Mathematical Modeling of Tuberculosis Dynamics With Hygiene Consciousness as a Control Strategy

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dc.contributor.authorZaberio, Mawira Phineas
dc.date.accessioned2021-03-03T11:40:57Z
dc.date.available2021-03-03T11:40:57Z
dc.date.issued2020
dc.descriptionA project submitted in partial fulfilment of the requirements of the award of the degree of Master of Science in Applied Mathematics in the School of Pure and Applied Sciences of Kenyatta University. JUNE 2020en_US
dc.description.abstractTuberculosis, an air-borne infectious disease, remains a major threat to public health in Kenya. In this study we derived a system of non-linear ordinary differential equations from SLICR mathematical model of TB to study the effects of hygiene consciousness as a control strategy against TB in Kenya. The effective basic reproduction number (R0) of the model was determined by the next generation matrix approach. We established and analysed the equilibrium points. Using the Routh-Hurwitz criterion for local stability analysis and comparison theorem for global stability analysis, the disease free equilibrium (DFE) was found to be locally asymptotically stable given that R0 < 1. Also by using the Routh-Hurwitz criterion for local stability analysis and Lyapunov function and LaSalle’s invariance principle for global stability analysis, the endemic equilibrium (EE) point was found to be locally asymptotically stable given that R0 > 1. Using MATLAB ode45 solver, we simulated the model numerically and the results suggest that hygiene consciousness can help in controlling TB disease if incorporated effectivelyen_US
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/21724
dc.language.isoenen_US
dc.publisherKenyatta Universityen_US
dc.subjectMathematical Modelingen_US
dc.subjectTuberculosis Dynamicsen_US
dc.subjectHygiene Consciousnessen_US
dc.titleMathematical Modeling of Tuberculosis Dynamics With Hygiene Consciousness as a Control Strategyen_US
dc.typeThesisen_US
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