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<p>This paper investigates the dynamics of terrorism and counter-terrorism by formulating a novel delay differential equation model. The model incorporates the recruitment lag before individuals join terrorist groups. Terrorism persists as a global challenge, and capturing the effects of recruitment delays is essential for realistic modelling and effective counter-terrorism planning. The model captures the interaction between susceptible individuals, active terrorists, and the deserted and rehabilitated population. It reflects the realistic time-delayed influence of recruitment. Two equilibrium states are identified: a terror-free state and a terror-persistent state. Rigorous mathematical analysis, based on the basic reproduction number <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({\mathscr {R}}_0\)</EquationSource> </InlineEquation> and the Routh–Hurwitz criterion, reveals the stability conditions that govern these equilibria. We show that terrorism dies out when <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\({\mathscr {R}}_0 &lt; 1\)</EquationSource> </InlineEquation>. In contrast, <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\({\mathscr {R}}_0 &gt; 1\)</EquationSource> </InlineEquation> leads to its persistence. Furthermore, the introduction of delay plays a critical role in destabilising the terror-persistent equilibrium. It gives rise to oscillatory behaviour through a Hopf bifurcation. This indicates that recruitment delays can act as a double-edged sword. While initially slowing terrorist growth, they may also trigger long-term cycles of terrorist resurgence. Numerical simulations confirm the analytical results and highlight the interplay between recruitment delays, counter-terrorism efforts, and the persistence of terrorism. The study provides valuable insights into how delays influence the effectiveness of counter-terrorism strategies. It offers guidance for policymakers and security analysts.</p>

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Exploring the Dynamics of a Mathematical Model of Terrorism with Time-Delay

  • 期刊论文

  • 发表日期：

    2025年11月15日

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  • Annesha Sarmah,
  • Anusmita Das,
  • Kaushik Dehingia,
  • Animesh Phukan,
  • Hemanta Kr. Sarmah,
  • Evren Hincal

摘要

This paper investigates the dynamics of terrorism and counter-terrorism by formulating a novel delay differential equation model. The model incorporates the recruitment lag before individuals join terrorist groups. Terrorism persists as a global challenge, and capturing the effects of recruitment delays is essential for realistic modelling and effective counter-terrorism planning. The model captures the interaction between susceptible individuals, active terrorists, and the deserted and rehabilitated population. It reflects the realistic time-delayed influence of recruitment. Two equilibrium states are identified: a terror-free state and a terror-persistent state. Rigorous mathematical analysis, based on the basic reproduction number \({\mathscr {R}}_0\) and the Routh–Hurwitz criterion, reveals the stability conditions that govern these equilibria. We show that terrorism dies out when \({\mathscr {R}}_0 < 1\) . In contrast, \({\mathscr {R}}_0 > 1\) leads to its persistence. Furthermore, the introduction of delay plays a critical role in destabilising the terror-persistent equilibrium. It gives rise to oscillatory behaviour through a Hopf bifurcation. This indicates that recruitment delays can act as a double-edged sword. While initially slowing terrorist growth, they may also trigger long-term cycles of terrorist resurgence. Numerical simulations confirm the analytical results and highlight the interplay between recruitment delays, counter-terrorism efforts, and the persistence of terrorism. The study provides valuable insights into how delays influence the effectiveness of counter-terrorism strategies. It offers guidance for policymakers and security analysts.