An epidemiological approach to insurgent population modeling with the Atangana–Baleanu fractional derivative

Abstract

Abstract Insurgency is a large loophole to any nation’s finances because of the monumental costs associated with fighting it. In this study, an epidemiological approach to modeling the dynamics of the spread of insurgents is introduced. Stability analysis of the steady states of the system were performed and the insurgency prevalence number R 0 , which is analogous to the reproduction number in epidemiological studies was obtained using the next generation matrix method. A fractional version of the model was introduced using the Atangana–Baleanu derivative and numerical simulations were performed for better understanding of the dynamics of the system. For effective counter-insurgency measures, the local and global sensitivity analysis of the insurgency prevalence number R 0 and the endemic states with respect to the parameters that define them were performed. Sensitivity analysis shows that counter-insurgency efforts must focus on increasing the recovery rate of insurgents and reducing the rate of radicalization of civilians. The developed model is a suitable tool with great potential for drawing inference in driving counter-insurgency policy making processes.