Modeling Domestic Violence and Predicting its Growth using Differential Equations. A Case Study of Women and Children in Tamale

Author(s): Abdul-Rahaman Haadi, Abdul-Karim Abdul-Razak

The paper focused on analytic and numerical modeling of Domestic Violence. In the case of the analytic modeling, this paper discusses a simple continuous model for the spread of Domestic Violence, using Ordinary Differential Equations. A mathematical model is inspired from the spread of Domestic Violence in Tamale Metropolitan in which the interaction of the widespread is likely to be minimized. A modeling technique Abusive, Susceptible and Violence Victims (ASV), similar to the Susceptible, Infectious and Recovered (SIR) model in Epidemics, is used for formulating the spread of Domestic Violence as a system of Differential Equations. Hence the population of three distinct classes- the Abusive, Susceptible/Unreported Victims, and the Reported Victims, are considered in the model. The system of Differential Equations is analyzed by linearization of nonlinear systems and non-dimensionlization, and to predict the behavior of the spread of the Domestic Violence. Finally, in the case of the numerical analysis, a general model for the population of Domestic Violence Victims is constructed. The present model shows that the given data is reasonably Logistic. Moreover, this model shows that the population of Domestic Violence Victims is limited. A projected limiting number is given by this model. Some typical mathematical models are introduced such as Exponential model and logistic model. The solutions of those models are analyzed.

Domestic Violence, Ordinary Differential Equations, linearization, ASV

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