Numerical Solution of Diabetes Mellitus Model without Genetic Factors with Treatment using Runge Kutta Method

Abstract

This study discusses the numerical solution of the model analysis of diabetes mellitus without genetic factors with treatment using the fourth order Runge-Kutta. The mathematical model in the form of a differential equations system that includes S (Susceptible), E (Exposed), I (Infected), and IT (Infected with Treatment) which has been simplified into the total population class (N), the latent population (E), the patient population without treatment (I) and the patient population with treatment (IT) as the initial value and the value of A, μ, δ1, δ2, α, β as parameters were resolved numerically using the fourth order Runge-Kutta method and performed as many iteration with interval time or h = 0,01 years. The data taken in Makassar City for each class population. Initial and parameters values are subtituted into numerical solutions to the model which are then simulated using Maple, indicating that at t = 5 years the magnitude of the entire population class (N) = 195.216, the latent population (E) = 31, the patient population without treatment (I) = 4.836 and the patient population with treatment (IT) = 1.454. The results concluded that the magnitude of the value for the rate of each class of population in the next five years decreased due to the population dead and/or move the next class of the population.