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 b, β1, β2, α1, α2, α3, μ1, and μ2 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 (S) decreased significantly in the 20th year with a total of 299,239 people, for subpopulation (E) 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 (I) subpopulation increased until 20th year with a total of 254 people, and for subpopulation (R) subpopulation increased significantly in 20th year with a total of 10,776 people.