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Mathematical Modelling of the Spatial Distribution of a COVID-19 Outbreak with Vaccination Using Diffusion Equation.

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Mathematical models using reaction-diffusion equations predict COVID-19 spread. Vaccination and reduced contact are key to lessening the pandemic

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • The COVID-19 pandemic, caused by SARS-CoV-2, has spread globally, necessitating predictive models for control.
  • Mathematical modeling, particularly using differential equations, is vital for understanding and managing viral disease dynamics.

Purpose of the Study:

  • To mathematically model the COVID-19 pandemic using a Susceptible, Exposed, Infected, Recovered, and Vaccinated (SEIRV) population model.
  • To analyze the stability, existence, uniqueness, and spatial distribution of the model's solutions.
  • To assess the impact of vaccination and spatial spread on COVID-19 dynamics.

Main Methods:

  • Formulation of a reaction-diffusion system for the SEIRV model.
  • Application of Lyapunov functions and the Routh-Hurwitz criterion for stability analysis.
  • Numerical simulations to investigate model behavior and parameter sensitivity.

Main Results:

  • Determined conditions for local and global asymptotic stability of model equilibria.
  • Analyzed the spatial distribution of disease spread based on the basic reproduction number (R0).
  • Sensitivity analysis identified key parameters influencing COVID-19 transmission.

Conclusions:

  • Reducing transmission through decreased contact and increasing high-efficacy vaccination rates are crucial for mitigating COVID-19.
  • The study provides insights for public health policymakers on effective COVID-19 management strategies.
  • Spatial dynamics significantly influence disease spread, highlighting the importance of localized interventions.