Chance-constrained stochastic optimal control of epidemic models: A fourth moment method-based reformulation

Area of Science:

• Mathematical epidemiology
• Stochastic optimal control
• Reliability engineering

Background:

• Managing uncertainty in epidemic models is crucial for effective control strategies.
• Traditional chance-constrained methods can yield unreliable results, especially at high precision.
• Existing reformulations may not adequately handle the complexities of stochastic epidemic dynamics.

Purpose of the Study:

• To propose a novel methodology for reformulating chance-constrained stochastic optimal control problems.
• To ensure reliable uncertainty management for epidemic outbreaks.
• To enhance the precision and robustness of epidemic control strategies.

Main Methods:

• Reformulation of chance constraints using the fourth moment method.
• Application of spectral techniques for surrogate modeling of stochastic variables.
• Efficient computation of required statistics for reliability analysis.
• Optimal control of stochastic mathematical models for COVID-19 transmission.

Main Results:

• The proposed fourth moment method provides reliable uncertainty management for epidemic outbreaks.
• Spectral surrogate models enable efficient computation of stochastic state variable statistics.
• The method avoids undesired outcomes observed with Chebyshev-Cantelli inequality-based reformulations.
• Numerical experiments demonstrate improved performance in COVID-19 transmission control models.

Conclusions:

• The fourth moment method offers a superior approach to chance constraints in stochastic optimal control for epidemics.
• The methodology ensures reliable uncertainty quantification and management.
• This work provides a robust framework for optimizing epidemic control strategies under uncertainty.