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Updated: Jun 28, 2025

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Modelling the COVID-19 Pandemic: Asymptomatic Patients, Lockdown and Herd Immunity.

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The SAIR model accounts for asymptomatic COVID-19 spread, unlike traditional SEIR models. Lyapunov theory proves its stability, and parameter estimation methods accurately predict disease trajectories using real-world data.

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Infectious Disease Dynamics

Background:

  • COVID-19 pandemic caused by SARS-CoV-2.
  • Traditional SEIR models do not account for asymptomatic transmission.
  • Asymptomatic individuals can transmit SARS-CoV-2 effectively.

Purpose of the Study:

  • Introduce and analyze the SAIR (Susceptible, Asymptomatic, Infected, Removed) epidemiological model.
  • Establish the global asymptotic stability of the SAIR model using Lyapunov theory.
  • Develop and apply parameter estimation methods for the SAIR model.

Main Methods:

  • Lyapunov theory for stability analysis.
  • Parameter estimation techniques applied to epidemiological data.
  • Model validation using country-specific COVID-19 data.

Main Results:

  • Global asymptotic stability of the SAIR model demonstrated.
  • Effective parameter estimation methods developed.
  • SAIR model predictions closely match real-world COVID-19 data from various countries, including India.

Conclusions:

  • The SAIR model provides a more accurate representation of COVID-19 dynamics than SEIR models.
  • Lyapunov theory is a powerful tool for analyzing epidemiological models.
  • Parameter estimation methods are crucial for validating and applying these models to public health.