Optimal and sub-optimal quarantine and isolation control in SARS epidemics

Area of Science:

• Epidemiology
• Mathematical Biology
• Control Theory

Background:

• The COVID-19 pandemic, caused by SARS-CoV-2, highlighted the urgent need for effective epidemic control strategies.
• Mathematical modeling plays a crucial role in understanding disease dynamics and evaluating interventions.

Purpose of the Study:

• To apply optimal and sub-optimal control theories to a Susceptible-Exposed-Quarantined-Infectious-Isolated-Recovered (SEQIJR) SARS model.
• To investigate the impact of quarantine and isolation strategies on epidemic control.
• To compare the effectiveness of optimal and sub-optimal control approaches.

Main Methods:

• Utilized Pontryagin's Maximum Principle for optimal control.
• Incorporated quarantine and isolation as control variables in the SEQIJR model.
• Implemented numerical optimal control laws using an iterative method.
• Computed sub-optimal solutions with a genetic algorithm.

Main Results:

• Maximal application of quarantine and isolation in the early epidemic stage significantly impacts control outcomes.
• Both optimal and sub-optimal controls demonstrate the critical importance of early interventions.
• Sub-optimal control strategies achieve near-optimal performance with simpler implementation for long-term use.

Conclusions:

• Early and maximal implementation of quarantine and isolation strategies is theoretically and practically vital for controlling SARS outbreaks.
• Sub-optimal control offers a viable, simpler alternative to optimal control for real-world epidemic management.
• Mathematical modeling provides theoretical support for public health interventions.