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Model of strategy control for delayed panic spread in emergencies
Rongjian Lv1, Hua Li2, Qiubai Sun2
1School of Electronics and Information Engineering, University of Science and Technology Liaoning, Anshan, Liaoning, China.
Mathematical Biosciences and Engineering : MBE
|February 2, 2024
Summary
This study introduces a SEIR delayed panic spread model to understand panic transmission during emergencies. A government control strategy, using state delayed feedback, was developed and simulated to effectively manage and eradicate panic within groups.
Area of Science:
- Mathematical Epidemiology
- Social Dynamics Modeling
- Nonlinear Control Systems
Background:
- Panic spreads rapidly in group settings during emergencies, similar to epidemic outbreaks.
- Understanding panic transmission mechanisms and decision-making is crucial for societal stability.
- Existing models often do not account for time delays or time-varying infection rates.
Purpose of the Study:
- To develop a mathematical model for panic spread incorporating time delays and time-varying infection rates.
- To propose and analyze a government control strategy to mitigate and eradicate panic.
- To ensure the stability and effectiveness of the proposed control strategy.
Main Methods:
- Adapted the SEIR (Susceptible-Exposed-Infectious-Recovered) epidemiological model to include panic dynamics.
- Introduced a time-varying infection rate and a delay effect between susceptible and exposed states.
- Applied exact linearization and state delayed feedback control to determine the control law and prove system stability.
Main Results:
- A novel SEIR delayed panic spread model was established, with its basic regeneration number calculated.
- A stable control law was derived to manage panic spread using state delayed feedback.
- Simulations demonstrated the effectiveness of the proposed strategy in eradicating panic and achieving asymptotic recovery.
Conclusions:
- The developed SEIR delayed panic spread model provides a robust framework for analyzing panic dynamics.
- The proposed government control strategy is theoretically sound and practically applicable for panic mitigation.
- The study successfully illustrates a method to control and eliminate panic in group settings, ensuring societal well-being.
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