This work is very well written and gives an interesting first overview of estimation difficulties, with theoretical elements and clear numerical examples. The model emphasizes the randomness of the epidemic onset and of the times that appear and neglects the question of the population heterogeneity, the effect of which is surely still poorly understood.
These parameters are sensitive and have predictive or interpretive consequences. Difficulties discussed are related to biases induced by "uniformly random selection in the population", the limited time interval for observations, the possible discrepancy between the actual time of infection and the time of symptom onset, or the multiplicity of potential infecting contacts. The model is in medium field (mixed population, homogeneous) with random times for the different transitions with memory (gamma laws in particular).
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