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Simplicial SIRS epidemic models with nonlinear incidence rates
Dong Wang1, Yi Zhao1, Jianfeng Luo1
1School of Science, Harbin Institute of Technology (Shenzhen), Shenzhen 518055, China.
Chaos (Woodbury, N.Y.)
|July 9, 2021
Summary
This study introduces a new mathematical model for epidemic spreading on social networks, incorporating network structure and nonlinear infection rates. The model captures complex dynamics like bistability and periodic outbreaks, offering new insights into disease transmission.
Area of Science:
- Mathematical epidemiology
- Network science
- Complex systems
Background:
- Epidemic dynamics on social networks are complex.
- Existing models struggle to couple network topology with intricate incidence rates.
Purpose of the Study:
- To propose a simplicial susceptible-infected-recovered-susceptible (SIRS) model.
- To investigate epidemic spreading by combining higher-order network structure with nonlinear incidence.
Main Methods:
- Reshaping network social systems into simplicial complexes.
- Implementing nonlinear reinforcement based on simplex dimensions for infection spread.
Main Results:
- The SIRS model captures discontinuous transitions, bistability, and periodic epidemic outbreaks.
- Derived thresholds for bistable regions and reinforcement factors.
- Analyzed stability of equilibrium points, identifying conditions for bistable states and limit cycles.
Conclusions:
- Expanded simplicial susceptible-infected-susceptible (SIS) models to SIRS models.
- Provides a novel perspective on combining higher-order structures with nonlinear incidence rates for complex systems.
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