Assessment of effective isolation, safe burial and vaccination optimal controls for an Ebola epidemic model

Since 1976 many outbreaks of Ebola virus disease have occurred in Africa, and up to now, no treatment is available. Thus, to fight against this illness, several control strategies have been adopted. Among these measures, isolation, safe burial and vaccination occupy a prominent place. In this paper therefore, we present a model which takes into account these three control strategies as well as the difference in immunological responses of infected by distinguishing individuals with moderate and severe symptoms. The sensitivity analysis of the control reproduction number suggests that, the vaccination response works better than the two other control measures at the beginning of the disease, and there is no need to vaccinate people in order to overcome Ebola. The global asymptotic dynamic of the model with controls is completely achieved exhibiting a sharp threshold behavior. Consequently, the global stability of the endemic equilibrium when the control reproduction number is greater than one, calls for the implementation of the three responses optimally. Thus, we define, analyze and implement different optimal control problems which minimize the cost of controls and the number of infected individuals through vaccination, isolation and safe burial. The obtained results highlight that, in order to mitigate Ebola outbreaks, an optimal vaccination strategy has more impact than the combination of isolation and safe burial responses. Therefore, the broad recommendation is that: if for any disease outbreak, the vaccine can be available quickly, one should think of implementing large vaccination programs rather than any other control measures.