National and Regional Influenza-Like-Illness Forecasts for the USA

Michal Ben-Nun; Pete Riley; James Turtle; David P. Bacon; Steven Riley

The first time dependent term, F 1 (t), allows for a dependence of the transmission rate 145 on specific-humidity, the second (F 2 (t)) on the school vacation schedule, and the third 146 (F 3 (t)) allows the user to model an arbitrary behavior modification that can drive the 147 transmission rate up or down for a limited period of time. For the purpose of the CDC 148 challenge we only considered models involving either F 1 (t), F 2 (t), both, or none (i.e., 149 the contact rate does not depend on time), and the functional form of these terms is 150 discussed in sections S1 Text and S2 Text of the Supporting Information. curve was also fitted directly (without any regional information) using all the models 164 and priors, but these direct results were only used at the end of the season when 165 estimating the performance of each of our procedures. 166 In the coupled scenario, the MCMC procedure uses Eqs. (2) (3) (4) along with Eq. (10) to 167 simultaneously generate candidate profiles for the coupled ten HHS regions. The 168 log-likelihood of the ten regional profiles is calculated and combined with the proper 169 relative weights to generate a national log-likelihood which is minimized. It is important 170 to note that in the coupled scenario we only optimize the national log-likelihood, and 171 not the individual region-level likelihoods, but the parameters we optimize are still 172 mostly region specific (only s d and γ are not). We also tried fitting the coupled model 173 to the regional log-likelihoods, however the results of the fits were not as accurate as the 174 ones obtained when the national likelihood is optimized (see Discussion). In the previous section we described a traditional MCMC procedure which uses a log 191 uniform distribution for the parameters, which we term an uninformative prior (UP).