Estimating influenza latency and infectious period durations using viral excretion data

Influenza infection natural history is often described as a progression through four successive stages: Susceptible-Exposed/Latent-Infectious-Removed (SEIR). The duration of each stage determines the average generation time, the time between infection of a case and infection of his/her infector. Recently, several authors have justified somewhat arbitrary choices in stage durations by how close the resulting generation time distribution was to viral excretion over time after infection. Taking this reasoning one step further, we propose that the viral excretion profile over time can be used directly to estimate the required parameters in an SEIR model. In our approach, the latency and infectious period distributions are estimated by minimizing the Kullback-Leibler divergence between the model-based generation time probability density function and the normalized average viral excretion profile. Following this approach, we estimated that the latency and infectious period last respectively 1.6 and 1.0 days on average using excretion profiles from experimental infections. Interestingly, we find that only 5% of cases are infectious for more than 2.9 days. We also discuss the consequences of these estimates for the evaluation of the efficacy of control measures such as isolation or treatment. We estimate that, under a best-case scenario where symptoms appear at the end of the latency period, index cases must be isolated or treated at most within 16h after symptoms onset to avoid 50% of secondary cases. This study provides the first estimates of latency and infectious period for influenza based directly on viral excretion data. It provides additional evidence that isolation or treatment of cases would be effective only if adopted shortly after symptoms onset, and shows that four days of isolation may be enough to avoid most transmissions.