Browsing by Author "Omondi, Evans Otieno"
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Item A Model of Tuberculosis and DiabetesCo-Infection with Optimal Control(2023-12-30) Musyokia, Eunice Mueni; Mutuku, Winfred Nduku; Imbusi, Nancy Matendechere; Omondi, Evans OtienoAims/ 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.