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This study presents a flexible numerical method for calculating reproduction numbers in complex population models. The approach accurately estimates epidemic potential across various age structures and transmission types.

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Area of Science:

  • Mathematical modeling
  • Population dynamics
  • Epidemiology

Background:

  • Estimating reproduction numbers is crucial for understanding disease spread.
  • Existing methods may lack flexibility for complex, age-structured populations.
  • General numerical methods are needed for diverse population models.

Purpose of the Study:

  • To introduce a general numerical method for approximating reproduction numbers.
  • To provide flexibility in defining birth and transition processes.
  • To apply the method to multi-group, age-structured population models.

Main Methods:

  • Formulation of age-integrated state in an extended space framework.
  • Discretization of birth and transition operators using pseudospectral collocation.
  • Application to models with continuous/piecewise continuous rates and various age/transmission interpretations.

Main Results:

  • The method successfully approximates reproduction numbers for a broad class of models.
  • It accommodates different interpretations of age (demographic, infection, disease) and transmission (horizontal, vertical).
  • Demonstrated computation of basic and type reproduction numbers as special cases.

Conclusions:

  • The proposed numerical method offers a versatile tool for analyzing population dynamics and epidemic spread.
  • It enhances the ability to model complex scenarios with age structure and varied transmission routes.
  • This approach facilitates a more accurate estimation of epidemic potential in diverse populations.