Mathematical Modeling of SEIR Type to Controlling Diabetes Mellitus Disease Using Insulin

Abstract

In this research the developed model is SEIR type mathematical modeling using insulin as a form of treatment. SEIR is abbreviation of susceptible (S), exposed (E), infected (I) and recovered (R). Expected goals include to making mathematical models for spread of diabetes mellitus, fixed point determination and basic reproduction number, stability analysis of fixed point, simulation of fixed point stability, simulation of population behavior to know the strategy of controlling diabetes mellitus. Analytical and numerical analysis results were obtained two fixed points, namely the point of no disease (disease-free equilibrium) and the point of disease (endemic equilibrium). Stability analysis of each fixed point indicates that the fixed point there is no stable disease when R₀ < 1, whereas the fixed point there is stable disease when R₀ > 1. Numerical simulations show that, with reduced Susceptible population contact rate with the exposed population causing  to decrease, so the spread of the disease does not appear in the population. These results indicate that one strategy of controlling the spread of diabetes mellitus can be done by reducing the rate of contact susceptible population with eksposed.