Simplicial epidemic model with birth and death.

Area of Science:

• Epidemiology
• Network Science
• Mathematical Biology

Background:

• Epidemic modeling is crucial for understanding disease dynamics.
• Group interactions and vital dynamics (birth/death) are key factors in disease spread.
• Existing models often simplify network structures or omit demographic effects.

Purpose of the Study:

• To propose a novel simplicial susceptible-infected-susceptible (SIS) epidemic model incorporating group interactions and vital dynamics.
• To analyze the influence of system parameters, particularly birth and death rates, on epidemic dynamics.
• To investigate the emergence of bistable states and their impact on disease persistence.

Main Methods:

• Formulation of site-based evolutions using quenched mean-field probability equations.
• Dimensionality reduction via the mean-field method for theoretical analysis.
• Extensive simulations on empirical and synthetic networks to validate model predictions.

Main Results:

• Birth and death rates affect the existence and stability of disease-free and endemic equilibria.
• The model exhibits bistability, including coexistence of stable disease-free and endemic states.
• A novel bistable state emerges: coexistence of a stable periodic outbreak and a disease-free state.
• Birth and death rates modify infected node density and outbreak thresholds.

Conclusions:

• Vital dynamics play a critical role in shaping epidemic patterns on networks.
• The proposed model provides a more comprehensive framework for studying epidemic spreading with demographic effects.
• Understanding bistability is essential for predicting and controlling disease outbreaks.