https://doi.org/10.1140/epjp/s13360-025-06063-z
Regular Article
Role of awareness programs on diabetes prevention and control of viral infection: a study of optimal control
1
Department of Basic Sciences and Humanities, Indian Institute of Information Technology, 813210, Bhagalpur, India
2
Department of Mathematics, Thapar Institute of Engineering and Technology, 147004, Patiala, India
3
Department of Mathematics, Institute of Science, Banaras Hindu University, 221005, Varanasi, India
Received:
27
October
2024
Accepted:
24
January
2025
Published online:
22
February
2025
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 
for the system, which serves as a threshold parameter. Our analysis indicates that the system experiences a transcritical bifurcation as 
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.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
