Dynamical Analysis and Optimal Control of a Tuberculosis-Diabetes Comorbidity Model with Reinfection and Relapse

Abstract

Tuberculosis (TB) is among the top global health issues, and its transmission dynamics are becoming more complex due to the growing prevalence of diabetes mellitus, which predisposes individuals to TB infection and worsens treatment outcomes. Therefore, the current study was motivated by the need to gain deeper insight into this interaction by developing a mathematical model of TB transmission that incorporated diabetes comorbidity, reinfection, relapse, and nonlinear incidence. The local stability of the disease-free equilibrium was determined by deriving and analyzing the basic reproduction number. Furthermore, the bifurcation analysis showed that the model may exhibit either forward or backward bifurcation. An optimal control framework was developed to analyze potential intervention measures. This included controls representing TB transmission reduction, diabetes prevention, and enhanced treatment for TB patients with and without diabetes. The model parameters were estimated using Indonesian epidemiological data, and the resulting parameter set was used to perform several numerical simulations to validate the analytical results. A global sensitivity analysis using partial rank correlation coefficient was performed to determine the most influential parameters. The optimal intervention strategies were evaluated using the average cost-effectiveness ratio which indicates that combining TB transmission reduction with enhanced treatment constitutes the most cost-effective intervention strategy. These findings highlight the importance of integrated TB control and diabetes management policies in reducing the burden of tuberculosis.

Keywords

• Backward bifurcation
• Costeffectiveness
• Epidemiological data
• Sensitivity analysis
• TB–Diabetes

Project Number

4306/B3/DT.03.08/2025

Thanks

This research is funded by the Indonesian Endowment Fund for Education (LPDP) on behalf of the Indonesian Ministry of Higher Education, Science and Technology and managed under EQUITY Program (Contract No. 4306/B3/DT.03.08/2025) through the Research Grant for Professor/Doctor from Dana Abadi Perguruan Tinggi (DAPT) Universitas Diponegoro with grant number 869-11/UN7.D2/PP/XII/2025.

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