ANALISIS MODEL MATEMATIKA PENYEBARAN PENYAKIT DIABETES DENGAN FAKTOR GENETIK

Abraham Abraham, Richardus San

Abstract


Diabetes mellitusis one of the health cases occurred due to the mixture of some kind of diseases. This disease arises when there is a deficiency of the pancreatic hormone insulin or the insulin does not function effectively to metabolise sugars. As a result, the concentration of glucose in the bloodis chronically higher than normal value. In this paper, it will be discussed a mathematical model type SEI that groups human population into three classes, namely Susceptible (S), Exposed (E) dan Infected (I). Steps to analyse the model are by definingthe equilibrium points when the system is disease-free (non endemic) and not disease-free (endemic); subsequently, analysis of stability of the both points is conducted.The determination of the value of BasicReproduction Number (R0)aims to observe whether the disease spreads or declines. If 𝑅0 < 1, then in the population diabetes mellitus will decline or evanesce; if 𝑅0 = 1, then this disease will remain (endemic) in the population; and if the 𝑅0 > 1, then it will ascend to become an epidemic within the population.

 

Keywords : Diabetes Mellitus, Mathematical Model Type SEI, Equilibrium Point, Basic Reproduction Number(𝑅0).


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