Multiple Estimates of Transmissibility for the 2009 Influenza Pandemic Based on Influenza-like-Illness Data from Small US Military Populations

Rapidly characterizing the amplitude and variability in transmissibility of novel human influenza strains as they emerge is a key public health priority. However, comparison of early estimates of the basic reproduction number during the 2009 pandemic were challenging because of inconsistent data sources and methods. Here, we define and analyze influenza-like-illness (ILI) case data from 2009–2010 for the 50 largest spatially distinct US military installations (military population defined by zip code, MPZ). We used publicly available data from non-military sources to show that patterns of ILI incidence in many of these MPZs closely followed the pattern of their enclosing civilian population. After characterizing the broad patterns of incidence (e.g. single-peak, double-peak), we defined a parsimonious SIR-like model with two possible values for intrinsic transmissibility across three epochs. We fitted the parameters of this model to data from all 50 MPZs, finding them to be reasonably well clustered with a median (mean) value of 1.39 (1.57) and standard deviation of 0.41. An increasing temporal trend in transmissibility (, p-value: 0.013) during the period of our study was robust to the removal of high transmissibility outliers and to the removal of the smaller 20 MPZs. Our results demonstrate the utility of rapidly available – and consistent – data from multiple populations.

1 MPZ = Military Installation by Zip Code. Anonymized individuals are identified by the zip-5 code of the clinic that they visited. Other possible locators would be: (1) the unit identifier code (UIC) of the unit the individual belongs to; (2) the zip-3 code of the UIC; or (3) the name (and/or location) of the installation to which their unit is assigned. However, these would likely introduce errors into our analysis, particularly when troops are temporarily transferred from one installation to another or troops are staged and/or deployed. MPZ, on the other hand, provides a measure of the instantaneous location of the individual when they present to the clinic with symptoms.
2 N total is the total population size for each MPZ, that is, the estimated number of individuals who are served by the clinics within a particular MPZ.
3 T 0 is the initial time of onset of the epidemic in the model, that is, when the first susceptible individual becomes infectious. To within a week or two, it is also a measure of the timing of the model-fit peak. 4 t 1 is the time at which R 0 changes to R * . 5 ∆t is the duration over which the basic reproduction number remains at R * . 6 T g is the generation time, or, in this model, the average time of infection. For the results shown here, T g was fixed at 2.6 days.
7 'Baseline' is the amount of noise added to the solution during the fitting procedure and is optimized in the same manner as the other parameters. At the first time step, the number of infectious individuals is: I = S × p Inf + seed Inf , where p Inf is the probability of becoming infected and seed Inf is the baseline noise. 8 p C is the proportion of active military individuals who are infectious that visit a clinic. 9 R 0 is the initial value of the basic reproduction number. 10 R 0 (25) is the 25% quantile. 11 R 0 (75) is the 75% quantile. 12 R * is the value that the basic reproduction number changes to at time t 1 . 13 R modal is the value of R, either R 0 or R * , corresponding to the most number of infections, that is, it is the value with the largest fraction of the area under the model fit profile.
14 R max is the value of R, either R 0 or R * , at the time of peak model incidence. 15 R best is the maximum value of R 0 or R * . 16 AIC c = Reduced Akaike Information Criterion. This is typically used when the number of parameters (K) is large relative to the sample size (n).
[17] suggest using AIC c unless n/K > 40. In our case, K is seven and n may be as large as one year, or 52 weeks, suggesting that n/K < 7.4, and AIC c , not AIC should be used throughout.