Analysis and Modeling of Tuberculosis Transmission Dynamics

dc.contributor.authorWanaina, Mary
dc.contributor.authorJerubet, Rodah
dc.contributor.authorKimathi, George
dc.date.accessioned2024-05-13T08:45:30Z
dc.date.available2024-05-13T08:45:30Z
dc.date.issued2019-06
dc.descriptionJournal Article
dc.description.abstractMycobacterium tuberculosis is the causative agent of Tuberculosis in humans [1,2]. A mathematical model that explains the transmission of Tuberculosis is developed. The model consists of four compartments; the susceptible humans, the infectious humans, the latently infected humans, and the recovered humans. We conducted an analysis of the disease-free equilibrium and endemic equilibrium points. We also computed the basic reproduction number using the next generation matrix approach. The disease-free equilibrium was found to be asymptotically stable if the reproduction number was less than one. The most sensitive parameter to the basic reproduction number was also determined using sensitivity analysis. Recruitment and contact rate are the most sensitive parameter that contributes to the basic reproduction number. Ordinary Differential Equations is used in the formulation of the model equations. The Tuberculosis model is analyzed in order to give a proper account of the impact of its transmission dynamics and the effect of the latent stage in TB transmission. The steady state's solution of the model is investigated. The findings showed that as more people come into contact with infectious individuals, the spread of TB would increase. The latent rate of infection below a critical value makes TB infection to persist. However, the recovery rate of infectious individuals is an indication that the spread of the disease will reduce with time which could help curb TB transmission.
dc.identifier.citationJerubet R., Kimathi G., and Wanaina M. (2019): Analysis and Modeling of Tuberculosis Transmission Dynamics. Journal of Advances in Mathematics and Computer Science
dc.identifier.issn2456-9968
dc.identifier.urihttps://repository.daystar.ac.ke/handle/123456789/4608
dc.language.isoen
dc.publisherJournal of Advances in Mathematics and Computer Science
dc.relation.ispartofseries32(5)
dc.subjectLatent TB
dc.subjecttransmission dynamics
dc.subjectbasic reproduction number
dc.subjectstability analysis and equilibrium points
dc.titleAnalysis and Modeling of Tuberculosis Transmission Dynamics
dc.typeArticle

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