A Model of Tuberculosis and DiabetesCo-Infection with Optimal Control

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dc.contributor.authorMusyokia, Eunice Mueni
dc.contributor.authorMutuku, Winfred Nduku
dc.contributor.authorImbusi, Nancy Matendechere
dc.contributor.authorOmondi, Evans Otieno
dc.date.accessioned2025-10-14T13:30:39Z
dc.date.available2025-10-14T13:30:39Z
dc.date.issued2023-12-30
dc.description.abstractAims/ objectives:Tuberculosis and diabetes co-infection is a complex health issue, thus, effectivemanagement requires understanding disease dynamics and interactions. This paper expands the existingmodel to incorporate the co-infection of diabetes and tuberculosis to understand disease complications better.Methodology:The study employs the next-generation matrix to calculateRCand utilizes LaSalle’sinvariance principle. It demonstrates that the model achieves global asymptotic stability at the disease-free equilibrium (DFE) whenRC≤1. The Volterra-Lyapunov matrix is then employed to establish globalasymptotic stability of the endemic equilibrium whenRC>1. Based on the Jacobian matrix, local stabilityanalysis suggests the potential for epidemic eradication whenRC≤1, whileRC≥1indicates a risk ofepidemic spread. Numerical solutions using ODE45 in Matlab R2021b are employed for the analysis. Results:The sensitivity analysis highlighted the significant impact of TB transmission coefficientβanddiabetes acquisition rateα1onRC, emphasizing the need for optimal control measures targeting thesefactors.Conclusion:A decrease in TB transmission coefficient led to a reduction inRCfrom1.0863to0.1845,suggesting the potential effectiveness of control strategies. The study also recommends exploring modelsconsidering different diabetes types in future research.
dc.identifier.urihttps://ir-library.ku.ac.ke/handle/123456789/31731
dc.language.isoen
dc.titleA Model of Tuberculosis and DiabetesCo-Infection with Optimal Control
dc.title.alternative30/12/2023
dc.typeArticle
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