# Nonlinear compartmental modeling of COVID-19 with dual dose vaccination using Mason graphs and variational iteration method

## TL;DR

This paper introduces a nonlinear model to study the spread of COVID-19 and the effects of dual-dose vaccination using Mason graphs and a mathematical method.

## Contribution

The novelty lies in using a nonlinear model with Mason graphs and the Variational Iteration Method to analyze vaccination effects on disease dynamics.

## Key findings

- The model shows that increasing vaccination rates reduce infection rates over time.
- Non-vaccinated individuals decrease due to awareness campaigns.
- The removed population decreases as more people get vaccinated.

## Abstract

In this research work, a novel non-linear mathematical model has been proposed considering susceptible, quarantined, infected, recovered, and removed compartments before and after the 1st dose and 2nd dose of vaccination. For this dynamics model, the novel coronavirus COVID-19, a contagious disease, is taken as a case study in which its transmission, impact of vaccination, and mitigation have been discussed. This model may be helpful in numerous fields of epidemiology and dynamical systems; moreover, Mason Graph has been used to describe the mathematical model. The stability analysis and disease-free equilibrium points have been deliberated for the model. In this work, the semi-analytical technique Variational Iteration Method has been employed, which will assist researchers in the future by showing that if the rate of immunized personnel rises, then the infection rate decreases. It has been observed that the non-vaccinated personnel decrease with the passage of time due to the awareness campaign programs of the governments. Furthermore, it was observed that the removed rate also decreases with the passage of time as the immunized personnel rises. Mathematical software MAPLE has been used to calculate the analytical solutions of the aforementioned mathematical model.