A Mathematical Modeling Study of COVID-19 With Reference to Immigration from Urban to Rural Population

TL;DR

This study develops a mathematical SEIR model to analyze COVID-19 spread influenced by urban-to-rural migration in India, incorporating immigration effects, stability analysis, and evaluating control strategies like vaccination and drugs.

Contribution

It introduces a novel SEIR model accounting for migration effects, with stability, sensitivity, and intervention analysis specific to rural-urban COVID-19 dynamics in India.

Findings

Model establishes positivity and boundedness of solutions.

Reproduction number and stability conditions derived.

Control interventions like vaccination are evaluated for effectiveness.

Abstract

In this study, we have formulated and analyzed a non-linear compartmental model (SEIR) for the dynamics of COVID-19 with reference to immigration from urban to rural population in Indian scenario. We have captured the effect of the immigration as two separate factors contributing in the rural compartments of the model. We have first established the positivity of the solution and the boundedness of the solution followed by the existence and uniqueness of the solution for this multi compartment model. We later went on to find out the equibria of the system and derived the reproduction number. Further we numerically depicted the local and global stability of the equilibria. Later we have done sensitivity analysis of the model parameters and identified the sensitive parameters of the system. The sensitivity analysis is followed up with the two parameter heat plots dealing with the sensitive parameters of the system. These heat plots gives us the parameter regions in which the system is stable. Finally comparative and effectiveness studies were done with reference to the control interventions such as Vaccination, Antiviral drugs, Immunotheraphy.