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Setting Limits on Supersymmetry Using Simplified Models
Published on: November 15, 2013
Global stability of an SIQR switched model with multiple two-threshold structures
Haifeng Wang1, Yanni Xiao2, Xingfu Zou3
1School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China.
Journal of Mathematical Biology
|July 18, 2026
Summary
Adaptive public health policies, considering hysteresis and heterogeneous controls, were modeled using an SIQR framework. Greater heterogeneity in disease control leads to higher infection peaks but faster convergence to a steady state.
Area of Science:
- Epidemiology
- Mathematical Biology
- Public Health
Background:
- Traditional epidemic models assume uniform, instantaneous responses to outbreaks, which is unrealistic.
- Adaptive public health policies are crucial for effective infectious disease prevention and control.
- Hysteresis effects and heterogeneous control measures significantly impact disease dynamics.
Purpose of the Study:
- To develop an SIQR epidemic model incorporating hysteresis and heterogeneous control measures.
- To analyze the impact of adaptive, prevalence-dependent control strategies on disease dynamics.
- To investigate the global stability of the model's steady-state set.
Main Methods:
- Formulation of an SIQR epidemic model with multiple two-threshold structures.
- Incorporation of the Preisach operator to model time-varying control strategies influenced by disease history.
- Application of Lyapunov functions to establish global stability of the steady-state set.
Main Results:
- Heterogeneity in control measures aids convergence to a steady state.
- Increased heterogeneity results in higher infection peaks and prolonged severe disease prevalence.
- Hysteresis in control events can lead to a continuum of endemic equilibria, altering suppression effectiveness.
Conclusions:
- Hysteresis phenomena in public health interventions significantly influence epidemic outcomes.
- Adaptive control policies should account for the historical effects of past interventions for optimized disease suppression.
- Heterogeneity in control strategies presents a trade-off between convergence speed and epidemic severity.
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