Modelling the Optimal Control of Transmission Dynamics of Mycobacterium ulceran Infection

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dc.contributor.authorKimaro, Magreth A.
dc.contributor.authorMassawe, Estomih S.
dc.contributor.authorMakinde, Oluwole D.
dc.date.accessioned2016-06-26T17:12:22Z
dc.date.available2016-06-26T17:12:22Z
dc.date.issued2015
dc.description.abstractThis paper examines optimal control of transmission dynamics of Mycobacterium ulceran (MU) infection. A nonlinear mathematical model for the problem is proposed and analysed qualitatively using the stability theory of the differential equations, optimal control and computer simulation. The basic reproduction number of the reduced model system is obtained by using the next generation operator method. It is found that by using Ruth Hurwitz criteria, the disease free equilibrium point is locally asymptotically stable and using centre manifold theory, the model shows the transcritical (forward) bifurcation. Optimal control is applied to the model seeking to minimize the transmission dynamics of MU infection on human and water-bugs. Pontryagin’s maximum principle is used to characterize the optimal levels of the controls. The results of optimality are solved numerically using MATLAB software and the results show that optimal combination of two controls (environmental and health education for prevention) and (water and environmental purification) minimizes the MU infection in the population.en_US
dc.identifier.citationKimaro, M.A., Massawe, E.S. and Makinde, D.O., 2015. Modelling the Optimal Control of Transmission Dynamics of Mycobacterium ulceran Infection. Open Journal of Epidemiology, 5(04), p.229.en_US
dc.identifier.doi10.4236/ojepi.2015.54027
dc.identifier.urihttp://hdl.handle.net/20.500.11810/2705
dc.language.isoenen_US
dc.publisherScientific Researchen_US
dc.subjectMUen_US
dc.subjectOptimal Controlen_US
dc.subjectStabilityen_US
dc.subjectPontryagin’s Maximum Principleen_US
dc.subjectReproduction Numberen_US
dc.titleModelling the Optimal Control of Transmission Dynamics of Mycobacterium ulceran Infectionen_US
dc.typeJournal Article, Peer Revieweden_US
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