Modeling and control of measles epidemic spread with immunodepressed individuals and possible complications

In this paper the problem of the measles epidemic spread is faced considering two aspects: the presence of immunosuppressed subjects that can not be vaccinated and the possibility, for the infected patients, of getting also a complication, not dangerous by itself, but potentially fatal for infected weakened people. These two novelties are taken into account in designing and scheduling suitable control actions such as vaccination, whenever possible, prevention, quarantine and treatment, when limited resources are available. The natural framework for this study is the optimal control theory. By using the Pontryagin principle, it is shown the prevailing role of the vaccination in guaranteeing the protection to immunosuppressed individuals, as well as the importance of a prompt response of the society, such as with the adoption of a quarantine, when an epidemic spread occurs.