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

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Modern epidemics exhibit spatial hotspots and periodic outbreaks.
• These complex spatiotemporal patterns are driven by transmission dynamics and human behavioral responses.

Purpose of the Study:

• To investigate the influence of many-body transmission and delayed behavioral responses on epidemic spatiotemporal patterns.
• To analyze epidemic dynamics on a multiplex simplicial complex incorporating behavioral response delays.

Main Methods:

• Developed a reaction-diffusion epidemic model on a multiplex simplicial complex.
• Employed linear stability analysis to identify conditions for Turing instability and delay-induced Hopf bifurcation.
• Utilized numerical simulations to validate theoretical findings.

Main Results:

• Higher-order topological structures and cross-diffusion expand instability domains, promoting spatial pattern formation.
• Higher-order aggregation of susceptible individuals triggers Turing instability; infected layer structure modulates its extent.
• Behavioral response delay acts as a bifurcation parameter, inducing temporal oscillations beyond a critical threshold.

Conclusions:

• Dispersing higher-order susceptible clusters and reducing response delays can mitigate epidemic spatial heterogeneity and recurrent outbreaks.
• Network topology and human behavior jointly shape complex contagion patterns, deepening the understanding of epidemic dynamics.