Optimal control and cost-effectiveness analysis of socio-nutritional and behavioral interventions for Tuberculosis management in Ghana

Abstract

Tuberculosis is classified as one of the deadliest diseases across the globe, which disproportionately affects developing countries. Notwithstanding the remarkable biomedical improvements, the control of Tuberculosis has been impeded by the interplay of structural vulnerabilities, poor nutrition, and adverse behavioral conditions. In this study, we develop an SLIR model that incorporates an empirically derived index of dietary risk, food insecurity, poor oral health, and psychological distress to assess their association with the transmission, reactivation, and recovery dynamics of Tuberculosis in Ghana. Through a sensitivity analysis, the study outlines the critical role of both biological and socio-behavioral parameters on the basic reproduction number $R_0$. Using WHO-reported Tuberculosis incidence data from 2012 to 2023, the estimated $R_0$ was obtained as 2.6556. It was revealed that the disease progression rate, transmission rate, and nutritional and behavioral parameters were key drivers of Tuberculosis dynamics. We then formulated an optimal control framework by incorporating time-dependent control strategies targeting nutritional support, oral health promotion, mental health services, and treatment adherence. Further numerical simulations show that combined socio-nutritional and behavioral interventions substantially reduce Tuberculosis prevalence and total infections, with the most effective strategies involving multi-pronged approaches sustained at high intensity in the early stages. The cost-effectiveness analysis of the model provides policy-relevant insights for designing multi-sector tuberculosis intervention programs in resource-constrained countries like Ghana.