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

Amine Alabkari, Khalid Adnaoui, Ahmed Kourrad, Abdelkarim Bennar

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.

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Published: 2021-04-14

How to Cite this Article:

Amine Alabkari, Khalid Adnaoui, Ahmed Kourrad, Abdelkarim Bennar, Optimal control of a community violence model: community violence treated as a contagious disease, Commun. Math. Biol. Neurosci., 2021 (2021), Article ID 34

Copyright © 2021 Amine Alabkari, Khalid Adnaoui, Ahmed Kourrad, Abdelkarim Bennar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Commun. Math. Biol. Neurosci.

ISSN 2052-2541

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