Observer-based output feedback for an age-structured SIRD model

TL;DR

This paper develops an observer-based output feedback control strategy for an age-structured SIRD epidemic model, aiming to reduce infection peaks through vaccination while ensuring system stability and respecting physical constraints.

Contribution

It introduces a novel observer-based control approach for an age-structured SIRD model, including stability analysis, constrained control design, and numerical validation.

Findings

The system's well-posedness and stability are established.

A constrained control law satisfying physical limits is designed.

Numerical simulations demonstrate the effectiveness of the control strategy.

Abstract

An age-structured Susceptible-Infected-Recovered-Deceased (SIRD) epidemic model is considered. The aim of this paper is to design an observer-based output feedback control law, representing an immunization process, typically vaccination, intended to decrease the peak of infected individuals in the population. At first, well-posedness and stability of the system in open-loop are investigated. Then, to obtain the observer-based output feedback law, a state feedback law is designed by using a normal form. Conditions to ensure stability are established. However, due to physical constraints, this law needs to be adapted. Therefore, a constrained state-feedback law is implemented. This law is designed to fulfill the physical constraints while having good properties (Lipschitz for instance), needed for the last part of the article. Finally, an observer-based output feedback law is obtained using high-gain observer. At each step of the design, convergence properties are obtained. Finally, numerical simulations are performed.