenomena analogous to those observed during the COVID-19 pandemic. Our results provide the policy implication that dispersing higher-order susceptible clusters and reducing response delays can mitigate spatial heterogeneity and recurrent outbreaks. This work deepens the understanding of epidemic dynamics by elucidating how network topology and human behavior jointly shape complex contagion patterns.

Semantics

Original Article