A new mathematical model of drinking alcohol among diabetes population taking anti-diabetic drugs: an optimal control approach

In this work, we present a new nonlinear mathematical model, describing the spread of high-risk alcohol consumption among people living with diabetes Type 2 and drug interactions with some diabetes medications with three control strategies to gain insights into this increasingly concerned about health and social phenomenon. Some properties of the solutions to the model including positivity, boundedness and existence are shown. The optimal control strategies are derived by proposing an objective functional and using Pontryagin's Maximum Principle. Numerical simulations are also conducted in the analytic results.