<p>Diabetes is a chronic metabolic disease in which blood glucose (sugar) levels remain abnormally high as the body either does not produce enough insulin or cannot use insulin effectively. People with diabetes are at greater risk of serious health problems such as heart attacks, strokes, kidney failure, and permanent vision loss caused by damage to the blood vessels in the eyes. In order to investigate how awareness campaigns can aid in the prevention of diabetes and the control of associated viral infections, we propose and analyze a nonlinear mathematical model. We assume that individuals who are initially ignorant of the risk factors for diabetes learn from others and subsequently take preventative measures. We also consider the influence of advertisements on TV and social media in raising public awareness. We fitted the proposed model to the annual diabetes prevalence data from the United States covering the period 2000–2024. We calculate the basic reproduction number (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">$\mathcal {R}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation>), a key threshold that determines whether the disease will persist or die out. Our analysis shows that as <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\mathcal {R}_0$</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="script">R</mi> <mn>0</mn> </msub> </math></EquationSource> </InlineEquation> crosses unity, there is a transcritical bifurcation, which marks a shift in the stability of the disease-free and endemic states, highlighting the conditions needed for effective diabetes control. Further, sensitivity analysis identifies the parameters that strongly affect the number of infected individuals. Moreover, we extend our model by introducing two control strategies aimed at reducing the prevalence of both diabetic and at-risk individuals. To solve the optimal control problem, we apply Pontryagin’s Maximum Principle together with the forward-backward sweep method. The result demonstrates that usage of social media and TV to spread awareness is much more effective in lowering diabetes risk than relying solely on the word-of-mouth communication.</p>

Effects of healthy lifestyle practices on prevention of viral infections and diabetes: Insights amid advertising campaigns and optimal control

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发表日期：

2026年3月7日

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Kalyan Kumar Pal,
Rajanish Kumar Rai,
Pankaj Kumar Tiwari,
Arvind Kumar Misra

摘要

Diabetes is a chronic metabolic disease in which blood glucose (sugar) levels remain abnormally high as the body either does not produce enough insulin or cannot use insulin effectively. People with diabetes are at greater risk of serious health problems such as heart attacks, strokes, kidney failure, and permanent vision loss caused by damage to the blood vessels in the eyes. In order to investigate how awareness campaigns can aid in the prevention of diabetes and the control of associated viral infections, we propose and analyze a nonlinear mathematical model. We assume that individuals who are initially ignorant of the risk factors for diabetes learn from others and subsequently take preventative measures. We also consider the influence of advertisements on TV and social media in raising public awareness. We fitted the proposed model to the annual diabetes prevalence data from the United States covering the period 2000–2024. We calculate the basic reproduction number ( $\mathcal {R}_0$ $R_{0}$ ), a key threshold that determines whether the disease will persist or die out. Our analysis shows that as $\mathcal {R}_0$ $R_{0}$ crosses unity, there is a transcritical bifurcation, which marks a shift in the stability of the disease-free and endemic states, highlighting the conditions needed for effective diabetes control. Further, sensitivity analysis identifies the parameters that strongly affect the number of infected individuals. Moreover, we extend our model by introducing two control strategies aimed at reducing the prevalence of both diabetic and at-risk individuals. To solve the optimal control problem, we apply Pontryagin’s Maximum Principle together with the forward-backward sweep method. The result demonstrates that usage of social media and TV to spread awareness is much more effective in lowering diabetes risk than relying solely on the word-of-mouth communication.