NUMERICAL SOLUTION OF THE SEIR MODEL USING THE FOURTH-ORDER RUNGE-KUTTA METHOD TO PREDICT THE SPREAD OF HEPATITIS B DISEASE IN AMBON CITY

Abstract

Hepatitis B is a dangerous type of hepatitis and has a high risk of death. This research aims to predict the spread of Hepatitis B in Ambon using the fourth-order Runge-Kutta method. The mathematical model for the spread of Hepatitis B takes the form of a system of differential equations that includes the variables Susceptible (S) namely the subpopulation that is susceptible to infection with the hepatitis B virus, Exposed (E), namely the subpopulation that is exposed to the hepatitis B virus when it comes into contact with the Infected (I) subpopulation, I, namely the subpopulation infected with hepatitis B and Recovered (R), namely the recovered subpopulation. The values ​​ , , , , , , , and are the parameter values ​​used to be solved numerically using the fourth order Runge Kutta method which was carried out in 20 iterations with step size h=1 using data from the Maluku Provincial Health Service and the Central Bureau of Statistics from 2013 to 2022. Hepatitis B is classified as a type of hepatitis disease that is dangerous and has a high risk of death. This study aimed to construct a model of the spread of Hepatitis B disease in Ambon City and solve the model using the fourth-order Runge-Kutta method. In the research results, it was obtained that subpopulation decreased significantly in the 20th year with a total of 299,239 people, for subpopulation increased in 18th year with a total of 4,309 people, and decreased in 20th year with a total of 4,298 people, for subpopulation subpopulation increased until 20th year with a total of 254 people, and for subpopulation subpopulation increased significantly in 20th year with a total of 10,776 people.