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Mathematical Modelling of Terrorism Dynamics and the Impact of Jail and Rehabilitation Interventions

Imrana Jega Aliyu, a, Abubakar S. F., a, Mohd. M. Dago, b

Abstract

Terrorism remains a critical global security challenge, causing significant loss of life, economic disruption, and social instability. While previous mathematical models have explored terrorism propagation, few have explicitly incorporated correctional and rehabilitation compartments as explicit control mechanisms. This study develops a deterministic compartmental model extending existing frameworks by integrating jailed and rehabilitated populations. The model stratifies the population into six compartments: Susceptible (S), Exposed (M), Terrorist Leaders (TL), Terrorist Soldiers (TS), Jailed (J), and Rehabilitated (R). We derive the basic reproduction number R0 using the next-generation matrix approach and establish the existence, uniqueness, positivity, and boundedness of solutions. Analytical results demonstrate that the terrorism-free equilibrium is locally and globally asymptotically stable when R0 < 1. Numerical simulations validate the analytical findings and highlight the critical role of rehabilitation programs and reduced contact rates in curbing terrorism propagation. The model provides actionable insights for policymakers on the efficacy of combined judicial, military, and rehabilitative interventions.

Keywords

Terrorism dynamicscompartmental modelbasic reproduction numberstability analysisrehabilitation interventionsmathematical epidemiology

References

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