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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.