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

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

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Author(s)

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

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391 1087 51-63 Volume 3 - Jul 2014

Abstract

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.

Keywords

Domestic Violence, Ordinary Differential Equations, linearization, ASV

References

  1. Adjetey, F. (1999) ‘Domestic Violence in Ghana: The Facts, The Law and the Way Forward’, paper presented at Reflection seminar on the untold stories of women’s experience on violence in the home, Accra
  2. Avoke, M., Hayford, S., Ihenacho, J. & Ocloo, M. (1999). Issues in Special Education, Accra
  3. Bawah, A. A., Akweongo, P., Simmons, R., and Phillips, J.F. (1999). “Women's Fears and Men's Anxieties: The Impact of Family Planning On Gender Relations in Northern Ghana”. Studies in Family Planning Vol. 30, No. 1, pp. 54-66
  4. Bortei-Doku Aryeetey, E., Kuenyehia A. (1998) ‘Violence against women in Ghana’, in A. Kuenyehia (ed.), Women and Law in West Africa: Situational Analysis of Some Key Issues Affecting Women. Accra: Women and Law in West Africa
  5. Cusack, K. Aniwa, M. Gadzekpo, A. & Prah, M. (1999), Violence against Women and Children in Ghana, Accra, Yemen Publishing Ltd
  6. Dennis G. Zill. (1997). A First Course in Differential Equations with Modeling Application. Brooks/Cole Publishing Company, 11 Forest Lodge Road, Specific Grove, CA 93950, USA. Sixth Edition, pp. 17-25, 72-77
  7. DOVVSU, (2012). Domestic Violence against Women and Children, Tamale
  8. Ellsberg M and Heise L. (2005). Researching Violence against Women: A Practical Guide for Researchers and Activists. Washington DC, United States: World Health Organization. www.who.int/gender/en or www.path.org. Retrieve; 13-10-2011
  9. Ghana Domestic Violence Bill, (2000). Government of Ghana
  10. Ghana Statistical Service (GSS) and Macro International Inc. (MI). 1999. Ghana Demographic and Health Survey 1998. Calverton, Maryland: GSS and MI
  11. Ghana Statistical Service (GSS), (2002 and 2011). 2010 Population and Housing Census: Provisional Results. The GSS, Accra
  12. Ghana Statistical Service (GSS), Noguchi Memorial Institute for Medical Research (NMIMR), and ORC Macro. 2004. Ghana Demographic and Health Survey 2003
  13. Hethcote, Herbert W. (2000). “The Mathematics of Infectious Diseases,” SIAM Review,42(4):599-653. http://www.un.org/ecosocdev/geninfo/afrec/vol15no4/154troko.htm. Retrieve; 08-09-2011
  14. Hui, L. (2007). Population Modeling by Differential Equations. Thesis submitted to the Graduate College of Marshall University
  15. Human Rights Watch. (1992). Untold Terror: Violence against Women in Peru's Armed Conflict. Washington D.C., Human Rights Watch, December, 62 pp
  16. International Federation of Women Lawyers (FIDA). (2003). Violence against Women. FIDA, Accra
  17. Jan M. (2002), Mathematical Modeling of Epidemics, University of Washington, Applied Mathematics Department
  18. Mba, C.J. (2002). “Ghana's Reproductive Revolution: Analysis of the Determinants of Fertility Transition” in African Population Studies journal, vol. 17, No.1, 2002, pp.47-67
  19. Meyer, P. S. (1994): Bi {Logistic Growth. Technological Forecasting and Social Change, 47, 89,102}
  20. Mimmo, I. (2005). The Mathematical Modeling of Epidemics. Mathematics Department, University of Trento
  21. Paul Ormerod; Craig Mounfield; Laurence Smith. (2001). Non-linear modeling of burglary and violent crime in the UK, Volterra Consulting Ltd. UK. pormerod@volterra.co.uk. Retrieve; 23-101-2012
  22. Teri, J. (2009). Mathematical Modeling of Diseases: Susceptible-Infected-Recovered (SIR) Model. University of Minnesota, Morris Spring
  23. Trottier, H. and Pierre, P. (2001). “Deterministic Modeling of Infectious Diseases: Applications to Measles and Other Similar Infections,” The Internet Journal of Infectious Diseases, 1(2):1-18
  24. Trottier, H. and Pierre, P. (2003). “Deterministic Modeling of Infectious Diseases: Applications to Measles and Other Similar Infections,” The Internet Journal of Infectious Diseases, 1(2):1-18
  25. United Nations Population Fund (UNFPA). (1999). Violence against Girls and Women. New York, UNFPA. P.24

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International Journal of Sciences is Open Access Journal.
This article is licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) License.
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