THE EFFECT OF INTERACTION RATE AND GENETIC RATE AS WELL AS THE CONTROL OF PILL MEDICINE AND INSULIN ON THE DIABETES POPULATION

• Main Author: Nur Haliza, Alya
• Format: Final Project
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/80598
• Institution: Institut Teknologi Bandung

Diabetes is an increase in blood sugar (glucose) levels in the body due to insufficient production of the hormone insulin. There are two types of diabetes that will be discussed: type 1 diabetes or autoimmune diabetes, and type 2 diabetes or diabetes mellitus. Individuals with type 1 diabetes may pass the condition on to their children, referred to as the possibility of increasing the diabetes population due to genetic factors. Meanwhile, type 2 diabetes is usually a result of an unhealthy lifestyle. An unhealthy lifestyle is often influenced by close association with individuals who have diabetes and also lead an unhealthy lifestyle. This mutual influence is referred to as an interaction factor. Someone who does not have diabetes is called a healthy population and will not immediately become a diabetic population. A healthy population influenced by genetic and interaction factors will initially transform into a condition known as pradiabetes. Therefore, a mathematical model will be constructed in the form of a three-compartment system of differential equations, representing the healthy population, pre-diabetes population, and diabetes population. Equilibrium points indicate the population states over a sufficiently long period. Stability analysis of equilibrium points is conducted for both non-diabetic and diabetic conditions through model analysis. Meanwhile, numerical analysis demonstrates the influence of genetic and interaction factors with parameter variations. To reduce the diabetes population, individuals with diabetes will be administered pill medication and insulin at specific dosages. To determine the optimal influence, an optimal control is applied to the administration of pill medication and insulin. The results indicate that genetic and interaction factors contribute to an increase in the pre-diabetes and diabetes populations, and a decrease in the healthy population. However, with the assistance of optimal control of pill medication and insulin for individuals with diabetes, the diabetes population decreases significantly, even reaching a reduction of 100% within a 100-day period.