We have estimated that there are likely to have been at least 113,000–375,000 cases of novel H1N1 influenza among Mexicans with onset during the month of April, 2009. Taking into account what we consider to be extreme sensitivity analyses, this estimate could change by approximately 2-fold in either direction. This exceeds the number of confirmed cases reported to WHO, 1204 as of May 8, 2009 (http://www.who.int/csr/don/GlobalSubnationalMaster_20090508_1815.jpg
), by a factor of approximately 100 or more.
It is unsurprising that we estimate a larger number than the number of cases confirmed in Mexico, since ascertainment there has been particularly focused on severe cases. Nevertheless, we regard this estimate as likely a lower bound on the actual number of cases in Mexico, for two principal reasons. First, the analytic approach assumes that the incidence rate in Mexicans in Mexico is equal to that in travelers. If indeed the infection has been transmitting extensively within Mexico, one would expect that the exposure of travelers to the virus would be somewhat less than that of residents, due to nonrandom mixing between residents and travelers; travelers should be less exposed to residents than other residents are. Prior models of influenza transmission (set in the United States) have assumed that 36–51% of influenza transmission takes place outside of home or school 
. One might roughly estimate that this is the proportion of transmission to which both visitors and residents would be exposed, suggesting that incidence in residents might be 2–3x as high as that in visitors; however, this approach has obvious limitations given the uncertainty of those estimates and the fact that they were made for a different country.
Second, while most cases ascertained in the traveler population to date have been mild, one nonetheless expects that many mild cases (as well as probable but unconfirmed cases) in travelers are absent from our calculations. A survey in New York City, where case ascertainment was aggressive surrounding the St. Francis School outbreak, indicated that over 1000 persons associated with the school experienced influenza-like illness, in a period where only 74 confirmed or probable cases were ascertained. If these figures reflect the typical rate of under-reporting in the United States, then the inferred figures from Mexico should increase by >1000/74
14-fold. Likewise, any foreign residents who became ill in Mexico (rather than in their home country) may have been missed in our counts of travelers. In essence, the method used here is a way to estimate cases in a population where they are likely being undercounted, based on travelers to countries in which undercounting, though present, is less severe. Since the inferred number of cases in Mexican residents scales linearly with the number observed in travelers, the number in Mexican residents is likely to be considerably higher than we have estimated.
Forty-eight deaths were observed up to May 9 among laboratory-confirmed cases in Mexico 
. While it might be tempting to calculate a case-fatality proportion by dividing this number by the estimated number of cases in Mexico, such a calculation would likely be misleading, for several reasons. In a growing epidemic, given a significant delay from illness onset to death 
, one expects to underestimate the case-fatality proportion as the deaths reflect cases from an earlier, smaller phase of the epidemic 
. Also, counting only laboratory confirmed deaths is likely to result in a significant underestimation of the true number of deaths, because of insensitivity depending on the timing and adequacy of the specimen, the fact that many severe pneumonia patients were not tested (approximately 1000–2000 such cases typically occur in Mexico in April 
), and the fact that a majority of influenza deaths are attributed to circulatory causes rather than identified as pneumonia or influenza 
. Nonetheless, as the number of deaths accumulates, especially if illness onset dates are available for fatal cases, our estimates may provide an appropriate denominator for revised estimates of the case-fatality proportion. The number of hospitalizations associated with suspect cases was 6,754 as of May 9 
, which combines with our denominator to give a hospitalization proportion of about 2%, closer to figures observed elsewhere.
We have shown in the estimates obtained using only travelers from each country individually. Here, the US-based estimates are the lowest, with greater estimates from those based on Canadians and still greater estimates based on Europeans. In part this may reflect a longer duration of trips for travelers from more distant destinations, but even using the destination-specific duration data does not remove this effect. As we note below, we cannot rule out the possibility that some transmission occurred on airplanes; such transmission might be more likely in travelers flying longer distances. Differences in patterns of exposure within Mexico, chance variation and other factors must account for the remaining differences.
This simple model has several principal limitations. First, we do not incorporate exposure of travelers who arrive by ship or overland, only by air. While we have excluded from the numerator the one traveler case with a known cruise ship exposure, we may have slightly overestimated the incidence in travelers by neglecting such exposures. Second, our calculations make the assumption that incidence is uniform geographically throughout Mexico and across age group. All but one state in Mexico have now reported cases (http://portal.salud.gob.mx/sites/salud/descargas/pdf/influenza/situacion_actual070511.pdf
), and all have at least suspect cases 
, so it is likely reasonable to assume that persons throughout Mexico were exposed to some extent. However, the exposure may not have been uniform. This may be a further reason to consider our estimate as a lower bound, since the detected cases are heavily concentrated in the State of Mexico and the Distrito Federal, the destination of <18% of visitors from these countries, while the most popular airport of entry for visitors from the US, UK and Canada in April 2009 was Cancun, which accounted for 47.5%–74.5% of visitors for each nationality but had relatively low reported incidence. As the pandemic has evolved, it has become clear that different age groups experience different risks of confirmed and probable infection with the pandemic virus, with the highest rates of confirmed and probable infection among persons under 25 years old (http://www.cdc.gov/h1n1flu/surveillanceqa.htm
). Finally, we assume that transmission to travelers occurred in Mexico, not on an aircraft. An influenza outbreak on an aircraft has been documented 
, and if a cluster of such infections were included in our numbers, it would result in an overestimate of incidence in Mexico. Notably, 36% of travel-associated cases in Spain for whom data were available were symptomatic during the inbound flight; given the incubation period of influenza, these travelers, at least, could not plausibly have become infected during the flight 
Our estimates of cases are larger, by about 10-fold, than those reported by Fraser et al. 
. Importantly, this reflects the fact that we base ascertainment on numbers available on May 6–8, while Fraser et al. base ascertainment on numbers available on April 30. With rapid epidemic growth, the difference of one week is likely to account for a difference of perhaps 2-8-fold. Also, Fraser et al. use a longer mean length of stay (9 days) and a larger travel volume. Estimates of the length of stay cited by Fraser et al. 
were close to 9 days in 2001-5 
, and we have considered a sensitivity analysis based on an updated version of that survey, using numbers specific to origin of the travelers. For our primary analysis, however, we used figures from the Ministry of Tourism indicating a mean length of stay of 3.4 days (see Methods
), while an independent study conducted by the National Association of Hotels and Motels finds a similar value of 3.6 days for the mean length of hotel stay by foreign visitors, and a very recent survey found that the majority of US leisure travelers interested in visiting Mexico take vacations for 4 nights or less (personal communication). Our travel volumes are lower in part because we have used citizenship rather than first destination outside Mexico (to better reflect likely final destination) and have used data on number of incoming passengers (corrected to estimate outgoing passengers) rather than flight data, which may perhaps reflect capacities rather than actual numbers. Altogether, these differences in data sources could account for approximately a 3-fold variation in estimates, apart from the variation due to different time periods considered.
Accurate estimation of the magnitude of an emerging epidemic is essential for maintaining situational awareness and determining a rational public health response. The simple approach applied here indicates that the likely number of cases of H1N1 influenza among Mexican residents during the month of April, 2009 was at least two orders of magnitude larger than that detected. While such calculations should not be interpreted as precise estimates of cumulative incidence, they provide important perspective in interpreting data from detected cases in situations where extensive surveillance is unlikely to occur.