Optimal control for virus spreading for an SIR model

TL;DR

This paper develops an improved optimal control framework for an SIR epidemic model with variable population, addressing previous functional limitations and analyzing solution dependencies on parameters.

Contribution

The paper introduces a corrected functional for optimal control in an SIR model, ensuring existence of solutions and analyzing parameter effects.

Findings

Existence of optimal control is established.

The corrected functional addresses previous limitations.

Solution dependence on model parameters is analyzed.

Abstract

In this paper, an SIR epidemic model with variable size of population is considered. We study optimal control problem for an SIR model with "vaccination" and "treatment" as controls. It is shown that an optimal control exists. We have already used functional, that lots of researchers use, and found that this functional is not appropriate, it has a defect. Now, we fixed this defect by changing this functional. We analyze the dependence of solutions on parameter of problems and discuss our result.