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Modeling COVID-19 transmission: effects of age structure and vaccination

Sajjad Ali1, Salah Boulaaras2, Nigar Ali1

  • 1Department of Mathematics, University of Malakand, Chakdara, Dir Lower, Khyber Pakhtunkhwa, Pakistan.

Scientific Reports
|July 30, 2025
PubMed

Insights

This study presents a mathematical model for COVID-19 dynamics, highlighting the critical impact of age structure and vaccination strategies on disease control and eradication efforts globally.

Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Public Health

Background:

  • Existing COVID-19 models often lack detailed age structure and realistic mixing patterns.
  • Understanding disease dynamics across different age groups is crucial for targeted interventions.

Purpose of the Study:

  • To develop a comprehensive mathematical model for COVID-19 transmission dynamics.
  • To investigate the influence of age structure, disease progression, and vaccination on epidemic control.
  • To provide a framework for Pakistan and global applicability.

Main Methods:

  • Development of a compartmental mathematical model incorporating age stratification and heterogeneous mixing.
  • Analysis of model well-posedness using the abstract Cauchy problem.
  • Calculation of threshold parameters and stability analysis for disease persistence/eradication.
  • Numerical simulations using the finite differences method.

Main Results:

  • The model confirms the significant role of age structure in COVID-19 transmission.
  • Vaccination strategies, when integrated with age-specific considerations, are shown to be effective in controlling the pandemic.
  • Analytical and numerical results align, validating the model's predictions.

Conclusions:

  • Age structure and vaccination are key determinants in managing COVID-19.
  • The developed model offers a robust mathematical foundation for informing public health policies.
  • The findings support the implementation of tailored, age-conscious control strategies.

Keywords:
Abstract Cauchy problemAge-structured modelCOVID-19 dynamicsHeterogeneous mixing intercohort mixingNumerical simulationsStability analysisVaccinationWell-posedness

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