Browsing by Author "Mwinyeheri, Thomas"

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    Modelling tuberculosis transmission in Zoonotic areas
    (University of Dar Es Salaam, 2013) Mwinyeheri, Thomas
    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 which is locally asymptotically stable for the basic reproductive number (R0 ) , 0 R 1 and at least one endemic equilibrium that is locally asymptotically stable provided that 0 R  1. The centre manifold theory is also used to analyse the local stability of endemic equilibrium and the system shows a backward bifurcation for the given parameters when the basic reproduction number is unity. 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. The overall contributions are presented by overall 0 (R ) which was broken to three basic reproductive numbers for fast progression 0 (RFAST ) , animal 0 (RANIMAL ) and human 0 (RHUMAN ) . This shows that both animal and humans together with fast progressors have contribution on TB transmissions.