Human mobility networks, travel restrictions, and the global spread of 2009 H1N1 pandemic

Abstract

After the emergence of the H1N1 influenza in 2009, some countries responded with travel-related controls during the early stage of the outbreak in an attempt to contain or slow down its international spread. These controls along with self-imposed travel limitations contributed to a decline of about 40% in international air traffic to/from Mexico following the international alert. However, no containment was achieved by such restrictions and the virus was able to reach pandemic proportions in a short time. When gauging the value and efficacy of mobility and travel restrictions it is crucial to rely on epidemic models that integrate the wide range of features characterizing human mobility and the many options available to public health organizations for responding to a pandemic. Here we present a comprehensive computational and theoretical study of the role of travel restrictions in halting and delaying pandemics by using a model that explicitly integrates air travel and short-range mobility data with high-resolution demographic data across the world and that is validated by the accumulation of data from the 2009 H1N1 pandemic. We explore alternative scenarios for the 2009 H1N1 pandemic by assessing the potential impact of mobility restrictions that vary with respect to their magnitude and their position in the pandemic timeline. We provide a quantitative discussion of the delay obtained by different mobility restrictions and the likelihood of containing outbreaks of infectious diseases at their source, confirming the limited value and feasibility of international travel restrictions. These results are rationalized in the theoretical framework characterizing the invasion dynamics of the epidemics at the metapopulation level.

Figure 1. Modeling the 2009 H1N1 pandemic spread with GLEaM.

A, Illustration of the global invasion of the 2009 H1N1 pandemic during the early stage of the outbreak. The arrows represent the seeding of unaffected countries due to infected individuals traveling from Mexico. The color code indicates the time of the seeding. The map shows the layer of the worldwide air transportation network, which is incorporated into GLEaM. B, Compartmental structure in each subpopulation of GLEaM. Each individual is classified by one of the following discrete states: susceptible, latent, symptomatic infectious who can travel, symptomatic infectious who are hampered in their travels by the severity of the illness, asymptomatic infectious, and permanently recovered/removed , . We assume that the latency period is equivalent to the incubation period and that no secondary transmissions occur during the incubation period. In addition, the asymptomatic individuals are assumed to be less infectious with respect to the symptomatic ones, with a relative infectiousness r_β, that is half the infectiousness of symptomatic individuals. All parameter values are reported in Table 3 of the SI.

Figure 2. Importation of cases.

A,B, Simulation results of the fraction Q of imported cases in United Kingdom (A) and Germany (B). The quantity Q is a measure of the relative weight of case importation with respect to local transmission events. The gray shaded areas show the 95% and 50% reference ranges of the simulation results obtained from 2,000 stochastic realizations. The surveillance data are indicated by red dots. C,D, Time evolution from April to November 2009 in the United Kingdom (C) and Germany (D) of the probability distribution to observe in any given realization of the epidemic the ratio Q between imported cases and the total number of cases. The probability distribution is obtained from the simulation of 2,000 stochastic realizations. Large values for the quantity Q are observed with high probability only in the early phase of the respective country's epidemic. The observed non-zero probability for a fraction of imported cases equal to zero at the early stage is due to the fact that the epidemic is imported in some cases by non-detectable individuals, such as latent and asymptomatic infectious individuals.

Figure 3. Effects of restrictions in the air travel to/from Mexico on the probability distributions of the seeding events.

Travel measures imposing a reduction of and are compared to the reference scenario where the observed drop in air travel to/from Mexico is taken into account. A,B, Probability distributions of the arrival time (defined as the date of arrival of the first symptomatic case) in the United Kingdom (A) and Germany (B) for different values of . Here we consider the importation from any possible source country, not only Mexico. The vertical dotted line indicates the observed arrival time in the country, as obtained from official reports, and the vertical solid line indicates the starting date of the travel restrictions, April 25, 2009, the day after the international alert. The probability distributions are obtained from 2,000 stochastic realizations and data are binned over 7 days. Even when imposing , the peak of the probability distribution is not delayed with respect to the real scenario. C,D, Cumulative probability distributions of the first seeding event from Mexico to the United Kingdom (C) and Germany (D) for different values of . Here we consider any source of infection in the seeding event, including symptomatic cases and non-detectable infected cases, such as latent and asymptomatic, as allowed by the computational approach. The distributions are computed over 2,000 stochastic realizations. The effect of travel restrictions is very limited in delaying the time at which the cumulative distribution reaches the unit.

Figure 4. Delaying effects in the international spread.

A, Delay in the case importation from Mexico to a given country compared with the reference scenario as a function of the travel reduction . The delay is measured in terms of the date at which the cumulative distribution of the seeding from Mexico (see Figure 2) reaches 90%. The dotted line shows the logarithmic behavior relating the delay as a function of the imposed restrictions. The largest delay, gained when imposing , is less than 20 days for all countries. The model also considers the implementation of sanitary interventions in Mexico during the early stage that was able to damp the exponential increase of cases in the outbreak zone. Travel restrictions would therefore lead to a larger impact during this phase due to the mitigating effect on the local epidemic. If a country is seeded during this phase, the resulting delay induced by the travel restrictions would be larger, thus creating the observed differences in the resulting delays by country. B, as in A, where earlier dates for the start of the intervention are considered, has a fixed : April 25, corresponding to the day after the international alert; April 16, corresponding to the epidemic alert in Mexico; March 28, corresponding to the onset of symptoms of the first case in the US; and 6 weeks before the international alert. In all these scenarios and for different countries, the delay is always less than 20 days, highlighting that even the enforcement of strong travel reduction as early as possible would have had little effect.

Figure 5. Network heterogeneity and failure of travel restrictions aimed at containment.

A, Schematic illustration of the simplified modeling framework based on a metapopulation scheme. At the macroscopic level the system is composed of a heterogeneous network of subpopulations. At the microscopic level, each subpopulation contains a population of individuals. The infection dynamics are described by a simple compartmentalization (compartments are indicated by different colored dots in the picture). Within each subpopulation, individuals are mixed homogeneously and can migrate from one subpopulation to another following the mobility connections of the network. In this way the disease can spread at the subpopulations level. B, Plot of the global invasion threshold R_* described by Eq. (2). Here, R_* is plotted as a function of the basic reproductive number R₀ and the traffic reduction , which is the parameter representing the percentage of variation in the total traffic in Eq. (2). Only in the case of extremely low values of R₀ or extremely large values of is it possible to reduce R_* below the threshold.