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The estimates of the basic reproductive number for the SA cases ranged from 1.7 to 4.7, while the estimates for the NYC cases ranged from 2.1 to 5.1. The estimated values of the basic reproductive number for the USA metapopulations (both for SA and NYC cases) ranged from 1.9 to 2.2. The estimates of the mean of the serial interval for the SA cases ranged from 2.1 to 4.3 days, while the estimates for the NYC cases ranged from 3.2 to 5.1 days. The estimated values of the mean of the serial interval for the USA metapopulations (both for SA and NYC cases) ranged from 2.3 to 3.2 days.
Following Fraser et al (2009), in the modal serial interval estimation method, we fit ni to the number of infectious individuals as a function of time. By fitting the model to the data, we obtain the number of infected individuals at t when an infected individual was diagnosed, Ii(t).
For each observed case that fits this inclusion criterion, we construct the expected number of unobserved cases, Ei ( t), using a Poisson regression with the linear predictor defined by the number of reported cases at t and the estimated serial interval for that week, si(t).
We illustrate this using the case study of the 2009-H1N1 pandemic. The early phase of the epidemic was characterised by virus spread via contacts between case clusters and onwards to the wider community. During this period, the number of new cases appears to follow a linear trend with slope of 1.07. This implies that a case should be expected to infect 0.87 other cases on average during its 2.33-day course. The median number of secondary cases is about 50 (34-69), so that a single case is expected to be responsible for about 12 infections. The number of daily new cases for a given week follows a Poisson distribution.
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