Analysis and Solution of The SEIRS Model for The Rubella Transmission with Vaccination Effect using Runge-Kutta Method

Abstract

Rubella disease is an infectious disease transmitted through the respiratory tract caused by a virus. In some cases, there are diseases that can enter an endemic condition, which is a condition in which the outbreak of a disease in a certain area over a long period of time. This condition can be modeled mathematically by using certain assumptions which will then seek for analytical and numerical solutions. This type of research is a literature study. This study examines the theory and application of the Runge-Kutta method in analyzing the spread of Rubella with the effect of vaccination. The Runge-Kutta method is widely used in solving ordinary differential equations and is more accurate than the Euler method. In this study, two methods were used to analyze it, namely the Runge-Kutta Order 4 and Order 5 methods which were used to analyze and compare the numerical results obtained, and the aim of the study was to obtain and interpret mathematically a mathematical model of the spread of Rubella’s disease with the effect of vaccination. and comparing the results obtained from the numerical solution using the Runge-Kutta Order 4 and Runge-Kutta Order 5 methods simulated with Maple software 13. From the results of this study, the results obtained in the 1st iteration of the numerical solution model for Rubella’s disease using the Runge-Kutta Order 4 is the value of 푆1 = 8771655, E 1 = 142, 퐼1 = 38, and R 1 = 30. While the results in the first iteration of the numerical solution model for Rubella’s disease using the Runge-Kutta Order 5 method were that the values of 푆1 = 8771759, E 1 = 142, 퐼1 = 37, and R 1 = 30 were obtained. So it can be concluded that the Order 5 Runge-Kutta is better than the Order 4 Runge-Kutta in predicting the state rate of the Rubella disease case population in the Suspectible, Exposed, Infected, Recovered, Suspected (SEIRS) model. Because the image / graph of Order 5 Runge-Kutta is more like / closer to the results of the analytical simulation using maple 13 software, which is as many as 27 infected individuals.

The NADI Mathematical Model on the Danger Level of the Bili-Bili Dam

“…There are many studies related to measuring the rate characteristics of an object. For example, analysis and simulation of a mathematical model for typhus disease in Makassar (Anas et al, 2021); analysis and solution of the SEIRS model for the rubella transmission with vaccination effect using the Runge-Kutta method (Asri et al, 2021); SEIRI model analysis using the mathematical graph as a solution for Hepatitis B disease in Makassar (Side et al, 2021); numerical solution of SIRS model for dengue fever transmission in Makassar City with Runge-Kutta method (Asri et al, 2021); a mathematical model for the novel coronavirus epidemic in Wuhan, China (Yang et al, 2020); review on Covid-19 disease so far (Djalante et al, 2020;Shahreen et al, 2020;Sohrabi et al, 2020). However, these studies were only limited to the process of deployment disease.…”

Developing computationally efficient optimal control strategies to eradicate Rubella disease

“…In many countries with successful immunization efforts, Rubella cases have dramatically decreased, and endemic transmission of the virus has been interrupted or eliminated. Mass vaccination campaigns have been instrumental in reducing the burden of Rubella and its associated complications [17,18].…”

“…The most effective measure for protecting humans against Rubella virus disease is the administration of the MMR (Measles, Mumps, and Rubella) vaccine. Vaccination is an essential measure to protect individuals from the disease and contribute to the overall control and prevention efforts [17,18,[51][52][53]. To incorporate this vaccination aspect, we extend the SEITR model (1) by introducing an additional compartment for vaccination denoted by V. We assume that susceptible individuals are being fully vaccinated at the rate ρ 1 .…”