An optimal control model to design strategies for reducing the spread of the Ebola virus disease

In this work, we formulate an epidemiological model for studying the spread of Ebola virus disease in a considered territory. This model includes the effect of various control measures, such as: vaccination, education campaigns, early detection campaigns, increase of sanitary measures in hospital, quarantine of infected individuals and restriction of movement between geographical areas. Using optimal control theory, we determine an optimal control strategy which aims to reduce the number of infected individuals, according to some operative restrictions (e.g., economical, logistic, etc.). Furthermore, we study the existence and uniqueness of the optimal control. Finally, we illustrate the interest of the obtained results by considering numerical experiments based on real data.