title: Optimal Control of a Delayed SIRS Epidemic Model with Vaccination and Treatment.
abstract: This article deals with optimal control applied to vaccination and treatment strategies for an SIRS epidemic model with logistic growth and delay. The delay is incorporated into the model in order to modeled the latent period or incubation period. The existence for the optimal control pair is also proved. Pontryagin's maximum principle with delay is used to characterize these optimal controls. The optimality system is derived and then solved numerically using an algorithm based on the forward and backward difference approximation.
authors.affiliation: Department of Mathematics and Computer Science, Faculty of Sciences Ben M'sik, Hassan II University, P.O Box 7955, Sidi Othman, Casablanca, Morocco, abtaabdelhadi@yahoo.fr.
authors.forename: Hassan
authors.initials: H
authors.lastname: Laarabi
authors.forename: Abdelhadi
authors.initials: A
authors.lastname: Abta
authors.forename: Khalid
authors.initials: K
authors.lastname: Hattaf
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D058872:Epidemics / Q000517:prevention & control*; D006801:Humans; D017053:Infection Control / Q000592:standards*; D008962:Models, Theoretical; D009018:Morocco / Q000453:epidemiology; D018746:Systemic Inflammatory Response Syndrome / Q000453:epidemiology / Q000628:therapy* / Q000635:transmission; D014611:Vaccination