Optimal control of a community violence model: community violence treated as a contagious disease

Abstract

Violence was, for a long time, misunderstood and misdiagnosed. This misdiagnosis led to ineffective and counterproductive treatments and control strategies. Recent advances in neuroscience and epidemiology show that violence is a contagious disease. In this paper, community violence is treated as an infection that spreads from person to person through victimization or through witnessing violence. A compartmental model is used for formulating the spread of cummunity violence as a system of differential equations. The distribution of treated individuals is considered as a control variable. Our objective is to characterize an optimal control (treatment) that minimizes the number of individuals who use violence and the cost associated with this treatment. A numerical simulation analysis is used to confirm the effectiveness of our control.