Tuberculosis Transmission Model with Chemoprophylaxis and Treatment |
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Authors: | C P Bhunu W Garira Z Mukandavire M Zimba |
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Institution: | (1) Modelling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology, P.O. Box 939 Ascot, Bulawayo, Zimbabwe;(2) Department of Environmental and Health Sciences, National University of Science and Technology, Bulawayo, Zimbabwe |
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Abstract: | A tuberculosis model which incorporates treatment of infectives and chemoprophylaxis is presented. The model assumes that
latently infected individuals develop active disease as a result of endogenous re-activation, exogenous re-infection and disease
relapse, though a small fraction is assumed to develop active disease soon after infection. We start by formulating and analyzing
a TB model without any intervention strategy that we extend to incorporate chemoprophylaxis and treatment of infectives. The
epidemic thresholds known as reproduction numbers and equilibria for the models are determined, and stabilities analyzed.
The reproduction numbers for the models are compared to assess the possible community benefits achieved by treatment of infectives,
chemoprophylaxis and a holistic approach of these intervention strategies. The study shows that treatment of infectives is
more effective in the first years of implementation (≈ 10 years) as treatment results in clearing active TB immediately and
there after chemoprophylaxis will do better in controlling the number of infectives due to reduced progression to active TB. |
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Keywords: | Tuberculosis model Chemoprophylaxis Treatment Relapse Exogenous Re-infection |
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