Formulation of Mathematical Model for TB Transmission in Zoonotic Areas with Existence of Endemic Equilibrium

Thomas Mwenyeheri, Nyimvua Shaban, Doroth Hove-Msekwa, Symon Bilesi Chibaya, Esther Ngadaya, Sayoki Mfinanga

Basics Sciences Department, Malawi University of Science and Technology, Thyolo, Malawi.
Department of Applied Mathematics, National University of Science and Technology, Bulawayo, Zimbabwe.
Department of Mathematics, University of Dar es salaam, Dar es salaam, Tanzania.
National Institute for Medical Research, Muhimbili Medical Research Centre, Dar es salaam, Tanzania.

DOI: 10.4236/jtr.2014.23017                

Abstract

A mathematical model incorporating animal TB and Human TB transmission is formulated and analysed in order to determine the role of animal TB and human TB in the overall TB transmission and also, to determine the parameters which govern the transmission of the TB disease. The model has five classes namely susceptible, exposed animal TB, and exposed human TB, infectious and recovery. The model assumed that there are two classes for infected individuals, those who acquired TB through animal and those who acquire TB from human. Qualitative results show that the model has the disease-free equilibrium and at least one endemic equilibrium that is locally asymptotically stable. The study includes numerical simulations as a way of supporting the analytical results. Graphical results indicate that animal TB has major contribution on overall TB transmission and the TB transmission can be reduced by ensuring intervention to both Animal TB and Human TB. Furthermore the equations indicate that there is at least one endemic equilibrium which translates that t animal and human have the contribution on TB transmission. This shows that both animals and humans together with fast progressors have contribution on TB transmissions.

Keywords

TB, Mathematical Modeling, Animal, Human, Diseases Free-Equilibrium, Endemic Equilibrium

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Adetunde, I.A. (2007) The Mathematical Models of the Dynamical Behavior of Tuberculosis Disease in the Upper East Region of the Northern Part of Ghana. A Case Study of Bawku. Research Journal of Applied Sciences, 2, 943-946.
[2]	CDC (2005) Tuberculosis Cases and Percentages by Pulmonary and Extra pulmonary Diseases. US Department of Health and Human Services, Atlanta.
[3]	World Health Organisation (1994) Zoonotic Tuberculosis (M. bovis): A Memoranda from WHO Meeting (with Participation of FAO). Bulletin of the WHO, 72, 851-857.
[4]	Caffery, J.P. (1994) Studies of Bovine Tuberculosis Eradication Programmes in Europe. Veterinary Microbiology, 40, 1-4. http://dx.doi.org/10.1016/0378-1135(94)90041-8
[5]	Shitaye, J.E., Tsegaye, W. and Pavlik, I. (2007) Bovine Tuberculosis Infection in Animal and Human Populations in Ethiopia: A Review. Veterinarni Medicina, 52, 317-332.
[6]	WHO (1999) Global TB Program. TB Advocacy, a Practical Guide [Pamphlet]. WHO, Geneva.
[7]	Beals, F.T. (2007) The Risk of Bovine Tuberculosis from Raw Milk Consumption with a Focus on Michigan in Wise Traditions in Food, Farming and the Healing Arts, the Quarterly Magazine of the Weston A. Price Foundation.
[8]	Anaelom, N.J., Ikechukwu, O.J., Sunday, E.W. and Nnaemeka, U.C. (2010) Zoonotic Tuberculosis: A Review of Epidemiology, Clinical Presentation, Prevention and Control. Journal of Public Health and Epidemiology, 2, 118-124.
[9]	Mfinanga, S.G., Mørkve, O., Kazwala, R.R., Cleaveland, S., Sharp, J.M., Shirima, G. and Nilsen, R. (2003) The Role of Livestock Keeping in Tuberculosis Trends in Arusha, Tanzania. International Journal of Tuberculosis and Lung Disease, 7, 695-704.
[10]	Apariocio, J.P., Capurro, A.F. and Castillo-Chaveze, C. (2000) Transmission and Dynamics of Tuberculosis on Generalized Households. Journal of Theoretical Biology, 206, 327-341. http://dx.doi.org/10.1006/jtbi.2000.2129