Control with uncertain data of socially structured compartmental epidemic models.

Area of Science:

• Epidemiology
• Mathematical Modeling
• Public Health

Background:

• Epidemic containment requires understanding disease spread dynamics.
• Classical models need enhancement to include social structures and data uncertainty.
• COVID-19 highlighted the importance of age-dependent transmission and incomplete data.

Purpose of the Study:

• To develop an optimal control framework for socially structured epidemic models with uncertain data.
• To derive feedback-controlled compartmental models for epidemic peak reduction.
• To evaluate the effectiveness of interventions based on social structure versus global strategies.

Main Methods:

• Formulation of an optimal control problem for a socially structured epidemic model.
• Development of an instantaneous approximation for control strategies.
• Derivation of feedback-controlled compartmental models.
• Incorporation of data uncertainty into the modeling process.

Main Results:

• The derived models effectively describe epidemic peak reduction.
• Social structure-based interventions can be as effective as global strategies for long-term control.
• Timing and intensity of interventions are critical, especially with uncertain data.

Conclusions:

• Optimal control provides a robust framework for managing epidemics with social structure and uncertainty.
• Targeted, socially-informed interventions offer efficient alternatives to broad, costly measures.
• Accurate data and strategic intervention timing are crucial for epidemic control.