Analysis of transmission pair data by He et al plus an 8.29-day incubation yields infectivity across the disease time course. Ave. # of infections from a case is still high after self-isolation of symptomatics. Silent spreading is a huge problem! https://www.nature.com/articles/s41591-020-1016-z
RT-PCR studies demonstrate declining sensitivity across the COVID-19 symptomatic disease time course.

https://faseb.onlinelibrary.wiley.com/doi/10.1096/fj.202001700RR
Much less has been learned about COVID-19 RT-PCR test sensitivity during the pre-symptomatic period which transitions from very low infectiousness to very high infectiousness just before symptom onset.
The function s(v) interpolates from post-symptomatic viral shedding v(t) from the infectivity curve to provide a relationship between COVID-19 viral shedding and test sensitivity.

https://www.nature.com/articles/s41467-020-20742-8.epdf?sharing_token=GA6FCqudo8iUNz3j5ToMuNRgN0jAjWel9jnR3ZoTv0OuoQWDwXvoOqvQ6JoxBthPWy_fq5wW05v-vYANCpXSxwopX978SsufJzbcAPeAzvx5JcvnQPfi-wMqhxEalwRBcUdXEV9lLlDTuzg-SjrEkYTFsXkB_mfTKQVgbpFCkf8%3D
's data-driven analysis provides evidence that the greatest benefit of COVID-19 testing—for the purpose of safely shortening quarantine—comes from testing on exit from quarantine compared to testing on entry to quarantine.

https://www.nature.com/articles/s41467-020-20742-8.epdf?sharing_token=GA6FCqudo8iUNz3j5ToMuNRgN0jAjWel9jnR3ZoTv0OuoQWDwXvoOqvQ6JoxBthPWy_fq5wW05v-vYANCpXSxwopX978SsufJzbcAPeAzvx5JcvnQPfi-wMqhxEalwRBcUdXEV9lLlDTuzg-SjrEkYTFsXkB_mfTKQVgbpFCkf8%3D
Compared to a 14-day COVID-19 quarantine with no testing,a 7-day quarantine with testing on exit provides equivalent or lowerprobability of post-quarantine transmission.

https://www.nature.com/articles/s41467-020-20742-8.epdf?sharing_token=GA6FCqudo8iUNz3j5ToMuNRgN0jAjWel9jnR3ZoTv0OuoQWDwXvoOqvQ6JoxBthPWy_fq5wW05v-vYANCpXSxwopX978SsufJzbcAPeAzvx5JcvnQPfi-wMqhxEalwRBcUdXEV9lLlDTuzg-SjrEkYTFsXkB_mfTKQVgbpFCkf8%3D
Each duration of COVID-19 quarantine has a corresponding optimal day to get a test. Testing at exit in a long quarantine is near as good as testing at 7 days, so the rule of thumb of testing on exit is still great to keep in mind for longer quarantines.

https://www.nature.com/articles/s41467-020-20742-8.epdf?sharing_token=GA6FCqudo8iUNz3j5ToMuNRgN0jAjWel9jnR3ZoTv0OuoQWDwXvoOqvQ6JoxBthPWy_fq5wW05v-vYANCpXSxwopX978SsufJzbcAPeAzvx5JcvnQPfi-wMqhxEalwRBcUdXEV9lLlDTuzg-SjrEkYTFsXkB_mfTKQVgbpFCkf8%3D
real-world tested our theory w/ offshore oil-rig workers: 47 positives were obtained with testing on entry and exit to quarantine, of which 16 had tested negative at entry; preventing an expected nine offshore transmission events—each of which would likely have led to outbreaks.
If you KNOW the day of infection and it was 7 days or more ago, the optimal test day is RIGHT AWAY. The reason the left side of these graphs dominate the optimality calculation is because there is so much more transmission to come from those who were recently infected.
Higher transmission levels such as with a lack of COVID-19 precautionary measures or with the new COVID-19 genetic variant, or higher asymptomaticity, all moderately increase post-quarantine transmission, but do not affect optimal test day.

https://www.nature.com/articles/s41467-020-20742-8.epdf?sharing_token=GA6FCqudo8iUNz3j5ToMuNRgN0jAjWel9jnR3ZoTv0OuoQWDwXvoOqvQ6JoxBthPWy_fq5wW05v-vYANCpXSxwopX978SsufJzbcAPeAzvx5JcvnQPfi-wMqhxEalwRBcUdXEV9lLlDTuzg-SjrEkYTFsXkB_mfTKQVgbpFCkf8%3D
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