Optimal control for a SIR epidemic model with limited quarantine

Area of Science:

• Epidemiology
• Mathematical Modeling
• Public Health Policy

Background:

• Non-pharmaceutical interventions like social distancing and lockdowns are crucial for mitigating infectious disease spread, such as COVID-19.
• These measures incur significant social and economic costs, limiting their long-term feasibility.
• Quarantine durations are often restricted, necessitating optimized intervention strategies.

Purpose of the Study:

• To determine optimal control strategies for minimizing epidemic impact.
• To investigate epidemic control using a Susceptible-Infected-Recovered (SIR) model with quarantine duration limits.
• To minimize cumulative infections and socioeconomic costs by optimizing the reproduction number over time.

Main Methods:

• Optimal control theory applied to an SIR model.
• Mathematical analysis of a time-limited quarantine strategy.
• Numerical computations to validate theoretical findings.

Main Results:

• The optimal strategy involves a single 'bang-bang' control: strict quarantine is implemented once for the maximum allowed duration.
• The optimal timing for initiating and concluding strict quarantine is determined by model parameters and initial conditions.
• Results demonstrate a clear, mathematically derived approach to pandemic intervention.

Conclusions:

• A single, extended quarantine period is more effective than intermittent or shorter measures.
• This strategy balances the need to control infections with minimizing long-term socioeconomic burdens.
• The findings offer valuable insights for public health policy during epidemics.