TITLE:
Formulation of Mathematical Model for TB Transmission in Zoonotic Areas with Existence of Endemic Equilibrium
AUTHORS:
Thomas Mwenyeheri, Nyimvua Shaban, Doroth Hove-Msekwa, Symon Bilesi Chibaya, Esther Ngadaya, Sayoki Mfinanga
KEYWORDS:
TB, Mathematical Modeling, Animal, Human, Diseases Free-Equilibrium, Endemic Equilibrium
JOURNAL NAME:
Journal of Tuberculosis Research,
Vol.2 No.3,
September
10,
2014
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.