Optimal control of an SIR epidemic through finite-time non-pharmaceutical intervention

Area of Science:

• Epidemiology
• Mathematical Biology
• Control Theory

Background:

• Controlling infectious disease spread is crucial.
• Mathematical models like the SIR model are essential for understanding epidemics.
• Intervention strategies, such as contact reduction, are vital for public health.

Purpose of the Study:

• To determine optimal strategies for controlling SIR-model epidemics.
• To minimize the total number of infected individuals in the long-time limit.
• To analyze the impact of control costs and healthcare resource limitations on epidemic management.

Main Methods:

• Utilizing the SIR (Susceptible-Infectious-Recovered) epidemic model.
• Applying optimal control theory to a finite-time interval intervention.
• Solving the Hamilton-Jacobi-Bellman equation numerically for cost-inclusive scenarios.

Main Results:

• Analytical solutions were derived for the no-cost control scenario.
• Numerical solutions demonstrated optimal control strategies under various cost functions.
• The study identified trade-offs between intervention intensity, duration, and epidemic outcomes.

Conclusions:

• Temporary reduction of infectious contact rates is an effective epidemic control strategy.
• Incorporating costs of intervention and healthcare strain refines optimal control solutions.
• The findings offer valuable insights for managing real-world pandemics through targeted interventions.