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

Abstract

The infectiousness of infected individuals is known to depend on the time since the individual was infected, 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 newly infected individuals. We test the consistency of 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.