Optimal control for a COVID-19 problem through a SIRD model

Amira Bouhali (1, 2) , Walid Ben Aribi (1) , Slimane Ben Miled (1) , Amira Kebir (1, 3)

1 LR11IPT09 - Laboratoire de Bioinformatique, biomathématiques, biostatistiques (BIMS)
2 ENIT - Ecole Nationale d'Ingénieurs de Tunis
3 IPEIT - Institut Préparatoire aux Etudes d'Ingénieur de Tunis

In this study, we present an epidemic controlled SIRD model of a vaccinated population with two types of control strategies: mask wear and screening. The aim of this study is to minimize the number of the deceased while keeping a minimal cost of mask advertising and screening. The model is proved to be well posed and to have an invariant region. Also, a study of the steady states' stability is effected using the basic reproduction number. As for the optimal control analysis, we study the existence of an optimal solution in two different cases: constant and variable mask wear. The characterization of the optimal control is carried out using Pontryagin's minimum principle in both cases. Numerical simulations are conducted for the constant mask wear case with different values of maximal screening for comparison. The findings of the optimal control analysis and numerical simulations both reveal that combining vaccination with the optimal pair of strategies contributes enormously to lowering the number of infected and dead individuals. Although zero infection is not achieved in the population, this study implies that carrying an optimal approach constitutes a major step in controlling the spread of the disease to the barest minimum.

Mots clés: Optimal control; Structured models; COVID 19; Basic reproduction number

Domaines: Mathématiques [math]

Amira Bouhali, Walid Ben Aribi, Slimane Ben Miled, Amira Kebir. Optimal control for a COVID-19 problem through a SIRD model. 2022. ⟨hal-03702574⟩