Analysis and Numerical Simulation of SEIRS Model with Vaccination on COVID-19 Spread

Abstract

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 and with the assumption of decreased immunity. The model has two equilibrium points, namely the disease-free equilibrium point and the endemic equilibrium point. The basic reproduction number is obtained through the Next Generation matrix method which is formed from the model at the disease-free equilibrium point. The stability analysis of the model was carried out by considering the Jacobian matrix of the model. To perform numerical simulation, the Fifth-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 recovery of the population.