Modeling the optimal control of transmission dynamics of mycobacterium ulcer an infection

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Date
2015
Journal Title
Journal ISSN
Volume Title
Publisher
Unversity of Dar es Salaam
Abstract
A mathematical model is proposed and analysed to study optimal control of transmission dynamics of Mycobacterium Ulceran (MU) infection. In modelling dynamics of the system, the study considered two populations; Human population and vector population (water-bugs). The model is divided into five classes namely, susceptible human, infected human, susceptible water-bugs, infected water-bugs and water contamination. The model is analysed qualitatively to determine the equilibrium points. The basic reproduction number and the sensitivity indices of the basic reproduction number ‘ ’ to the parameters in the model are calculated. The stability of the equilibrium points is also analysed. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable when the reproduction number is less than unity and unstable when reproduction number is greater than unity. Centre manifold theory is used to analyse the local stability of endemic equilibrium and the system shows a transcritical (forward) bifurcation when the basic reproduction number crosses the unity. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. This is done by introducing two controls. Pontryagin’s maximum principle is used to characterize the optimal levels of the two controls. The results of optimality are solved numerically using MATLAB software. The results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) will minimize the MU infection in the population.
Description
Available in print form, East Africana Collection, Dr. Wilbert Chagula Library, Class mark (THS EAF RC116.M8K55)
Keywords
Mycobacterial diseases, Prevention, Mathematical models, Tanzania
Citation
Kimaro, M. A. (2015) Modeling the optimal control of transmission dynamics of mycobacterium ulcer an infection, Master dissertation, University of Dar es Salaam, Dar es Salaam