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Countering Violent Extremism: A mathematical model

The term radicalization refers to the process of developing extremist religious political or social beliefs and ideologies. Radicalization becomes a threat to national security when it leads to violence. Prevention and de-radicalization initiatives are part of a set of strategies used to combat violent extremism, which taken together are known as Countering Violent Extremism (CVE). Prevention programs aim to stop the radicalization process before it starts. De-radicalization programs attempt to reform convicted extremists with the ultimate goal of social reintegration. We describe prevention and de-radicalization programs mathematically using a compartmental model. The prevention initiatives are modeled by including a vaccination compartment, while the de-radicalization process is modeled by including a treatment compartment. The model exhibits a threshold dynamics characterized by the basic reproduction number $ R _0 $. When $ R _0< 1 $ the system has a unique equilibrium that is asymptotically stable. When $ R _0 >1 $ the system has another equilibrium called &#34;endemic equilibrium&#34;, which is globally asymptotically stable. These results are established by using Lyapunov functions and LaSalle&#39;s invariance principle. We perform numerical simulations to confirm our theoretical results.