Analisis dan Simulasi Numerik Model Seirs pada Penyebaran Covid-19 dengan Parameter Vaksinasi

Abstract

COVID-19 is a disease that has become a worldwide pandemic. This research aims to construct a mathematical model on the spread of COVID-19 in Indonesia, analyze the stability of the model, and perform numerical simulations. In this research, the SEIRS model was constructed for the spread of COVID-19. This model was constructed by considering the effect of vaccination parameters. The model consists of Susceptible (S), Exposed (E), Infected (I), and Recovered (R) subpopulations with the assumption of decreased immunity. The model has two equilibrium points, namely the disease-free equilibrium point (E0) and the endemic equilibrium point (E1). The basic reproduction number (R0) is obtained through the Next Generation matrix method which is formed from the model at point E0. The stability analysis of the model was carried out by considering the Jacobian matrix of the model. At point E0, the model will be locally asymptotically stable if the R0≤1. Meanwhile, at point E1 the model will be locally asymptotically stable if the R0>1. To perform numerical simulation, the 5th order Runge-Kutta method is used to provide a numerical solution for the model. From the simulations that have been carried out, it can be seen that vaccination can slow down the spread of COVID-19 and accelerate the population to enter the Recovered class.