Modeling and Multi-objective Optimal Control of Thedynamics of Counterterrorism in the Sahel Region in Africa

Abstract

Terrorist activity in the Sahel region has been on the increase for almost a decade.  Groups advocating extremist ideologies with a political or religious base are carrying out attacks against states with the aim of imposing a totalitarian ideology, sometimes against a backdrop of political crisis and famine. In this state of crisis and sometimes communal conflict, it is questionable whether ideological terrorism can really be eradicated in the Sahel. In this study, we develop a model of the dynamics of ideological terrorism based on the terrorism situation in the Sahel. In particular, this model incorporates popular resistance to terrorism through the class of volunteers for the defense of the homeland, but we also take into account the indoctrination of certain sections of the population vulnerable to fanatical ideology. We estimate $\mathcal{R}_0$ , the number of elementary replications of extremist behavior, which enables us to predict the evolution of extremism. We also identify four thresholds $\mathcal{R}_1$, $\mathcal{R}_2$, $\mathcal{R}_3$ and $\mathcal{R}_4$ of sufficient conditions for the eradication of ideological terrorism and brigandage. A multi-objective optimal control of a counter-terrorism strategy is also presented. Finally, we perform a numerical simulation of the analysis and control results to test our hypotheses.