Optimal control and mathematical models in epidemiology - Paião, Ana Pedro Lemos (2019)
In this PhD thesis, we prove sufficient optimality conditions for delayed optimal control problems, by transforming them into equivalent non-delayed problems. Such transformation is done by considering a technique proposed by Guinn in 1976 and later promoted by Maurer and his collaborators. In this way, we are able to use well-known sufficient optimality conditions for non-delayed optimal control problems and to return to the delayed ones. We propose and study several models that can translate the spread of cholera and that consider different types of treatment or prevention measures. Corresponding optimal control problems are formulated and studied. Such theoretical analysis are then applied to real cholera outbreaks that occured in Haiti and Yemen.