Role of awareness programs on diabetes prevention and control of viral infection: a study of optimal control

Abstract

Diabetes is a chronic metabolic disorder characterized by elevated blood glucose levels due to insufficient insulin production or ineffective use of insulin. While primarily driven by genetics and lifestyle, viral infections like enteroviruses, cytomegalovirus, hepatitis C, HIV, and COVID-19 have also been linked to triggering both type 1 and type 2 diabetes (T2D), possibly through immune system-induced metabolic changes. In this study, we propose and analyze a nonlinear mathematical model to investigate the effects of awareness campaigns on diabetes prevention and control of viral infection. We assume that individuals who are initially unaware of diabetes risk factors become informed through word-of-mouth communication, and adopt preventive behaviors. The model also includes the impact of social media and television advertisements in raising public awareness. We derive the basic reproduction number \((\mathcal {R}_0)\) for the system, which serves as a threshold parameter. Our analysis indicates that the system experiences a transcritical bifurcation as \(\mathcal {R}_0\) crosses the unit value, indicating a shift in the stability of equilibria, and the potential for diabetes control. Additionally, we conduct a sensitivity analysis to identify the most influential parameters impacting the number of infected cases. The model is further expanded to incorporate two control strategies aimed at reducing the prevalence of both diabetic and at-risk individuals. Pontryagin’s Maximum principle, along with the forward-backward sweep method, is employed to solve the optimal control problem. Our findings evoke that interventions involving social media and television advertisements are more effective in promoting awareness and reducing the spread of diabetes risk compared to word-of-mouth communication alone.