Asian Research Journal of Mathematics

Aims/ objectives: Tuberculosis and diabetes co-infection is a complex health issue, thus, effective management requires understanding disease dynamics and interactions. This paper expands the existing model to incorporate the co-infection of diabetes and tuberculosis to understand disease complications better.
Methodology: The study employs the next-generation matrix to calculate R_C and utilizes LaSalle’s invariance principle. It demonstrates that the model achieves global asymptotic stability at the disease-free equilibrium ( DF E ) when RC ≤ 1 . The Volterra-Lyapunov matrix is then employed to establish global asymptotic stability of the endemic equilibrium when RC > 1 . Based on the Jacobian matrix, local stability analysis suggests the potential for epidemic eradication when R_C ≤ 1 , while R_C ≥ 1 indicates a risk of epidemic spread. Numerical solutions using ODE45 in Matlab R2021b are employed for the analysis.
Results: The sensitivity analysis highlighted the significant impact of TB transmission coefficient β and diabetes acquisition rate α1 on R_C , emphasizing the need for optimal control measures targeting these factors.
Conclusion: A decrease in TB transmission coefficient led to a reduction in R_C from 1.0863 to 0.1845 , suggesting the potential effectiveness of control strategies. The study also recommends exploring models considering different diabetes types in future research.