Analyzing the Dynamics of a Terrorism Model using Mathematical Approaches

This paper presents a mathematical analysis of a deterministic model that explores the interactions between terrorism and counter-terrorism strategies. The model includes a ratio-dependent incidence rate, which enables tracking of changes as the proportion of terrorists relative to susceptibles rises. The dynamics of terrorism are described and investigated using a system of ordinary differential equations. The mathematical analysis of the model reveals two equilibrium states: a terror-free state and a terrorpersistent state, with stability assessed via the basic reproduction number R0. Both local and global stability behaviours of these equilibria are thoroughly examined. The findings reveal that the terror-free equilibrium is both locally and globally asymptotically stable when R0 < 1, indicating the conditions under which terrorism can be eradicated. Conversely, the terror-persistent equilibrium is locally asymptotically stable when R0 > 1, signifying the potential for sustained terrorism under certain conditions. Additionally, the terror-persistent state is globally asymptotically stable under specific scenarios, depending on model parameters. Finally, numerical simulations are conducted to validate the theoretical findings