Optimal management of the vaccination process in SIRD epidemic models under constraints

TL;DR

This paper develops a method for optimal vaccination management in SIR epidemic models considering resource constraints, using parametric strategies to overcome challenges of classical control approaches.

Contribution

It introduces a parametric strategy approach to optimize vaccination in constrained SIR models, simplifying the control problem.

Findings

Effective vaccination strategies under resource constraints identified.

Reduction of complex control problems to finite-dimensional optimization.

Potential for improved epidemic management policies.

Abstract

The paper considers the problems of optimal vaccination control in the classical SIR model under constraints on the resource capabilities of the insurance medical system, in particular under constraints on the possible absolute rate of vaccination of the population and the limitation on the available number of vaccines. The application of classical optimal control methods, the dynamic programming method and the Pontryagin maximum principle for such a model encounters difficulties associated with the possible non-smoothness of the Bellman function, and in the Pontryagin method the problem is to solve a boundary value problem with discontinuous control. Therefore, in the paper, optimal control is sought in the class of the so-called parametric strategies, which reduces the original problem to a finite-dimensional optimization problem with respect to unknown parameters.