Control of Blood Sugar in Diabetes and COVID-19 Comorbidity with Physical Exercise: Modelling by Impulsive System of Differential Equations

Considerable amount of research effort has been concentrated on modelling and predicting the progress of coronavirus infection, its impacts, and the ramifications of various measures taken by affected nations, such as social distancing, vaccination, and provision of long-term health care. More recently, medical doctors have become aware of an unexpected coronavirus complication that can emerge in a short period of time after the initial COVID-19 infection, or sometimes several months afterward. NHS research confirmed that the risk of death is increased significantly in coronavirus patients with diabetes. Our main purpose is to obtain a better understanding of the impacts of physical exercise on the glucose-insulin dynamics in patients with diabetes-COVID-19 comorbidity. To control diabetes, it is important to keep track, with the aid of an appropriate model, of one’s blood sugar levels and to know what levels are too high after a meal, while physical activity can lower your blood sugar by making your body more sensitive to insulin. Here, we, therefore, propose and analyse a model of the glucose-insulin control system, comorbidity of coronavirus infection, that incorporates variations in blood sugar due to food intake as well as the role that exercising can take in keeping plasma glucose at a suitable level. The solutions of the model are shown to be bounded and persistent under suitable conditions on the system parameters. The stability and periodicity of the system are also investigated. The delineating conditions on pertinent physical parameters that allow us to obtain the desired outcome are interpreted and discussed.