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 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. Another essential aspect of understanding an epidemic is the contact between individuals which mainly depends on their location at home or work. To investigate such a question, we will discuss a new model including the people at home, commuting, and working in a city.