On the implementation of a variational iteration method for a seiqr covid-19 epidemic model

We consider a SEIQR epidemic model which describes the spread of COVID-19. The SEIQR epidemic model is built by introducing an isolation compartment in the SEIR model. We implement the variational iteration method (VIM) to find the approximate solution for the SEIQR model. We first implement the VIM by applying restricted variations for both linear and nonlinear terms in the correction functionals and find the Lagrange multiplier for the VIM. The comparison between the solution obtained by such VIM and the solution obtained by the fourth-order Runge-Kutta method shows that the VIM is accurate only for relatively small time domains. For larger time domains, the VIM solution is inaccurate and unrealistic. Then we improve the previous VIM by reducing the restricted variations and show that the improved VIM is more accurate than the previous VIM for larger time domains.