remarkable feature which is unpredicted by many traditional models for the evolution of infectious diseases. This finding bring to mind a previous study on the distribution of epidemic events in isolated populations [13]. In both cases, the cumulative distribu- tion of events follows a power law behavior, with exponent a,0.3 for isolated populations and 0.035,a,0.40 for the 2009 influenza pandemic. A possible factor contributing to the observed scale invariance is human mobility - which has been considered a fundamental ingredient for infectious diseases to spread rapidly through the world population [14–16]. Human mobility may alter the evolution of local epidemics, with the entry of new infectious individuals in a given region, causing a non-local effect [17]. Surprisingly, human travel exhibits scaling laws such as the power law distribution that we find for influenza pandemics [14]. Therefore, it is natural to consider human mobility, including the air traffic in the worldwide air-transportation network, as a possible mechanism contributing for the power law behavior shown in Fig. 2A. In contrast, other factors may contribute for the deviation from power law behavior observed for larger times. Country-based contingency plans, for example, have been implemented in order to control the international spread of influenza pandemic. Studies have estimated the impact of restricting international travel and imposing entry or exit screening of passengers at airports [18]. Other local contingency plans, which may be a function of the country’s level of preparedness to deal with the pandemic, have been implemented in order to reduce the spread of influenza infections [17]. In addition, it is well known that seasonality and weather conditions, such as temperature and relative humidity, affect the dynamics of influenza transmission [19–20]. We cannot discard the possibility that such factors, which can largely vary Spreading Patterns of the Influenza A from country to country, may contribute towards changing the shape of the cumulative distribution of cases among countries. Our findings suggest a crossover in the shape of the cumulative distribution of cases among countries - from power law for initial times to log-normal for larger times. However, we remark that a log-normal distribution can be mistaken locally for a power law. In fact, a log-normal distribution can mimic a power law over a relatively large interval. Concerning its origin, typically log-normal forms underlie random multiplicative process [12] – a pure random multiplicative process is defined as yðtz1Þ~lðtÞyðtÞ, being lðtÞ a random number. Thus, factors such as the ones described above may be acting in a multiplicative way in the dynamics of influenza pandemic. This may be a possible origin of the log-normal behavior or R(y) observed for large times. Next we present an alternative way to interpret our empirical findings. We compare our results with the predictions of a simple stochastic model. Let us consider that the number of cases in a given country follows a process given by the rule yðtz1Þ~yðtÞzlðtÞyðtÞ, 3 ð Þ Where y(t+1) and y(t) are the number of cases in the times t+1 and t respectively, and lðtÞ is a random number following an exponential distribution with mean m. Each country evolves independently of the others countries. The system evolves starting from a given initial condition – for example, a particular number of countries with y(t = 0) = 1. For each time step two new countries are added to the system, each one with probability p. The rule described in Eq. 3 indicates that the number of cases in the time t+1 depends of the number of cases in the time t. This assumption is compatible with the dynamics of an infectious Figure 4. Simulation of the stochastic model. The model is given by Eq. (3), with m~ 1 and p = 0.85. Initial condition: there are only one country 24 with y(t = 0) = 1. (A) Temporal evolution of the total number of confirmed cases, Y(t), on mono-log scale, for time steps from 1 to 70. The solid line is given by Y (t)*exp(lt), with l = 0.05. (B) Temporal evolution of the total number of countries with confirmed cases, W(t), for the same time steps. The solid line is W (t)*1:7t. (C) Cumulative distribution, R(y), for t = 10 steps (squares), t = 30 (up triangles), t = 50 (down triangles) and t = 70 (circles). For comparison, we show a power law given by Eq. (1), for t = 10, and a lognormal curve given by Eq. (2) for t = 10 steps. doi:10.1371/journal.pone.0017823.g004 PLoS ONE | www.plosone.org 3 March 2011 | Volume 6 | Issue 3 | e17823