Analisis Kestabilan dan Kontrol Optimal pada Model Matematika Radikalisasi

Abstract

Radicalization is a process of adopting extremist views that lead to violent acts. Efforts that can be made to eradicate extreme violence are prevention, disengagement and deradicalization. This study aims to determine the mathematical model of radicalization using the susceptible, extremists, recruiters, treatment and Aware model (SERTA),   and to obtain stability analysis results and optimal control of the model. This is a fundamental or theoretical study. According to the model analysis, there are two equilibrium points namely the free and endemic equilibrium points. The stability analysis of the system resulted in a basic reproduction number of 0,012297 for the equilibrium point free and 1,339847 for endemic. The use of Pontryagin’s maximum principle will produce optimal control value is obtained, namely:

(u_1 ) ̇=min{1,maks(0,1/c_1  (λ_1-λ_5 )S)},

(u_2 ) ̇=min{1,maks(0,1/c_2  [(〖2λ〗_2-λ_4-λ_5 )E+(λ_3-λ_4 )R])},

(u_3 ) ̇=min{1,maks(0,1/c_3  (λ_2-λ_5 )δT)}.

Numerical simulations show that providing u_1, u_2 and u_3 controls can minimize the number of extremist and recruiter populations and minimize the aware population.