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

  • Anita Papalia athematics Department, Faculty of Mathematics and Natural Sciences, Universitas Pattimura, Indonesia
  • Yopi Andry Lesnussa Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Pattimura, Indonesia
  • Monalisa E. Rijoly Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Pattimura, Indonesia
  • Olumuyiwa James Peter Department of Mathematical and Computer Sciences, University of Medical Sciences, Nigeria
DOI: https://doi.org/10.30598/barekengvol18iss3pp2047-2056
Keywords: Hepatitis B, Runge-Kutta Method, SEIR Model

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.

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Published
2024-07-31
How to Cite
[1]
A. Papalia, Y. Lesnussa, M. Rijoly, and O. Peter, “NUMERICAL SOLUTION OF THE SEIR MODEL USING THE FOURTH-ORDER RUNGE-KUTTA METHOD TO PREDICT THE SPREAD OF HEPATITIS B DISEASE IN AMBON CITY”, BAREKENG: J. Math. & App., vol. 18, no. 3, pp. 2047-2056, Jul. 2024.
Issue
Vol 18 No 3 (2024): BAREKENG: Journal of Mathematics and Its Application
Section
Articles

Copyright (c) 2024 Anita Papalia, Yopi Andry Lesnussa, Monalisa E. Rijoly, Olumuyiwa James Peter

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