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Two competing simplicial irreversible epidemics on simplicial complex.

Wenjie Li1, Yanyi Nie1, Wenyao Li2

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Higher-order interactions significantly impact competing epidemic dynamics. Increased infection rates can lead to sharp growth or delayed outbreaks, with epidemic dominance depending on infection rate differences.

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Area of Science:

  • Epidemiology
  • Network Science
  • Mathematical Modeling

Background:

  • Higher-order interactions are crucial for understanding complex epidemic dynamics.
  • Existing models often simplify network structures, neglecting nuanced interaction patterns.

Purpose of the Study:

  • To propose and analyze a novel competing epidemic spread model on higher-order networks.
  • To investigate the impact of varying infection rates on epidemic dynamics and coexistence.

Main Methods:

  • Development of a competing susceptible-infected-removed (SIR) epidemic model on simplicial complexes.
  • Theoretical analysis using an extended microscopic Markov chain approach.
  • Simulation on synthetic (homogeneous, heterogeneous) and real-world networks.

Main Results:

  • An increase in the 1-simplex infection rate can cause a transition from continuous to sharp epidemic growth.
  • Higher 1-simplex infection rates delay outbreak thresholds and influence epidemic coexistence.
  • Significant differences in 1-simplex infection rates lead to dominance by one epidemic, while symmetrical rates accelerate spread.

Conclusions:

  • Higher-order network structures and infection rates critically shape competing epidemic behaviors.
  • The model provides insights into factors governing epidemic spread, coexistence, and dominance.
  • Understanding these dynamics is vital for effective public health interventions in complex social networks.