The rate of convergence to early asymptotic behaviour in age-structured epidemic models

TL;DR

This paper investigates the speed at which age-structured epidemic models reach their early asymptotic behavior, revealing that convergence can be slow under certain parameters, which impacts model accuracy.

Contribution

It applies dynamical systems theory to analyze convergence rates in age-structured epidemic models, highlighting the importance of considering slow convergence in model parameterization.

Findings

Convergence to early asymptotic behavior can be slow for some parameters.

Slow convergence affects the accuracy of epidemic predictions.

Model parameterization should account for potential delays in reaching asymptotic states.

Abstract

Age structure is incorporated in many types of epidemic model. Often it is convenient to assume that such models converge to early asymptotic behaviour quickly, before the susceptible population has been appreciably depleted. We make use of dynamical systems theory to show that for some reasonable parameter values, this convergence can be slow. Such a possibility should therefore be considered when parameterising age-structured epidemic models.