A Kermack-McKendrick model with age of infection starting from a single or multiple cohorts of infected patients

TL;DR

This paper investigates the identifiability of a Kermack-McKendrick epidemic model incorporating age of infection, demonstrating methods to estimate the reproduction number from data and applying it to SARS-CoV-1 case data.

Contribution

It introduces a novel approach to determine the daily reproduction number using a Volterra integral equation within the age-of-infection framework.

Findings

Reproduction number can be estimated from the flow of new infections.

Method validated with deterministic and stochastic simulations.

Applied successfully to SARS-CoV-1 data.

Abstract

During an epidemic, the infectiousness of infected individuals is known to depend on the time since the individual was infected, that is called the age of infection. Here we study the parameter identifiability of the Kermack-McKendrick model with age of infection which takes into account this dependency. By considering a single cohort of individuals, we show that the daily reproduction number can be obtained by solving a Volterra integral equation that depends on the flow of new infected individuals. We test the consistency our the method by generating data from deterministic and stochastic numerical simulations. Finally we apply our method to a dataset from SARS-CoV-1 with detailed information on a single cluster of patients. We stress the necessity of taking into account the initial data in the analysis to ensure the identifiability of the problem.