Epidemic management with admissible and robust invariant sets

Area of Science:

• Epidemiology
• Mathematical Biology
• Control Theory

Background:

• The Susceptible-Infectious-Recovered (SIR) and Susceptible-Exposed-Infectious-Recovered (SEIR) models are fundamental in understanding epidemic dynamics.
• Managing epidemics requires effective intervention strategies to control the spread of infectious diseases.
• Uncertainty in model parameters and the basic reproduction number can complicate epidemic control.

Purpose of the Study:

• To analyze SIR and SEIR epidemic models using set-based methods.
• To define admissible and maximal robust positively invariant (MRPI) sets for these models.
• To demonstrate the application of MRPI sets in epidemic management under various conditions and interventions.

Main Methods:

• Set-based analysis applied to SIR and SEIR models.
• Utilizing barrier theory to define MRPI sets.
• Developing intervention strategies (social distancing, quarantining, vaccination) to respect defined set boundaries.

Main Results:

• Characterization of MRPI sets for SIR and SEIR models.
• Demonstration that MRPI sets can guarantee adherence to hard caps on infective individuals.
• Intervention strategies are designed to prevent breaching infection caps, irrespective of the basic reproduction number.

Conclusions:

• MRPI sets provide a robust framework for epidemic control.
• The methodology is effective for both perfect and uncertain epidemic models.
• This approach offers a rigorous way to specify interventions for maintaining desired epidemic states.