The Menace of Ghost Workers, Job Racketeers, and Creators of Online Job Offer Scam Sites on Unemployment in Nigeria: A Mathematical Model Analysis and Control

Abstract

This article involves a mathematical model portraying the repercussions of criminal activities perpetrated by job racketeers, ghost workers, and creators of phishing online scam sites, adversely impacting unsuspecting job seekers and exacerbating the challenges faced by the youthful job-seeking populace. The model captures the dynamics among unemployed individuals, job racketeers, law enforcement agents, ghost workers, and the employed and non-human components within the job vacancy and cyber landscapes of the host population. Non-linear first-order ordinary differential equations are employed to characterize these dynamic interactions. The qualitative properties of the model are analyzed using Lipschitz continuity, positivity, and invariant region analysis. The model is established to be both locally and globally asymptotically stable, contingent upon the absence or presence of equilibrium solutions associated with crimes linked to unemployment. Moreover, optimal control theory is integrated into the model to ascertain the optimal level of efforts necessary for mitigating these crimes. Government control policies are introduced, focusing on media education to enlighten the unemployed populace on recognizing, identifying, and reporting job racketeers ${k}_{1}(t)$. Additionally, computer education is emphasized for detecting, identifying, and reporting phishing online scam sites ${k}_{2}(t)$, along with measures for uncovering, eliminating, and disclosing the identities of ghost workers ${k}_{3}(t)$, as well as flagging and removing online scam sites ${k}_{4}(t)$. The Pontryagin maximum principle (PMP) is employed to characterize the control model, while the forward–backward sweep method is utilized to obtain the approximate solution to the optimality system. The simulations show the reliability of the model with controls, demonstrating their efficacy in reducing crimes associated with unemployment. The variables and parameters linked to unemployment related crime prevalence in Nigeria are integral to these simulations. Notably, varying the control profiles indicates a substantial reduction in these societal problems within a year. This comprehensive analysis provides valuable insights for policymakers and stakeholders in formulating strategies to combat and mitigate the multifaceted challenges arising from criminal activities in the realm of unemployment.