Mathematical models of diabetes in the United States population
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In this work, we study diabetes in the United States (US) population using two mathematical models. The first model is based on an existing model of Boutayeb et al. (2004) and it is a system of two differential equations that models the dynamics of diabetics without complications and diabetics with complications over time. This model uses a constant recruitment parameter for the new diabetes cases, and it includes a parameter representing the physical activity effort of diabetics without complications. We shall study the existence and boundedness of the model solutions, equilibrium point and its stability and sensitivity analysis of the equilibrium point. In addition, we will use the Centers for Disease Control and Prevention (CDC) US diabetes data from year 2000 to 2015 to fit the exponential growth model of the diabetes in the US. Then we use the exponential growth to model the US diabetes population. The resulting model is a system of two differential equations that models the dynamics of diabetics without complications and diabetics with complications over time that uses the exponential growth and includes a parameter representing the physical activity effort of diabetics without complications. We shall study the existence of model solutions, equilibrium point and its stability. Computer simulations of both mathematical models with the US model parameter values are used to test the outcome of implementing diabetes control strategies of diabetes education and physical activity on the numbers of diabetics with application to the US diabetes population. Computer simulations of both models suggest that complications of diabetes are decreased when only the physical activity strategy is implemented, when only the diabetes education strategy is implemented and when both strategies of physical activity and diabetes education are implemented.