A Mathematical Model of HIV and Tb Co-Infection with Interventions, a Case of Siaya County in Kenya

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dc.contributor.advisorWinfred Mutukuen_US
dc.contributor.authorVincent, Otieno Brian
dc.date.accessioned2023-08-10T12:34:41Z
dc.date.available2023-08-10T12:34:41Z
dc.date.issued2023
dc.descriptionA Project Presented to the School of Pure and Applied Sciences at Kenyatta University in Partial Completion of the Requirements for the Award of the Degree of Masters of Science in Applied Mathematics, November 2022en_US
dc.description.abstractIn this research, we take into consideration a model of co-infection between HIV/AIDS and TB with treatment of infectious and inactive forms of TB and HIV preventive and therapeutic strategies. Speci cally we consider condom use, early ART and withdrawal from sexual activities by individuals who are infected by HIV as controls. The model is positively bounded. The spectral radius of the next generation matrix has been used to determine the model's fundamental reproduction number. The model displays these equilibria: a disease free and a co-infection equilibrium. By utilizing Routh-Hurwitz standard and center manifold theory, the model has been qualitatively examined. When R0 < 1,we discovered that the disease free equilibrium point was locally asymptotically stable and not globally asymptotically stable. Sensitivity analysis of R0T and R0H identi es $1 and $2, TB and HIV infection rates through e ective contact respectively, as the main variables that if targeted, R0T and R0T are reduced. From numerical simulation,we show that increasing HIV interventions reduces cases of latent TB progressing to active TB and therefore is an additional strategy in the ght against TB disease.en_US
dc.description.sponsorshipKenyatta Universityen_US
dc.identifier.urihttp://ir-library.ku.ac.ke/handle/123456789/26755
dc.language.isoenen_US
dc.publisherKenyatta Universityen_US
dc.subjectA Mathematical Modelen_US
dc.subjectHIV and Tb Co-Infectionen_US
dc.subjectInterventionsen_US
dc.subjecta Case of Siaya Countyen_US
dc.subjectKenyaen_US
dc.titleA Mathematical Model of HIV and Tb Co-Infection with Interventions, a Case of Siaya County in Kenyaen_US
dc.typeThesisen_US
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