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

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.

Spectral Method in Epidemic Time Series: Application to COVID-19 Pandemic

“…That is, we assume that and are constant functions (over a short period of time) and estimate the daily reproduction number. That is the case for the discrete time model in [ 13 ] and more recently for the continuous time model in [ 1 ]. The major default in [ 13 ] is that the estimated does not remain positive.…”

“…For that purpose, we reconsider the discrete-time epidemic model with the age of infection presented in Demongeot et al [ 1 ]. This model is a discrete-time version of the Volterra integral formulation of the Kermack–McKendrick model with age of infection [ 2 ].…”

“…The quantity is the average number of secondary infected produced by a single infected on the day d since infection (see [ 1 ] for more details). Therefore, the basic reproduction number is the following quantity where n is the maximal duration (in days) of the infection.…”