Susceptible-infected-recovered-susceptible processes competing on simplicial complexes

Area of Science:

• Epidemiology
• Complex Systems Science
• Mathematical Modeling

Background:

• Contagions interact with other propagating quantities, not in isolation.
• Higher-order interactions are prevalent in real-world systems.
• Susceptible-Infected-Recovered-Susceptible (SIRS) models are crucial for understanding disease dynamics.

Purpose of the Study:

• To propose a novel stochastic model for competing SIRS processes in simplicial complexes.
• To develop and analyze deterministic microscopic Markov chain (MMC) and mean-field (MF) versions of the model.
• To investigate conditions for infection persistence and explore emergent phenomena.

Main Methods:

• Development of a stochastic model for competing SIRS processes on simplicial complexes.
• Formulation of deterministic MMC and MF models derived from the stochastic framework.
• Analysis of model dynamics, including steady states and oscillations.
• Numerical simulations to verify analytical predictions and uncover emergent behaviors.

Main Results:

• The stochastic model exhibits eight distinct classes of dependence on initial conditions.
• MMC models reproduce all eight classes, while MF models capture seven.
• A unique class with three steady states is observed in MMC and stochastic models but missed by MF.
• MF models show an additional class with infinite steady states in the absence of higher-order interactions.
• Both MMC and MF models demonstrate sustained oscillations, with one contagion disappearing and the other reaching a limit cycle.
• Critical mass effects, discontinuous phase transitions, and bistability were observed.

Conclusions:

• The proposed models accurately capture complex contagion dynamics, including higher-order interactions.
• Discrepancies between stochastic, MMC, and MF models highlight the importance of interaction complexity.
• The models provide insights into critical mass, phase transitions, and multistability in competing contagions.
• The study advances the understanding of epidemic modeling in complex network structures.