Unifying Viral Genetics and Human Transportation Data to Predict the Global Transmission Dynamics of Human Influenza H3N2

Lemey, Philippe; Rambaut, Andrew; Bedford, Trevor; Faria, Nuno; Bielejec, Filip; Baele, Guy; Russell, Colin A.; Smith, Derek J.; Pybus, Oliver G.; Brockmann, Dirk; Suchard, Marc A.

To compare the performance of different migration rate models in predicting global pandemic spread, we simulate a stochastic meta-population susceptible-infected-recovered (SIR) model with n = 14 populations, matching the 14 air communities analyzed in the phylogeographic model. The model tracks the number of susceptible (S), infected (I) and recovered (R) individuals in each population each day of the simulation. The simulations begin with a single initial infection in Mexico on January 5th 2009 [31] . Infection spreads through mass-action within each population according to the following epidemiological parameters. Population-specific host population size is equal to human population size (Text S1). Basic epidemiological parameters are based on empirical estimates from H1N1: the duration of infection was chosen as 3 days [31] and the basic reproductive number (R 0 ) or average number of secondary infections arising from a primary infector during their infectious period in a completely susceptible population was chosen as 1.3 [31] . This results in a transmission rate b~0:433. Although estimates of R 0 for pandemic H1N1 vary across studies, the exact R 0 value is unlikely to affect the comparative simulations we perform as this is expected to equally impact the overall expansion rate and not the relative migration dynamics across populations. Force of infection l j within population j scales with infected frequency across populations following l j~P n i~1 r ij bI i S j =N j , where the coupling coefficient r ij represents the rate of contacts from population i to population j relative to within-population contacts and r jj~1 . Other pairwise coupling coefficients are taken to be proportional to pairwise migration estimates, so that r ij~c m ij , where m ij is the air travel based or phylogenetically estimated rate of migration from population i to population j per year and parameter c is fitted to the data. Parameter c is the only free parameter in this model and we set this to the value that maximizes correspondence between simulations and observations (see below). This ensures that we can use phylogeographic migration rates as per capita migration rates in the simulation model, despite their different scales. Compartments are updated according to a t-leaping algorithm [32] with one-day intervals.