Modeling the spatiotemporal transmission of Ebola disease and optimal control: a regional approach

• Published in: International journal of dynamics and control 2019-09, Vol.7 (3), p.1110-1124
• Main Authors: Laaroussi, Adil El Alami, Ghazzali, Rachid, Rachik, Mostafa, Benrhila, Soukaina
• Format: Article
• Language: English
• Subjects: Complexity; Computer simulation; Control; Control and Systems Theory; Disease control; Dynamical Systems; Ebola virus; Engineering; Epidemics; Optimal control; Outbreaks; Primates; Vibration; Viral diseases
• ISSN: 2195-268X; 2195-2698
• DOI: 10.1007/s40435-019-00525-w

Ebola is a severe disease causing death to humans and nonhuman primates. It emerged in West Africa in December 2013. According to the World Health Organization, it is one of the most infectious and deadly infectious agents in the world. Ebola outbreak seems to be a particular risk in conflict-affected contexts: we apply an optimal regional control to stop the mortality of infected people in a specific region in order to protect it from neighboring areas. We aim to define and characterize an optimal control which minimizes both, the number of infected people and the cost of treatment. The existence of the positive solution for the system is proved. We also prove the existence of an optimal control which minimizes the cost function, and we give a characterization of this control in terms of state function and adjoint function. To illustrate the effectiveness of our theoretical results, we give numerical simulations for several scenarios. The obtained results present a good framework for interventions to protect a specific region against transmission of the epidemic by neighboring regions in case of conflict.