Mathematical Model on the Dynamics of Crimes of Murder Incorporating Amnesty and Rehabilitation as Control Strategies
DOI:
https://doi.org/10.62054/ijdm/0104.06Keywords:
Amnesty, Control. Crimes, Murder, Rehabilitation,Abstract
In this paper, a mathematical model for the dynamics of murderous crimes is developed, considering rehabilitation and amnesty as control strategies. The basic features of the model, such as the positivity and boundedness of the model solution, were explored. Three positive equilibrium points were computed: a murder-free equilibrium, an amnesty and rehabilitation-free equilibrium, and a murder-present equilibrium with amnesty and rehabilitation. Using a next-generation matrix approach, a murder threshold quantity, represented by R0, was computed. This quantity measures the average number of non-murderers that a single murderer will persuade to commit murder. A local stability analysis of the murder-free equilibrium point was conducted, revealing that, under certain conditions, the equilibrium point is locally asymptotically stable. Furthermore, a global stability analysis of the murder-free equilibrium point was carried out, and the result showed that the equilibrium point is globally asymptotically stable, provided that ex-convicts who received amnesty do not commit murder again. Moreover, computational results of the model equations demonstrated that the murder conversion rate, police arrest rate, and amnesty grant rate play important roles in a community's ability to control murder cases.
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