Mathematical modelling of social phenomena is a quickly developing area of research. Mathematical and Computational modelling is a tool to exploring terrorism across the world. The theoretical approach to model terrorism is similar to that of modelling in epidemiology (in some sense terrorism can be considered as a disease). This includes implementation of various systems of Differential Equations as well as complex networks to provide more realistic predictions. This text contains a formulation and analysis of deterministic mathematical model that seeks to study the dynamics of terrorism with the aim to understand its operation and the effectiveness of the counterterrorism measures already applied. The special focus of this text is on modelling and predicting the Boko Haram extremist organisation in Nigeria with the aim to propose strategies of terrorism eradication. The developed principles of eradication derived from the case study will be helpful to fight terrorism across theworld.