July 2018, 5(3): 243-264. doi: 10.3934/jdg.2018016

A bare-bones mathematical model of radicalization

Department of Mathematics, Wilfrid Laurier University, Waterloo, ON, Canada

* Corresponding author: msantoprete@wlu.ca

Received  March 2018 Revised  June 2018 Published  July 2018

Radicalization is the process by which people come to adopt increasingly extreme political or religious ideologies. While radical thinking is by no means problematic in itself, it becomes a threat to national security when it leads to violence. We introduce a simple compartmental model (similar to epidemiology models) to describe the radicalization process. We then extend the model to allow for multiple ideologies. Our approach is similar to the one used in the study of multi-strain diseases. Based on our models, we assess several strategies to counter violent extremism.

Citation: C. Connell McCluskey, Manuele Santoprete. A bare-bones mathematical model of radicalization. Journal of Dynamics & Games, 2018, 5 (3) : 243-264. doi: 10.3934/jdg.2018016
References:
[1]

E. T. Camacho, The development and interaction of terrorist and fanatic groups, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 3086-3097. doi: 10.1016/j.cnsns.2013.04.006.

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C. Castillo-Chavez and B. Song, Models for the transmission dynamics of fanatic behaviors, Bioterrorism-mathematical Modeling Applications in Homeland Security. Philadelphia: SIAM, 28 (2003), 155-172.

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S. Galam and M. A. Javarone, Modeling radicalization phenomena in heterogeneous populations, PloS one, 11 (2016), e0155407. doi: 10.1371/journal.pone.0155407.

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W. M. Haddad, V. Chellaboina and Q. Hui, Nonnegative and Compartmental Dynamical Systems, Princeton University Press, Princeton, New Jersey, 2010. doi: 10.1515/9781400832248.

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J. Horgan, Walking Away from Terrorism: Accounts of Disengagement from Radical and Extremist Movements, Routledge, 2009.

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R. A. JeffsJ. HaywardP. A. Roach and J. Wyburn, Activist model of political party growth, Physica A: Statistical Mechanics and its Applications, 442 (2016), 359-372. doi: 10.1016/j.physa.2015.09.002.

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M. Martcheva, Introduction to Mathematical Epidemiology, vol. 61, Springer, 2015. doi: 10.1007/978-1-4899-7612-3.

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C. McCluskey, Lyapunov functions for tuberculosis models with fast and slow progression, Mathematical Biosciences and Engineering, 3 (2006), 603-614. doi: 10.3934/mbe.2006.3.603.

[10]

B. Obama, President Obama: Our fight against violent extremism, Los Angeles Times, 17 February 2015. Retrieved from http://www.latimes.com/nation/la-oe-obama-terrorism-conference-20150218-story.html [Last accessed: 8 December 2015].

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J. M. Post, Countering islamist militancy: An epidemiologic approach, in Tangled Roots: Social and Psychological Factors in the Genesis of Terrorism (ed. J. Victoroff), IOS Press, Amsterdam, 2006, chapter 23,399–409.

[12]

Public Safety, Building resilience against terrorism: Canada's counter-terrorism strategy, 2013, Retrieved from http://www.publicsafety.gc.ca/cnt/rsrcs/pblctns/rslnc-gnst-trrrsm/index-eng.aspx [Last Accessed: 12 February 2016].

[13]

U. S. Department of Homeland Security, Countering violent extremism, October 14, 2015. Retrieved from http://www.dhs.gov/topic/countering-violent-extremism [Last Accessed: 12 February 2016].

[14]

P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6.

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M. Yacoubian and P. Stares, Rethinking the war on terror, United States Institute of Peace Briefing, 2.

show all references

References:
[1]

E. T. Camacho, The development and interaction of terrorist and fanatic groups, Communications in Nonlinear Science and Numerical Simulation, 18 (2013), 3086-3097. doi: 10.1016/j.cnsns.2013.04.006.

[2]

C. Castillo-Chavez and B. Song, Models for the transmission dynamics of fanatic behaviors, Bioterrorism-mathematical Modeling Applications in Homeland Security. Philadelphia: SIAM, 28 (2003), 155-172.

[3]

S. Galam and M. A. Javarone, Modeling radicalization phenomena in heterogeneous populations, PloS one, 11 (2016), e0155407. doi: 10.1371/journal.pone.0155407.

[4]

W. M. Haddad, V. Chellaboina and Q. Hui, Nonnegative and Compartmental Dynamical Systems, Princeton University Press, Princeton, New Jersey, 2010. doi: 10.1515/9781400832248.

[5]

Home Office, Prevent strategy, June 2011. https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/97976/prevent-strategy-review.pdf [Last Accessed: 12 February 2016].

[6]

J. Horgan, Walking Away from Terrorism: Accounts of Disengagement from Radical and Extremist Movements, Routledge, 2009.

[7]

R. A. JeffsJ. HaywardP. A. Roach and J. Wyburn, Activist model of political party growth, Physica A: Statistical Mechanics and its Applications, 442 (2016), 359-372. doi: 10.1016/j.physa.2015.09.002.

[8]

M. Martcheva, Introduction to Mathematical Epidemiology, vol. 61, Springer, 2015. doi: 10.1007/978-1-4899-7612-3.

[9]

C. McCluskey, Lyapunov functions for tuberculosis models with fast and slow progression, Mathematical Biosciences and Engineering, 3 (2006), 603-614. doi: 10.3934/mbe.2006.3.603.

[10]

B. Obama, President Obama: Our fight against violent extremism, Los Angeles Times, 17 February 2015. Retrieved from http://www.latimes.com/nation/la-oe-obama-terrorism-conference-20150218-story.html [Last accessed: 8 December 2015].

[11]

J. M. Post, Countering islamist militancy: An epidemiologic approach, in Tangled Roots: Social and Psychological Factors in the Genesis of Terrorism (ed. J. Victoroff), IOS Press, Amsterdam, 2006, chapter 23,399–409.

[12]

Public Safety, Building resilience against terrorism: Canada's counter-terrorism strategy, 2013, Retrieved from http://www.publicsafety.gc.ca/cnt/rsrcs/pblctns/rslnc-gnst-trrrsm/index-eng.aspx [Last Accessed: 12 February 2016].

[13]

U. S. Department of Homeland Security, Countering violent extremism, October 14, 2015. Retrieved from http://www.dhs.gov/topic/countering-violent-extremism [Last Accessed: 12 February 2016].

[14]

P. Van den Driessche and J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Mathematical biosciences, 180 (2002), 29-48. doi: 10.1016/S0025-5564(02)00108-6.

[15]

M. Yacoubian and P. Stares, Rethinking the war on terror, United States Institute of Peace Briefing, 2.

Figure 1.  Transfer diagram for the bare-bones model. It shows the progression of radicalization from the Susceptible (S) class to the extremist (E), and recruiter (R) classes
Figure 2.  Transfer diagram for the model with two competing ideologies
Figure 3.  Transfer diagram for the model with two ideologies and cross-interaction
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