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Analysis and event-triggered control for a stochastic epidemic model with logistic growth
Tingting Cai1,2, Yuqian Wang3, Liang Wang4
1College of Eco-Environmental Engineering, Yunnan Forestry Technological College, Kunming 650224, China.
Mathematical Biosciences and Engineering : MBE
|March 11, 2023
Summary
This study introduces a stochastic epidemic model to control disease spread. Event-triggered controllers effectively reduce endemic diseases to extinction by managing transmission coefficients.
Area of Science:
- Epidemiology
- Mathematical Biology
- Control Theory
Background:
- Deterministic epidemic models provide a foundation for understanding disease dynamics.
- Stochastic models incorporate randomness, offering a more realistic approach to disease transmission.
- Logistic growth is a key factor in population dynamics and disease spread.
Purpose of the Study:
- To analyze a stochastic epidemic model with logistic growth.
- To establish conditions for disease-free equilibrium stability.
- To design event-triggered controllers for disease eradication.
Main Methods:
- Stochastic differential equation theory
- Stochastic control methods
- Analysis of model solutions near epidemic equilibrium
- Numerical simulations
Main Results:
- The disease becomes endemic when the transmission coefficient surpasses a specific threshold.
- Sufficient conditions for the stability of the disease-free equilibrium were determined.
- Two event-triggered controllers were successfully designed to eliminate endemic diseases.
- Numerical examples validated the controller's effectiveness.
Conclusions:
- The stochastic model provides insights into disease dynamics and control.
- Event-triggered control strategies are effective in eradicating endemic diseases.
- Controlling transmission coefficients is crucial for disease management.
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