Analysis and optimal control for SEIR mathematical modeling of COVID-19

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Résumé

In this paper a mathematical model of SEIR type is formulated. represented by modeling the coronavirus epidemic. In this present study, we consider a mathematical model that incorporates the whole population and variability in transmission between reported and unreported populations. The global stability of the disease free equilibrium (DFE) point is established. The basic reproduction number R0 is calculated. We introduce into our model two controls which are vaccination ofsusceptible humans denoted by u and treatment of infected humans designed by v. In addition, this model takes into consideration the control of contact between infectious individuals and susceptible persons A numerical simulation of the model is made.

Mots-clés

COVID-19 pandemic, SEIR model, epidemic modeling, optimal control, vaccination, treatment of infected individuals, basic reproduction number, global stability, disease-free equilibrium, unreported cases, contact control