This study aims to assess the prevalence of diabetes and kidney infection, evaluating the impact of awareness at local as well as global levels. Analytically, we derive a threshold quantity \(\kappa_0\) , which determines whether kidney failure/infection will occur. Our analysis reveals the presence of transcritical bifurcation as \(\kappa_0\) crosses unity, signaling a shift in the stability of system’s equilibria and highlighting conditions for effective control of diabetes and kidney disease. Further, sensitivity analysis identifies the most influential parameters affecting the number of individuals at risk of kidney complications. The model is extended to include two time-dependent controls, designed to reduce the prevalence of both diabetic and kidney-related complications. To analyze the optimal control problem, Pontryagin’s Maximum Principle is applied, whereas the forward-backward sweep method is utilized to compute its solutions. Our analysis highlights that web-based advertising interventions are significantly more effective than word-of-mouth communication alone in the diabetes and kidney disease. Moreover, the comparison of the impacts of the two control strategies provides insights for targeted public health interventions.
