Department of Infectious Disease Epidemiology, London School of Hygiene and Tropical Medicine, London, UK

Computational Epidemiology Laboratory, Institute for Scientific Interchange (ISI), Torino, Italy

INSERM, U707, Paris, France

Faculté de Médecine Pierre et Marie Curie, UPMC Université Paris 06, UMR S 707, Paris, France

Institute for Scientific Interchange (ISI), Torino, Italy

Abstract

Background

Confirmed H1N1 cases during late spring and summer 2009 in various countries showed a substantial age shift between importations and local transmission cases, with adults mainly responsible for seeding unaffected regions and children most frequently driving community outbreaks.

Methods

We introduce a multi-host stochastic metapopulation model with two age classes to analytically investigate the role of a heterogeneously mixing population and its associated non-homogeneous travel behaviors on the risk of a major epidemic. We inform the model with demographic data, contact data and travel statistics of Europe and Mexico, and calibrate it to the 2009 H1N1 pandemic early outbreak. We allow for variations of the model parameters to explore the conditions of invasion under different scenarios.

Results

We derive the expression for the potential of global invasion of the epidemic that depends on the transmissibility of the pathogen, the transportation network and mobility features, the demographic profile and the mixing pattern. Higher assortativity in the contact pattern greatly increases the probability of spatial containment of the epidemic, this effect being contrasted by an increase in the social activity of adults vs. children. Heterogeneous features of the mobility network characterizing its topology and traffic flows strongly favor the invasion of the pathogen at the spatial level, as also a larger fraction of children traveling. Variations in the demographic profile and mixing habits across countries lead to heterogeneous outbreak situations. Model results are compatible with the H1N1 spatial transmission dynamics observed.

Conclusions

This work illustrates the importance of considering age-dependent mixing profiles and mobility features coupled together to study the conditions for the spatial invasion of an emerging influenza pandemic. Its results allow the immediate assessment of the risk of a major epidemic for a specific scenario upon availability of data, and the evaluation of the potential effectiveness of public health interventions targeting specific age groups, their interactions and mobility behaviors. The approach provides a general modeling framework that can be used for other types of partitions of the host population and applied to different settings.

Background

The data collected during and after the 2009 H1N1 pandemic has contributed to achieve major insights regarding key factors of the transmission dynamics of the novel strain of influenza. Two aspects emerging from surveillance and serological data during the initial phase of the outbreak became strikingly clear: (i) international movements of passengers by air travel drove the spatial dissemination of the pathogen at the global level

Imported vs. indigenous H1N1 cases and age-specific travel statistics for various countries

**Imported vs. indigenous H1N1 cases and age-specific travel statistics for various countries.** (**A**) Fraction of indigenous cases and of imported cases during the initial phase of the H1N1 pandemic outbreak in the [0–19] years age class, calculated from surveillance data for the following countries: The Netherlands **B**) Percentage of air-travel passengers in the younger age classes for a set of airports around the world. The age classification used by the demographic statistics vary across countries (Helsinki^{1}, Finland; Teheran^{3}, Iran; Los Angeles^{2}, USA; Amsterdam^{5}, The Netherlands; Heathrow^{4}, Gatwick^{4}, Stansted^{4}, Luton^{4}, UK; Venice^{6}, Italy; Hannover^{7}, Frankfurt^{8}, Hamburg^{8}, Munich^{8}, Germany) with the corresponding age brackets for the children class (expressed in years): 1=[0,15]; 2=[0,18]; 3=[0,19]; 4=[0,20]; 5=[0,21]; 6=[0,25]; 7=[0,26]; 8=[0,30]. Sources of the data are reported in the Additional file

**Age-specific contacts and travel patterns in the spatial spread of 2009 H1N1 influenza pandemic.**

Click here for file

The role of children or adults in driving a major epidemic can be assessed with a simplified modeling approach expressed into two age classes and quantifying the probability of temporary extinction of seed individuals in each class depending on their mixing patterns

Methods

Demographic and travel data

We consider a metapopulation framework to simulate the spread of an infectious disease across subpopulations of individuals through mobility connections. The approach is generically applicable to various real-world systems and here we focus on modeling an emerging influenza pandemic across urban areas through air travel. We consider the distinct cases of 8 countries in Europe, and Mexico, for which data needed to inform the model are available.

The network specifying the coupling between different populations in real systems is in many cases very heterogeneous, and examples range from transportation infrastructures to mobility patterns of various type _{
ij
} travelling between any pair of linked airports _{
ij
} along the link connecting airports _{
i
} and _{
j
}
_{
ij
}〉 ∝ (_{
i
}
_{
j
})^{
θ
}, with

Since we are interested in exploring how non-homogeneous travel habits, coupled with non-homogeneous mixing patterns, may drive the conditions for the spatial invasion of an epidemic, we collected age travel statistics across different countries. These are typically obtained from travel surveys at airports, and collect a variety of information about passengers and their travel behavior including demographic data. Figure

Demographic data for the age distribution of the population by country was obtained from Eurostat

Theoretical and data-driven age mixing patterns

In addition to the travel behavior and demographic features of the population, we need to consider the mixing pattern among population classes. For the purpose of the study, we consider data-driven mixing patterns by country

We consider the population divided into two classes, children and adults identified by subscripts

Children are assumed to represent a fraction _{
c
} = _{
a
} = (1 -

We define the contact matrix **
C
** = {

where _{
c
} and _{
c
} are the average number of contacts per unit time established by individuals in the children and adult classes, respectively, and _{
c
} and _{
a
} are the fractions of contacts that occur between individuals of the same age class. The variables _{
c
} and _{
a
} represent a measure of social activity of the individuals, whereas _{
c
} and _{
a
} describe how these contacts are established among classes. A variety of different assumptions can be done to describe the social mixing pattern, as the variables of the contact matrix of the above expression are not uniquely defined and need to be parameterized through available demographic and serologic data _{
c
} (_{
a
}) the average fraction of contacts that a child (adult) establishes with an adult (child), i.e. across age groups, we can simply express _{
c
} (_{
a
}) in terms of _{
c
} (_{
a
}) as _{
c
} = 1 - _{
c
} (_{
a
}
_{a}), thus the contact matrix can be rewritten as

where we have used the relation _{
c
} = _{
a
}/_{
c
}. Interactions are reciprocal such that the number of contacts between children and adults is the same as the number of contacts between adults and children, requiring the matrix to be symmetric, i.e. _{
ca
} = _{
ac
} or _{
c
}
_{
a
}(1 − _{
c
}
_{
a
}(1 −

The matrix is fully expressed in terms of the average number of contacts in the children class, _{
c
}, the fraction of children

Schematic example of different assortativity levels in mixing patterns

**Schematic example of different assortativity levels in mixing patterns.** Throughout the paper we use _{c}**A**: maximum assortativity, corresponding to no mixing between the two classes (_{a} = _{c} = 0); **B**: intermediate assortativity, i.e. a given fraction of the children contacts are directed to adults (like e.g. a random mixing scenario), the others being of the child-child type; **C**: no assortativity in the children age class, as all contacts established by children are directed to the adults class (_{c} = 1 and thus

**Variable**

**Definition**

Children fraction of the population

_{
a
}, _{
c
}

Average number of contacts per unit time established by individuals in the children and adult classes, respectively

_{
a
}/_{
c
}

Ratio of the average number of contacts

_{
c
}
_{
a
}(1 −

Total fraction of contacts across age classes

Children fraction of the traveling population

To compare the theoretical results to realistic situations, we estimate the parameters **
C
** = {

In addition we also informed our model with the mixing patterns for Mexico, obtained from studies on the early outbreak of the 2009 H1N1 pandemic in the country

**Country**

**
ε
**

Belgium

0.21

1.13

0.125

Germany

0.18

0.75

0.098

Finland

0.21

0.79

0.091

Great Britain

0.22

0.75

0.115

Italy

0.17

0.62

0.083

Luxembourg

0.22

0.93

0.107

The Netherlands

0.22

0.83

0.094

Poland

0.21

0.97

0.100

Mexico

0.32

0.32

0.063

Spatial metapopulation model with age structure

We consider a population of individuals that is spatially structured into ^{−γ
} for analytical convenience, mimicking in this way the airline network as drawn from realistic data. Following the scaling properties observed in real-world mobility data, we define the number of individuals moving from the subpopulation of degree ^{'} as _{
kk'} = _{0}(^{'})^{
θ
}. We fix the exponent _{0} to 1.0, based on the empirical findings _{0} are also explored to simulate the implementation of travel-related intervention strategies such as reductions of the travel flows following the start of the outbreak.

We model the travel diffusion process to match the patterns _{
kk'}, assuming that travelers are randomly chosen in the population with the per capita diffusion rate _{
kk '} = _{
kk'}/_{
k
} where _{
k
} is a variable indicating the population size

The variables introduced to define the metapopulation model solely depend on the degree

**Variable**

**Definition**

Degree of a subpopulation, i.e. number of airline connections to other subpopulations

_{
k
}

Total number of subpopulations, number of subpopulations with degree

_{
k
}

Population size of subpopulations with degree

_{
kk '} = _{0}(^{'})^{
θ
}

Number of passengers flying from a subpopulation with degree

_{0}

Mobility scale

_{
kk '} = _{
kk '}/_{
k
}

Diffusion rate of passengers flying from a subpopulation with degree to a subpopulation with degree

The model defined so far considers a single class of individuals who homogeneously mix in the population. Here we introduce the age structure in order to consider different mixing patterns and travel probabilities depending on the age class, based on the results presented in the previous subsections. We consider a simple SIR compartmental model to describe the infection dynamics of the influenza epidemic, where individuals are assigned to mutually exclusive compartments – susceptible (S), infectious (I), and recovered (R) individuals **
R
** = {

Analogously, the per-capita diffusion rate for adults is given by

In the Additional File we also consider a more refined compartmentalization that incorporates a latency period of duration ^{− 1} to account for the time elapsing from exposure to infectiousness. This corresponds to a more accurate approximation for the description of the disease etiology of influenza. Moreover, it also allows us to extend the applicability of our modeling framework to other infectious diseases where this period may last several days, therefore being non-negligible, as in the case of the severe acute respiratory syndrome (SARS)

2009 H1N1 pandemic case study

To clarify the impact of the study’s findings in a practical situation, we apply our framework to the case study of the 2009 H1N1 pandemic influenza. We parameterize the metapopulation model to the available epidemiological estimates of the outbreak, to the demographic and travel statistics, and to the contact pattern data. We assume a fully susceptible population, and consider values of the reproductive number _{0} consistent with the estimations obtained for the pandemic through several methods. In particular, we focus on the range from _{0} = 1.05, corresponding to the lower bound of the estimate obtained from global modeling approaches for the countries in the Northern hemisphere during summer, once seasonal rescaling is taken into account _{0} = 1.2 corresponding to the estimates available for Japan _{0} ∈ [1.4, 1.6] as estimated from the early outbreak data of the H1N1 pandemic

The consideration of _{0} = 1.05 is also important for two additional reasons. First, this value is used here to provide a comparison between the effects that school holidays may have had in the transmission scenario in Europe during Summer 2009 due to the altered contact pattern with respect to school term _{0} for the UK in the range [1.4, 1.6] when schools were open, such reductions would thus correspond to approximately _{0} = 1.05 during school holidays _{0} = 1.05, is also for testing scenarios where a higher value of _{0} may have been reduced following the application of intervention strategies that do not alter the interaction or travel behaviors of individuals, such as e.g. through vaccination or antiviral treatment.

For each value of _{0} considered, the transmission rate ^{− 1} to 2.5 days

In addition to the value _{0} = 1, corresponding to the estimate for the mobility scale regulating the travel fluxes obtained from the air mobility network, we also explore _{0} = 0.5 to simulate the travel-related controls imposed by some countries associated with the self-imposed travel limitations that contributed to a decline of about half the international air traffic to/from Mexico following the international alert in April 2009 (see

Results are obtained for eight European countries for which demographic, travel, and contact data are available, and for Mexico, this latter case informed with the age-dependent transmission matrix of Refs.

We also consider the case of pre-existing immunity in older population and parameterize our model based on the serological evidence indicating that about 30 to 37% of the individuals aged ≥ 60 years had an initial degree of immunity prior to exposure

Results and discussion

Calculation of the global invasion threshold

The reproductive number _{0} provides a threshold condition for a local outbreak in the community; if _{0} > 1 the epidemic will occur and will affect a finite fraction of the local population, otherwise the disease will die out _{0} > 1, the epidemic may indeed fail to spread spatially if the mobility rate is not large enough to ensure the travel of infected individuals to other subpopulations before the end of the local outbreak, or if the amount of seeding cases is not large enough to ensure the start of an outbreak in the reached subpopulation due to local extinction events. All these processes have a clear stochastic nature and they are captured by the definition of an additional predictor of the disease dynamics, _{*} > 1, regulating the number of subpopulations that become infected from a single initially infected subpopulation _{0} at the individual level. An expression for _{*} has been found in the case of metapopulation epidemic models with different types of mobility processes, including homogeneous, traffic-driven, and population-driven diffusion rates _{*}.

Let us consider the invasion process of the epidemic spread at the metapopulation level, by using the subpopulations as our elements of the description of the system. We assume that the outbreak starts in a single initially infected subpopulation of a given degree

The r.h.s. of equation (5) describes the contribution of the subpopulations ^{'} − 1 possible connections along which the infection can spread. The infection from ^{'}); (ii) the reached subpopulations are not yet infected, as indicated by the probability _{
k
} is the number of subpopulations with degree

i.e. the final proportion _{
i
} of the _{
c
} and _{
a
} indicate the attack rates in the children and adult age classes, respectively, and they are given by the solution to _{
c
} and _{
a
} as a function of the reproductive number _{0}, considering the partition of the population in children and adults observed in the 8 European countries of the Polymod dataset

Final size, extinction probability, and global invasion threshold vs. _{0}

**Final size, extinction probability, and global invasion threshold vs. **_{0}**. A**-**B**: Final sizes and extinction probabilities per age class as functions of the reproductive number _{0}. The various curves for the eight European countries under study are shown by means of a shaded area, with the exception of Belgium, see below. The maximum value for the epidemic size in children (and minimum for the epidemic size in adults) is obtained for Italy; the opposite is obtained for Poland. The situation is reversed for the extinction probabilities – the maximum value for the extinction probability in children (and minimum for the extinction probability in adults) is obtained for Poland; the opposite is obtained for Italy. In both plots, Belgium is a standalone example, with _{c} > _{a} and _{c} > _{a}, differently from all other countries and due to the fact that it is the only population in the dataset to have _{0}^{− 1}). **C**: Global invasion threshold _{*} as a function of the reproductive number _{0}, for different values of the parameters describing the mobility process. Air mobility networks having degree distributions ^{− γ} with _{kk '} = _{0}(^{'})^{θ} obtained for

If we indicate with _{
c
} (_{
a
}) the probability of extinction given that a single infected individual of class _{
ij
} of the next generation matrix _{
i
} = [1 + _{
ii
}(1 − _{
i
}) + _{
ji
}(1 − _{
j
})]^{− 1}, with _{0} < 1, the only solution is _{
c
} = _{
a
} = 1, i.e. the epidemic dies off. Otherwise, the system has solutions (_{
c
}, _{
a
}) in the range [0,1], as shown in Figure _{
a
} ranges between 96.5% in the case of Italy and 99% in the case of Poland for _{0} = 1.05, and between 83.5% and 88% for _{0} = 1.2, showing that there were small chances for the H1N1 pandemic outbreak to start in the summer in those countries, in agreement with the observed unfolding _{
c
} is slightly larger than _{
a
}, again induced by the larger average number of contacts in the adult class, differently from all other countries for which the data is available. Finally, in the case of homogeneous mixing in a non-partitioned population, we recover the probability of extinction to be equal to _{0}
^{−1} (dashed line in the figure).

The quantities reported in panels A,B of Figure _{0} close to 1), introduced or emerged in the system through a localized seeding event (so that the number of infected subpopulations can be neglected at the early stage of the spatial invasion), and considering the case of a mobility network lacking topological correlations (in this approximation the conditional probability ^{'}) can be simplified, see the Additional file

thus defining the global invasion threshold of the metapopulation system. Equation (7) defines the threshold condition for the global invasion: if _{*} assumes values larger than 1, the epidemic starting from a given subpopulation will reach global proportion affecting a finite fraction of the subpopulations of the system; if instead _{*} < 1, the epidemic will be contained at its source and will not spread further to other locations. The global invasion threshold is a complex function of the disease history parameters, and of the parameters describing the age-specific mixing patterns and travel behavior through _{
c
}, _{
a
}, _{
c
}, _{
a
}. Its dependence on the population spatial structure is embodied by travel fluxes and the topology of the mobility network, through _{0}, ^{
a
}〉. However it is important to note that this indicator does not depend on the number of subpopulations _{*} on these multiple factors, examine their role in driving the pandemic extinction or invasion, and provide possible applications examples for a set of countries considering the 2009 H1N1 pandemic.

Impact of air mobility

The term _{0}(^{2 + 2 θ
} − ^{1 + 2 θ
})/_{0} and ^{− γ
}. The large degree fluctuations found in real transportation systems and mobility patterns _{*} to considerable high values, even when small values of the reproductive number are considered. Figure _{*} on the reproductive number accounting for changes in the topological heterogeneity of the mobility network (^{2 + 2 θ
} − ^{1 + 2 θ
})/_{*} ranging from ~10 for _{0} = 1.05 up to approximately 10^{3} for _{0} = 2, a value of the reproductive number consistent with the estimate for the 1918–1919 pandemic _{*} > 1, the absolute value of the estimator _{*} provides a quantitative indication of the effective reduction that needs to be reached through public health interventions in order to bring _{*} below its threshold value, i.e. the difference _{*} − 1. The _{*} values for _{0} in the case of larger heterogeneities in the air mobility patterns (

For both network topologies considered, the epidemic is above the threshold value of 1, and the outbreak is predicted to spread globally in the system for all diseases considered (_{0} ≥ 1.05), consistently with the H1N1 influenza virus invasion at the global level. The partition into classes, though lowering the epidemic sizes and increasing the probability of extinction ^{2 + 2 θ
} − ^{1 + 2 θ
})/_{*} is so large that it cannot be easily counterbalanced by reductions of the mobility scale _{0} corresponding to interventions through air travel restrictions. This was already observed in numerical results obtained from data-driven modeling approaches and in analytical predictions based on simple homogeneous mixing among individuals within the subpopulation of the system

Epidemic containment is instead reached for _{0} < 1.2 when exploring homogeneous traffic flows (i.e.

Impact of the contacts ratio

The global invasion threshold is a function of the extinction probabilities and of the epidemic sizes per age class for which an explicit solution cannot be obtained in the general case. An approximate solution can be recovered for small _{
a
}/_{
c
}:

Besides these two limit cases, we investigate in Figure _{*} as a function of the contacts ratio

Impact of contacts ratio

**Impact of contacts ratio **** η.**Global invasion threshold

The global invasion threshold is predicted to increase with _{*} reaches its critical level for relatively small values of _{0} < 1.2 (Figure

Countries characterized by particularly low values of

Finally, we report on the effects of the inclusion of the latency period in the compartmental model. The results reported in the Additional file _{*}, while keeping the qualitative picture unchanged (Additional file

Impact of assortativity and age profile

We now examine the dependence of the critical condition for the global invasion on the assortativity level of the population partition, by plotting in Figure _{*} as a function of the parameters _{*} is an increasing function of the across-groups mixing

Impact of assortativity and of school term vs. school holidays

**Impact of assortativity and of school term vs. school holidays.** Global invasion threshold _{*} as a function of the across-groups mixing _{0} = 1.05, panel **A**) and school term (_{0} = 1.4, panel **B**), based on contact data in the UK _{*} < 1, whereas the colored area refers to the region of the parameter phase space that is above the threshold condition. The rectangular box indicates the area corresponding to the European intervals for the parameters

The rectangle shown in the panels indicates the ranges of the country values for _{*} with respect to a variation of

The two panels differ for the value of the reproductive number considered that takes into account the effective reduction in the transmission potential observed during school holidays (panel A, corresponding to _{0} = 1.05) with respect to school term (panel B, _{0} = 1.4). These values are estimated for the UK on the basis of contact data for the country in the two periods

Additional countries with similar age profile may be mapped onto the two-dimensional plots of Figure

If we assume that children travel according to the statistics obtained from travel data (i.e. _{*}, as expected, given that a fraction of the individuals driving the local outbreaks also represent potential seeds in new locations not yet affected by the epidemic (see Figure

Impact of age-specific travel behavior and age profile

**Impact of age-specific travel behavior and age profile. A**: Global invasion threshold _{*} as a function of the across-groups mixing _{0} = 1.05. The solid colored lines correspond to the cases when only adults travel (_{*} = 1. **B**: Global invasion threshold _{*} as a function of the across-groups mixing _{0} = 1.05 and _{0} = 1.4, assuming

Besides mixing patterns and travel statistics, countries also differ for their age profiles (considered in the model through the parameter _{0} = 1.05). Remarkably, the increase of the fraction of children and the change in the contact ratio, with no change in the across-groups mixing pattern (i.e. same

In the case of _{0} = 1.4, i.e. the lower bound of the estimate of the reproductive number for Mexico based on the early outbreak of the 2009 H1N1 pandemic

Effect of pre-existing immunity and travel reductions

If we consider pre-existing immunity in the population, calculating the fraction of individuals in the adult age class that corresponds to the estimated values from serological data available after the 2009 H1N1 pandemic _{*} = 1 in the _{*} = 1; a larger mixing across age classes is therefore needed for the pathogen to spatially propagate in case a fraction of the older age class is immune, whereas a more assortative population is predicted to be able to contain the emerging epidemic. The effect is very small for the case of Mexico, while for Europe it is more visible given that the considered European population is, on average, older than the Mexican one, and thus a larger fraction of the adult population is assumed to be immune in Europe with respect to Mexico (9.6% in Europe vs. 4.4% in Mexico). The points (_{0} ≥ 1.2 in Europe and _{0} ≥ 1.4 in Mexico.

Case with immunity

**Case with immunity.** Threshold condition _{*} = 1 as a function of the across-groups mixing **A**) and Mexico (panel **B**): comparison of the no-immunity case with the case of pre-existing immunity and of travel reduction, modeled by setting _{0} = 0.5, consistently with the empirically observed drop to/from Mexico during the early stage of the 2009 H1N1 pandemic _{0} = 1.2 in Europe and _{0} = 1.4 in Mexico, i.e. the lower bound of the reproductive number estimated for the country from the initial outbreak data

As an additional factor, we also consider the effect resulting from the application of travel reductions. We simulate the travel controls applied by some countries in addition to the self-reaction of the population avoiding travel to the affected area that was observed during the early stage of the 2009 H1N1 pandemic _{0} = 0.5, i.e. a uniform reduction along all travel connections, independently of the age of travelers. Such reductions reduce the phase space of parameters leading to global invasion, as expected, however they would not be able to lead to a containment of the disease once the model is fitted to the Mexican and European data and to the H1N1 pandemic scenario, confirming previous findings

Limitations of the study

Our study is based on a multi-host stochastic metapopulation model that considers several simplifying assumptions that we discuss in this subsection.

The partition of the population into children and adult classes is clearly very schematic, especially if we consider that finer level classifications are available for demographic data at the global scale, and for contacts data, though in a very small set of countries that are the ones considered in this study. Similar considerations arise in the case of additional heterogeneities to be included in the model, as for instance differing patterns of transmission between households, schools, and workplace settings. A higher level of structuring of the population into classes is expected to decrease the epidemic sizes per comparable groups of classes, and to increase the probability of extinction of the epidemic, with respect to our predictions (see for instance the discussions in

Another assumption concerns the exponentially distributed infectious period. More realistic descriptions of the infectious period – including constant, gamma-distributed or data-driven infectious periods – were found to alter the model results by reducing the probability of extinction. Such findings were however obtained in a single population model with homogeneous mixing

Our analytical approach also assumes that the importation or the emergence of an infectious disease is highly localized at the beginning of the outbreak, so that it is possible to approximate the spatial spreading process in terms of a branching process evolving in a set of subpopulations not yet affected by the disease. This is similar to the approximations used to calculate the basic reproductive number in a fully susceptible population, and it is required to treat the model analytically. While this assumption can generally be considered as a good approximation to describe the early phase of an outbreak, more complicated seeding events may occur that would require numerical approaches able to explicitly take into account the initial conditions and assess the epidemic risks.

Our model is fit to demographic statistics of a set of countries and it is informed with H1N1 epidemic estimates to provide quantitative information on the risk for the pandemic invasion in such countries. However, in all our predictions we assume the same population structure (_{
i
}, _{
i
}, _{
i
}, _{
i
}} (with

Recent work relying on large-scale transmission models has explored the ability of these approaches to predict the timing of spread of the 2009 A/H1N1 influenza pandemic around the world

Finally, we note that changes in time of population behavior as a response to the ongoing outbreak cannot be dynamically incorporated in the model. These may refer for example to changes in the contact patterns due to self-awareness or changes at the community level due to the implementation of intervention strategies to control the epidemic

Conclusions

The 2009 H1N1 pandemic represents an example of the important role that age classes have on the local and global spread of the disease during its early stage; the local outbreaks being mainly driven by children leading to epidemics in schools, whereas the adults were mainly responsible for the international dissemination by means of air travel. We introduced and solved a multi-host stochastic metapopulation model to quantify these aspects and characterize the conditions of the population partition and heterogeneous travel behavior that lead to the pandemic global invasion. Notwithstanding the high level of assortativity observed in contact patterns data by age, that increase the probability of pandemic extinction, the model explains the spread at the global level observed in the 2009 H1N1 pandemic as induced by the interplay between the heterogeneity of the air mobility network structure, favoring the spread, and the population partition. A major epidemic is always achieved for _{0} ≥ 1.2 even in the case children are assumed not to travel, when the model is parameterized with European countries data and statistics. Results are also consistent with the occurrence of sporadic outbreaks in continental Europe during summer 2009 and widespread transmission in the UK, once the model is informed with the substantial reduction in transmission associated to school holidays.

Despite the presence of various other epidemiological factors that may influence the epidemic outcome, our results suggest that the variations of demographic and mixing profiles across countries are an important source of heterogeneity in the epidemic outcome. This applies in particular to the contacts ratio that is observed to vary significantly and to have a large impact on the invasion potential. Such findings calls for the need to develop further studies in order to identify the social factors that affect this parameter and design targeted interventions, such as work-related measures, that may lower it, thus reducing the risk of an outbreak.

Given the availability of data regarding demographic, mixing and travel profiles, the model results can be used to assess the risks of a given outbreak scenario in a specific country for a newly emerging pathogen. Collecting data on population partitions and mixing matrices or developing alternative methods to estimate the contact patterns based on the demographic information available

Though based on simplifying assumption, the model is able to account for the heterogeneities in the spatial distribution of the population, in the mixing patterns and in the travel behavior, and provide a solution to assess the risk of a major epidemic. We considered a definition for the children age class up to 15 or 18 years old, justified by the available data and statistics, however the approach is transparent to this choice and analogous results to the ones presented can be reached by informing the model with a different definition of classes, as long as statistics informing the groups-specific parameters

Competing interests

All authors declare that no competing interest exists.

Authors’ contributions

AA, CP, and VC have all contributed to conceive, design and carry out the study and draft the manuscript. All authors approved the final version of the manuscript.

Acknowledgments

The authors would like to thank Niel Hens for providing us the daily contact data of the POLYMOD study and for his useful comments; Caterina Rizzo for the age profile of the laboratory confirmed cases in Italy during summer 2009; Stephen Eubank for providing us the synthetic contact data for Portland; and Jose J Ramasco and Pablo Jensen for useful discussions. This work has been partially funded by the ERC Ideas contract no. ERC-2007-Stg204863 (EPIFOR) and the EC-Health contract no. 278433 (PREDEMICS) to VC and CP; the EU-FP7 contract no. 231807 (EPIWORK) to AA; the ANR contract no. ANR-12-MONU-0018 (HARMSFLU) to VC.

Pre-publication history

The pre-publication history for this paper can be accessed here: