Optimal Control Modeling of Diabetes and Hypertension Co-Infection with Lifestyle and Treatment Interventions

Abstract

The dual burden of diabetes and hypertension represents a major global health challenge, especially in low- and middle-income countries where the comorbidity contributes significantly to morbidity, mortality, and healthcare costs. This study develops and analyzes an optimal control model to evaluate the effectiveness of lifestyle modification and pharmacological treatment strategies in managing diabetes–hypertension co-infection. The model incorporates two state variables representing the progression of diabetes and hypertension, and two control variables representing the intensities of lifestyle and treatment interventions. Using adjoint variables, the model measures the sensitivity of the disease burden to changes in interventions. Results indicate that aggressive interventions at the early stage of disease progression yield the greatest long-term benefits, as reflected in elevated adjoint values. However, at certain points, continued interventions become counterproductive, necessitating temporary suspension of control measures. Diabetes burden shows higher fluctuations compared to hypertension, which stabilizes earlier under moderate interventions. By one year (t = 365), both diseases achieve stability with moderate, sustained interventions, demonstrating that continuous intensive treatment is not required for long-term control. The findings underscore the need for adaptive, time-dependent management strategies that integrate lifestyle modification with pharmacological treatment to ensure effective, sustainable, and cost-efficient control of diabetes and hypertension co-infection.