Abstract
Nowadays, Diabetes is one of the most common diseases, which has a huge and growing socio-economic burden affecting individuals, families, and the whole society. In this paper, we propose an optimal control approach modeling the evolution from pre-diabetes to diabetes with and without complications and the effect of living environment. We show the existence of an optimal control and then use a numerical implicit finite-difference method to monitor the size of population in each compartment.
Highlights
Today, all countries of the world su er from the high number of people with diabetes, which is increasing and expanding at the extreme level
International Diabetes Federation (IDF) says that the number of people with diabetes is more than 425 million people, most of them are 65 years old, which increases the risk of the disease that does not exclude children and adolescents under 20 years. e last estimates of the number of people with diabetes in this category are that more than one million people have diabetes type I or type II
According to IFD statistics, diabetics have a two- to three-fold increased risk of cardiovascular disease, as well in more than a third of them, the incidence of retinopathy among all people with diabetes is the main cause of vision loss of adults at work and they accuse an increasing incidence of end-stage renal diseases (ESRD) up to 10 times in the disease
Summary
All countries of the world su er from the high number of people with diabetes, which is increasing and expanding at the extreme level. Erefore, in our proposed model we wanted to highlight the impact of the living environment on diabetic patients (availability of healthy food, diet, exercise, weight for instance) and its main role in the development of complications, which o en ends either with loss of vision or amputation of the toes, feet, and lower legs or Paraplegia and so on To achieve this objective, we consider a compartment model that describes the dynamic of a population of diabetics that is divided into four classes, i.e: the potential diabetic specialy pre-diabetics by through genetics ( ), diabetics without complications ( ), diabetics with complications ( ), and we add a compartment ( ) people who are likely to have diabetes through the e ect of living environment or psychological problems.
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