Well Posedness and Control in a NonLocal SIR Model

TL;DR

This paper establishes the mathematical well-posedness and stability of a non-local SIR model with vaccination strategies, enabling the analysis and optimization of vaccination timing and dosing for disease control.

Contribution

It provides foundational well-posedness and stability results for an SIR model with discontinuous vaccination strategies, facilitating optimal control analysis.

Findings

Proves existence and uniqueness of solutions for the model.

Ensures stability under vaccination strategies.

Supports the derivation of optimal vaccination policies.

Abstract

SIR models, also with age structure, can be used to describe the evolution of an infective disease. A vaccination campaign influences this dynamics immunizing part of the susceptible individuals, essentially turning them into recovered individuals. We assume that vaccinations are dosed at prescribed times or ages which introduce discontinuities in the evolutions of the S and R populations. It is then natural to seek the 'best' vaccination strategies in terms of costs and/or effectiveness. This paper provides the basic well posedness and stability results on the SIR model with vaccination campaigns, thus ensuring the existence of optimal dosing strategies.