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Global stability in a mathematical model of de-radicalization

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  • Santoprete, Manuele
  • Xu, Fei

Abstract

Radicalization is the process by which people come to adopt increasingly extreme political, social or religious ideologies. When radicalization leads to violence, radical thinking becomes a threat to national security. De-radicalization programs are part of an effort to combat violent extremism and terrorism. This type of initiatives attempt to alter violent extremists radical beliefs and violent behavior with the aim to reintegrate them into society. In this paper we introduce a simple compartmental model suitable to describe de-radicalization programs. The population is divided into four compartments: (S) susceptible, (E) extremists, (R) recruiters, and (T) treatment. We calculate the basic reproduction number R0. For R0<1 the system has one globally asymptotically stable equilibrium where no extremist or recruiters are present. For R0>1 the system has an additional equilibrium where extremists and recruiters are endemic to the population. A Lyapunov function is used to show that, for R0>1, the endemic equilibrium is globally asymptotically stable. We use numerical simulations to support our analytical results. Based on our model we assess strategies to counter violent extremism.

Suggested Citation

  • Santoprete, Manuele & Xu, Fei, 2018. "Global stability in a mathematical model of de-radicalization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 151-161.
    • Handle: RePEc:eee:phsmap:v:509:y:2018:i:c:p:151-161
    DOI: 10.1016/j.physa.2018.06.027
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    References listed on IDEAS

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    1. Jeffs, Rebecca A. & Hayward, John & Roach, Paul A. & Wyburn, John, 2016. "Activist model of political party growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 442(C), pages 359-372.
    2. Nizamani, Sarwat & Memon, Nasrullah & Galam, Serge, 2014. "From public outrage to the burst of public violence: An epidemic-like model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 620-630.
    3. Serge Galam & Marco Alberto Javarone, 2016. "Modeling Radicalization Phenomena in Heterogeneous Populations," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-15, May.
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    Cited by:

    1. Santoprete, Manuele, 2019. "Countering violent extremism: A mathematical model," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 314-329.
    2. Sooknanan, Joanna & Seemungal, Terence A.R., 2023. "Criminals and their models - a review of epidemiological models describing criminal behaviour," Applied Mathematics and Computation, Elsevier, vol. 458(C).
    3. Wang, Chaoqian, 2020. "Dynamics of conflicting opinions considering rationality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).

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