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An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm.

Benjamin Wacker1, Jan Schlüter1,2

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Summary
This summary is machine-generated.

This study introduces a susceptible-infectious-recovered (SIR) model incorporating age and sex for disease transmission predictions. The model ensures mathematical properties and demonstrates accurate short-term forecasting capabilities.

Keywords:
SIR modelage structureexistence and uniquenessnonlinear ordinary differential equationsnumerical algorithmsex structure

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Area of Science:

  • Epidemiology
  • Mathematical Biology
  • Computational Science

Background:

  • Disease transmission is significantly influenced by demographic factors such as age and sex.
  • Existing epidemiological models may not fully capture the nuances of disease spread across diverse population subgroups.
  • Short-term disease prediction requires models that can account for key demographic variables.

Purpose of the Study:

  • To develop and analyze a compartmental SIR model that stratifies the population by age and sex for enhanced disease transmission prediction.
  • To rigorously examine the mathematical properties of the proposed SIR model, including existence, uniqueness, and stability.
  • To create and validate a numerical algorithm for the SIR model, ensuring its discrete version retains the desirable characteristics of the continuous model.

Main Methods:

  • Formulation of a compartmental SIR model with age and sex stratification, excluding vital dynamics.
  • Mathematical analysis of the model's qualitative behavior, proving global existence, uniqueness, non-negativity, boundedness, and monotonicity.
  • Development of an explicit-implicit numerical algorithm to solve the model equations.
  • Verification that the numerical solution preserves the properties of the continuous model.

Main Results:

  • The proposed SIR model demonstrates global existence and uniqueness of solutions.
  • Key properties such as non-negativity, boundedness, and monotonicity were proven for the model's solutions.
  • The developed numerical algorithm accurately reflects the behavior of the continuous SIR model.
  • Theoretical findings were illustrated through a numerical example, confirming model efficacy.

Conclusions:

  • The age- and sex-structured SIR model provides a robust framework for short-term disease transmission prediction.
  • The model's mathematical properties ensure reliable and predictable outcomes.
  • The validated numerical algorithm facilitates practical application of the model in epidemiological forecasting.