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Sliding mode control of outbreaks of emerging infectious diseases

Yanni Xiao1, Xiaxia Xu, Sanyi Tang

  • 1Department of Applied Mathematics, Xi'an Jiaotong University, PR China.

Bulletin of Mathematical Biology
|July 28, 2012
PubMed

Insights

This study introduces a mathematical model for infectious disease management using a threshold policy. The findings show that strategic control interventions can prevent outbreaks or maintain disease levels effectively.

Area of Science:

  • Mathematical Biology
  • Epidemiology
  • Control Theory

Background:

  • Classic epidemic models often lack dynamic control strategies.
  • Implementing control measures based on infection thresholds is crucial for disease management.

Purpose of the Study:

  • To propose and analyze a mathematical model for infectious disease systems incorporating a piecewise control function based on a threshold policy.
  • To investigate the long-term dynamics and stability of the proposed non-smooth system.

Main Methods:

  • Development of a piecewise mathematical model for infectious disease dynamics.
  • Analysis of the system's long-term behavior, including sliding motion on the switching surface.
  • Investigation of endemic states and sliding equilibrium.

Main Results:

  • The model exhibits sliding motion, representing rapid switching between control and no control.
  • Model solutions converge to endemic states or a sliding equilibrium depending on the threshold level.
  • The study demonstrates that threshold-based policies can effectively manage disease spread.

Conclusions:

  • A threshold policy with appropriate control intensity and density can prevent disease outbreaks.
  • This strategy allows for maintaining the number of infected individuals at a predetermined level.
  • The findings offer valuable insights for designing effective public health interventions.

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