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A compartmental model for epidemiology with human behavior and stochastic effects
Christian Parkinson1, Weinan Wang2
1Department of Mathematics & Department of Computational Mathematics, Science & Engineering, Michigan State University, East Lansing, MI, USA.
Mathematical Biosciences
|December 4, 2025
Summary
This study introduces an epidemiological model where noncompliance with health protocols spreads like a social contagion. Our findings analyze disease spread dynamics and stability under uncertainty.
Area of Science:
- Epidemiology
- Mathematical Biology
- Sociology
Background:
- Disease spread is influenced by public adherence to health protocols.
- Noncompliance can propagate through social networks, impacting disease dynamics.
Purpose of the Study:
- To develop a compartmental model incorporating social contagion of noncompliance.
- To analyze disease-free equilibrium stability in deterministic and stochastic frameworks.
- To investigate the impact of transmission rate uncertainty on disease spread.
Main Methods:
- Derivation of the basic reproductive ratio for the deterministic model.
- Analysis of local stability for disease-free equilibrium points.
- Incorporation of stochastic effects on transmission rates.
- Application of stochastic Lyapunov functions for system analysis.
Main Results:
- Characterization of disease-free equilibrium stability.
- Proof of global existence and nonnegativity for the stochastic model.
- Demonstration of model behavior through numerical simulations.
Conclusions:
- The model provides insights into the interplay between disease spread and social contagion of noncompliance.
- Stochasticity in transmission rates significantly affects epidemiological dynamics.
- The framework is valuable for understanding and managing infectious disease outbreaks influenced by public behavior.
Keywords:
Disease free equilibriumHuman behavioral effectsMathematical epidemiologyStochastic Lyapunov functionsStochastic effectsMore Related Videos
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