An unprecedented global effort in surveillance has been carried out by national and international health agencies for the current novel Influenza A (H1N1) pandemic

Here, we use the Global Epidemic and Mobility (GLEaM) model ^{3} stochastic simulations of the current pandemic and provide an estimate of the number of H1N1 cases in Mexico at the date of May the 8th. This is an ab-initio computational estimate and to further cross-validate our results, we compare the number of infected individuals traveling from Mexico to other countries from our simulations and compare these numbers with surveillance reports

The global epidemic and mobility metapopulation (GLEaM) model is based on a geographically structured metapopulation approach

It is also worth stressing here some of the model assumptions. The model is not an agent-based model and does not include additional structure within a subpopulation, therefore it cannot provide detailed information at the level of households or workplaces. The fraction of infected population is likely overestimated because of the assumptions of an entirely susceptible populations and of subpopulations with homogeneous mixing. Current data on the severity of the pandemic has revealed an age pattern for influenza attack rate shifted towards the younger age classes of the population

The spreading rate of the epidemic is governed by the basic reproduction number and the generation interval of the specific viral strain considered. In order to obtain best estimate for these parameters the model has been used to perform a MLE of the parameters against the actual chronology of newly infected countries _{0} and the basic model parameters e and µ defining the inverse average exposed and infectious time durations, respectively. In the following we consider as the baseline case the set of parameters defined by the best estimates: ε^{-1}=1.1 days, µ^{-1}=2.5 days, R_{0} =1.75 ^{th} , 2009, as reported by official sources ^{th} and ending May 10th following Ref. ^{th} and the imported cases in the UK, US, Brazil, Germany and France. Each simulation represents a stochastic realization of the process and we aggregate data on 2x10 ^{3} realizations providing reference ranges for all quantities. The data of imported cases are compared with those reported in Ref.

By using GLEaM it is possible to provide a model estimate of the number of imported cases arriving from Mexico to a set of selected countries. The estimated 99% reference range is shown in Table 1. The dates and target countries are chosen to facilitate the comparison with the numbers found in the literature ^{th}. Only 2/3 of the exposed travelers are then considered in the cumulative number of cases as only this fraction will eventually develop symptoms, according to the model assumptions. The numbers of imported cases to each country are typically small, and as such prone to large stochastic fluctuations. However the surveillance values are all within the 99% reference ranges of the 2,000 realizations of our model. We will provide elsewhere a full sensitivity analysis of the results but we observe very small variations with respect to the presented results in the range of parameters explored. This is because any MLE for R_{0}

Table 2 shows GLEaM predictions for the size of the epidemic in Mexico on April 30^{th} and compare the results with the estimations of Refs.

While GLEaM takes into account a higher level of geographical organization than previous approaches, its estimates still contain a number of assumptions and approximations. The contagion within each census area is approximated by means of a homogeneous mixing process. Once a person arrives at a census area by plane, he/she comes integrated into the local population. This implies that, as in

AV is consulting and has a research agreement with Abbott for the modeling of H1N1 diffusion. The other authors have declared that no competing interests exist.

Simulation Results | 0 - 534 | 0 - 44 | 0 - 62 | 0 - 55 | 0 - 45 |

Surveillance data | 85 (170) | 17 | 11 | 9 | 3 |

Simulation Results | [121,000 - 1,394,000] |

Lower bound range of Ref. |
113,000-375,000 |

Estimate of Ref. |
2,000 - 280,000 |

Mexican official report |
3,350 |

The authors thank IATA and OAG for providing their databases. We are also grateful to the Staff of the Big Red Computer and the Computational Facilities at Indiana University, as well as to Ciro Cattuto for his support with the computational infrastructure at the ISI Foundation.