Vaccination rules for a true-mass action SEIR epidemic model based on an observer synthesis. Preliminary results

TL;DR

This paper introduces a control strategy for a SEIR epidemic model that uses an observer to estimate unknown states and parameters, aiming to optimize vaccination efforts and disease eradication.

Contribution

It proposes a linear vaccination control method combined with an observer to handle unknown states and parameters in a SEIR model.

Findings

The control strategy achieves asymptotic convergence of immune population to total population.

The remaining populations (susceptible, infected, infectious) converge to zero.

The approach effectively estimates unknown model parameters and states.

Abstract

This paper presents a simple continuous-time linear vaccination-based control strategy for a SEIR (susceptible plus infected plus infectious plus removed populations) propagation disease model. The model takes into account the total population amounts as a refrain for the illness transmission since its increase makes more difficult contacts among susceptible and infected. The control objective is the asymptotically tracking of the removed-byimmunity population to the total population while achieving simultaneously the remaining population (i.e. susceptible plus infected plus infectious) to asymptotically converge to zero. A state observer is used to estimate the true various partial populations of susceptible, infected, infectious and immune which are assumed to be unknown. The model parameters are also assumed to be, in general, unknown. In this case, the parameters are replaced by available estimates to implement the vaccination action.