Fractional Optimal Control of Ransom Kidnapping Epidemic

Abstract

Recently, kidnapping-for-ransom has become a primary and lucrative source of funding sustaining the
activities of terror groups. Considering the menace as a social epidemic, this paper presents a fractional
order mathematical model for the kidnap coinfection dynamics with recruitment and abduction occurring simultaneously. After establishing well-posedness for the positivity and boundedness, the model’s two feasible equilibria (kidnap-free and persistent) are globally asymptotically stable if the kidnap propagation parameter Rk is respectively, less or bigger than unity. To minimize the menace with minimum cost of security and implementation, optimal control strategies were formulated. It is found that anti-kidnapping efforts to witchhunt kidnappers (in their hideout) and rescue the abducted are found to be effective in addition to community vigilance.