International Journal of Research and Innovation in Applied Science (IJRIAS) | Volume IV, Issue II, February 2019|ISSN 2454-6194 www.rsisinternational.org Page 11 Assessing the Effectiveness of “Carrots and Sticks” Approach on Terrorists‟ Strength and Sustainability: A Mathematical Deterministic Model Israel J. Udoh 1 , Michael O. Oladejo 2 & Hycienth O. Orapine 3 1 Applied Mathematics & Simulation Advanced Research Centre (AMSARC), Sheda Science & Technology Complex (SHESTCO), Km 10 Gwagwalada-Lokoja Express Way, PMB 186, Garki, Abuja Nigeria 2,3 Department of Mathematical Science, Nigerian Defence Academy, PMB 2109, Kaduna, Nigeria Abstract: - In an effort to marshal resources toward building coalition against international terrorism, countries and international bodies heavily rely on strategies that such as the “sticks and carrots” approach to change the incentives of both the terrorists and their supporters. This study presents a novel mathematical deterministic model whose variables are parameters of the internal and external dynamics of the organization: analytically and numerically solve to study the dynamical evolution of the terrorists’ strength under the simultaneous interdiction the leaders and foot-soldiers. The result shows that, though the “carrots and sticks” may be cost intensive and challenging, yet it has the propensity to drive the growth rates and the terrorists’ strength to a vulnerable value. Significantly, the study also revealed that the “carrots” approach only has propensity of interdicting more recruiters’ class than otherwise. However, taking a fifty year forecast of the terrorist evolution indicates that, the war on terror may take longer than necessary to accomplish by “carrots and sticks” approach only. Given the veracity of our model, it should be possible to evaluate the efficacy of the various policies of government and hence measure the degree of success or failure of a given counterterrorism measure. Key words: “Carrots and Sticks” approach, Mathematical deterministic model, counterterrorism I. INTRODUCTION nsecurity and terrorism, in particular has been a major driving force behind the deplorable socio-economic and political development and the escalation of institutions of organized crimes in most countries of the world, especially, African countries, in recent times. Methods to finding a long term solution to the hydra-headed problems of terrorism by relevant world governments in the last decades can be psychologically categorized into two major approaches: the “Carrots” and the “Sticks” or tactically, the “Water” and “Fire” strategies. Modern terrorism, though hidden under ethnicity and religious ideology sentiments to garner moral supports, recruit operatives and spread its erroneous propagandas, its cardinal objective is purely political. Hence, methods that are devoid of parochial, ethnic and religious sentiments would yield a more credible and result-oriented counter-terrorism (CT) measures. Research findings over the last decades suggest that most of the approaches employed by relevant world governments to counter terrorism and terrorist activities, falls under the conventional warfare strategies (stick or fire approach), with very minimal consideration to the “Carrots” or “Water” approach, mostly at extreme cases when terrorism boil-down to “kidnapping for ransom” and hostage taking. The “carrots and sticks” approach; a social science metaphor for “reward” and “punishment” or “positive incentives” and “negative incentives” system, date back to Pavlov traditional theory of motivation[25]. According to the proponents of motivation theory of counter-terrorism[2],[45],[55], though very challenging and cost intensive to implement, “carrots” and “sticks” can elicit compliance or cooperative behaviour from adaptable adversary. Similarly, in civil conflict situations, conciliatory and coercive effort of the state can elicit cooperative behaviour from contending parties. A theoretical study observes that, when participation in group activities is optional, punishing uncooperative behaviour is the cheaper method[3],[47].The philosopher John Locke once wrote:“good and evil, reward and punishment, are the only motives to a rational creature”[38]. Although Locke was referring primarily to the discipline of children, reward and punishment are motivational forces for behaviour across many domains of social life. Understanding the consequences of such „carrots and sticks‟ is a core topic in the behavioural sciences, particularly in studies of cooperative behaviour that benefits others or the group at a cost to the cooperating individual [3],11]. Many problems in modern human societies, from interactions in the workplace to tackling civil conflicts, require genetically unrelated individuals to cooperate in situations in which collective welfare is jeopardized by few individuals or individual self-interest. So how do rewards and punishments curb selfishness and help elicit compliance or cooperative behaviour among contending parties in civil conflicts like terrorism? Theoretical and experimental research on the evolution of cooperation has concentrated on punishment, with relatively few studies investigating reward[3],[47],[50],[53]. Furthermore, most studies have focused on „peer punishment‟, I