Numerical Solution Of The SIRV Model Using The Fourth-Order Runge-Kutta Method

Abstract

This study aimed to predict the spread of the Covid-19 virus in Maluku Province using the fourth-order Runge-Kutta method. The mathematical model of the spread of the Covid-19 virus is a system of differential equations which includes Susceptible (S) variables, namely human subpopulations that are susceptible to Covid-19 virus infection, Infected (I), namely human subpopulations infected with the Covid-19 virus, Recovered (R) namely subpopulation of people who have recovered and Vaccination (V) namely a subpopulation that has been vaccinated and is immune to the Covid-19 virus, used as initial values. The values of  are parameter values that are numerically solved by the fourth-order Runge-Kutta method performed for 24 literations with . Data were obtained from the Maluku Provincial Health Office from March 2022 - November 2022. Based on the data obtained, the average of the data is used as the initial value, where . The initial and parameter values were substituted into the numerical solution and simulated using Matlab. The rate value of each class for the next 24 months for the Susceptible (S), Infected (I), and Recovered (R) classes has decreased until it approaches zero equilibrium. It shows that the subpopulation of the three classes no longer exists, and the Vaccinated (V) class has increased significantly because almost all of the population has been vaccinated in the next 24 months. It shows that after an individual is vaccinated, he does not return to being vulnerable.