The global transmission and control of influenza

New strains of influenza spread around the globe via the movement of infected individuals. The global dynamics of influenza are complicated by different patterns of influenza seasonality in different regions of the world. We have released an open-source stochastic mathematical model of the spread of influenza across 321 major, strategically located cities of the world. Influenza is transmitted between cities via infected airline passengers. Seasonality is simulated by increasing the transmissibility in each city at the times of the year when influenza has been observed to be most prevalent. The spatiotemporal spread of pandemic influenza can be understood through clusters of global transmission and links between them, which we identify using the epidemic percolation network (EPN) of the model. We use the model to explain the observed global pattern of spread for pandemic influenza A(H1N1) 2009-2010 (pandemic H1N1 2009) and to examine possible global patterns of spread for future pandemics depending on the origin of pandemic spread, time of year of emergence, and basic reproductive number (). We also use the model to investigate the effectiveness of a plausible global distribution of vaccine for various pandemic scenarios. For pandemic H1N1 2009, we show that the biggest impact of vaccination was in the temperate northern hemisphere. For pandemics starting in the temperate northern hemisphere in May or April, vaccination would have little effect in the temperate southern hemisphere and a small effect in the tropics. With the increasing interconnectedness of the world's population, we must take a global view of infectious disease transmission. Our open-source, computationally simple model can help public health officials plan for the next pandemic as well as deal with interpandemic influenza.     

Climatic similarity and biological exchange in the worldwide airline transportation network

Recent increases in the rates of biological invasion and spread of infectious diseases have been linked to the continued expansion of the worldwide airline transportation network (WAN). Here, the global structure of the WAN is analysed in terms of climatic similarity to illuminate the risk of deliberate or accidental movements of climatically sensitive organisms around the world. From over 44,000 flight routes, we show, for each month of an average year, (i) those scheduled routes that link the most spatially distant but climatically similar airports, (ii) the climatically best-connected airports, and (iii) clusters of airports with similar climatic features. The way in which traffic volumes alter these findings is also examined. Climatic similarity across the WAN is skewed (most geographically close airports are climatically similar) but heavy-tailed (there are considerable numbers of geographically distant but climatically similar airports), with climate similarity highest in the June-August period, matching the annual peak in air traffic. Climatically matched, geographically distant airports form subnetworks within the WAN that change throughout the year. Further, the incorporation of passenger and freight traffic data highlight at greater risk of invasion those airports that are climatically well connected by numerous high capacity routes.     

Size Matters: Concurrency and the Epidemic Potential of HIV in Small Networks

Background

Generalized heterosexual epidemics are responsible for the largest share of the global burden of HIV. These occur in populations that do not have high rates of partner acquisition, and research suggests that a pattern of fewer, but concurrent, partnerships may be the mechanism that provides the connectivity necessary for sustained transmission. We examine how network size affects the impact of concurrency on network connectivity.

Methodology/Principal Findings

We use a stochastic network model to generate a sample of networks, varying the size of the network and the level of concurrency, and compare the largest components for each scenario to the asymptotic expected values. While the threshold for the growth of a giant component does not change, the transition is more gradual in the smaller networks. As a result, low levels of concurrency generate more connectivity in small networks.

Conclusions/Significance

Generalized HIV epidemics are by definition those that spread to a larger fraction of the population, but the mechanism may rely in part on the dynamics of transmission in a set of linked small networks. Examples include rural populations in sub-Saharan Africa and segregated minority populations in the US, where the effective size of the sexual network may well be in the hundreds, rather than thousands. Connectivity emerges at lower levels of concurrency in smaller networks, but these networks can still be disconnected with small changes in behavior. Concurrency remains a strategic target for HIV combination prevention programs in this context.     

The impact of seasonal and year-round transmission regimes on the evolution of influenza A virus

Punctuated antigenic change is believed to be a key element in the evolution of influenza A; clusters of antigenically similar strains predominate worldwide for several years until an antigenically distant mutant emerges and instigates a selective sweep. It is thought that a region of East-Southeast Asia with year-round transmission acts as a source of antigenic diversity for influenza A and seasonal epidemics in temperate regions make little contribution to antigenic evolution. We use a mathematical model to examine how different transmission regimes affect the evolutionary dynamics of influenza over the lifespan of an antigenic cluster. Our model indicates that, in non-seasonal regions, mutants that cause significant outbreaks appear before the peak of the wild-type epidemic. A relatively large proportion of these mutants spread globally. In seasonal regions, mutants that cause significant local outbreaks appear each year before the seasonal peak of the wild-type epidemic, but only a small proportion spread globally. The potential for global spread is strongly influenced by the intensity of non-seasonal circulation and coupling between non-seasonal and seasonal regions. Results are similar if mutations are neutral, or confer a weak to moderate antigenic advantage. However, there is a threshold antigenic advantage, depending on the non-seasonal transmission intensity, beyond which mutants can escape herd immunity in the non-seasonal region and there is a global explosion in diversity. We conclude that non-seasonal transmission regions are fundamental to the generation and maintenance of influenza diversity owing to their epidemiology. More extensive sampling of viral diversity in such regions could facilitate earlier identification of antigenically novel strains and extend the critical window for vaccine development.     

On recombination-induced multiple and simultaneous coalescent events

Coalescent theory deals with the dynamics of how sampled genetic material has spread through a population from a single ancestor over many generations and is ubiquitous in contemporary molecular population genetics. Inherent in most applications is a continuous-time approximation that is derived under the assumption that sample size is small relative to the actual population size. In effect, this precludes multiple and simultaneous coalescent events that take place in the history of large samples. If sequences do not recombine, the number of sequences ancestral to a large sample is reduced sufficiently after relatively few generations such that use of the continuous-time approximation is justified. However, in tracing the history of large chromosomal segments, a large recombination rate per generation will consistently maintain a large number of ancestors. This can create a major disparity between discrete-time and continuous-time models and we analyze its importance, illustrated with model parameters typical of the human genome. The presence of gene conversion exacerbates the disparity and could seriously undermine applications of coalescent theory to complete genomes. However, we show that multiple and simultaneous coalescent events influence global quantities, such as total number of ancestors, but have negligible effect on local quantities, such as linkage disequilibrium. Reassuringly, most applications of the coalescent model with recombination (including association mapping) focus on local quantities.     

Disease Interventions Can Interfere with One Another through Disease-Behaviour Interactions

Theoretical models of disease dynamics on networks can aid our understanding of how infectious diseases spread through a population. Models that incorporate decision-making mechanisms can furthermore capture how behaviour-driven aspects of transmission such as vaccination choices and the use of non-pharmaceutical interventions (NPIs) interact with disease dynamics. However, these two interventions are usually modelled separately. Here, we construct a simulation model of influenza transmission through a contact network, where individuals can choose whether to become vaccinated and/or practice NPIs. These decisions are based on previous experience with the disease, the current state of infection amongst one''s contacts, and the personal and social impacts of the choices they make. We find that the interventions interfere with one another: because of negative feedback between intervention uptake and infection prevalence, it is difficult to simultaneously increase uptake of all interventions by changing utilities or perceived risks. However, on account of vaccine efficacy being higher than NPI efficacy, measures to expand NPI practice have only a small net impact on influenza incidence due to strongly mitigating feedback from vaccinating behaviour, whereas expanding vaccine uptake causes a significant net reduction in influenza incidence, despite the reduction of NPI practice in response. As a result, measures that support expansion of only vaccination (such as reducing vaccine cost), or measures that simultaneously support vaccination and NPIs (such as emphasizing harms of influenza infection, or satisfaction from preventing infection in others through both interventions) can significantly reduce influenza incidence, whereas measures that only support expansion of NPI practice (such as making hand sanitizers more available) have little net impact on influenza incidence. (However, measures that improve NPI efficacy may fare better.) We conclude that the impact of interference on programs relying on multiple interventions should be more carefully studied, for both influenza and other infectious diseases.     

Analysis of México’s Narco-War Network (2007–2011)

Since December 2006, more than a thousand cities in México have suffered the effects of the war between several drug cartels, amongst themselves, as well as with Mexican armed forces. Sources are not in agreement about the number of casualties of this war, with reports varying from 30 to 100 thousand dead; the economic and social ravages are impossible to quantify. In this work we analyze the official report of casualties in terms of the location and the date of occurrence of the homicides. We show how the violence, as reflected by the number of casualties, has increased over time and spread across the country. Next, based on the correlations between cities in the changes of the monthly number of casualties attributed to organized crime, we construct a narco-war network where nodes are the affected cities and links represent correlations between them. We find that close geographical distance between violent cities does not imply a strong correlation amongst them. We observe that the dynamics of the conflict has evolved in short-term periods where a small core of violent cities determines the main theatre of the war at each stage. This kind of analysis may also help to describe the emergence and propagation of gang-related violence waves.     

Evolutionary analysis of inter-farm transmission dynamics in a highly pathogenic avian influenza epidemic

Phylogenetic studies have largely contributed to better understand the emergence, spread and evolution of highly pathogenic avian influenza during epidemics, but sampling of genetic data has never been detailed enough to allow mapping of the spatiotemporal spread of avian influenza viruses during a single epidemic. Here, we present genetic data of H7N7 viruses produced from 72% of the poultry farms infected during the 2003 epidemic in the Netherlands. We use phylogenetic analyses to unravel the pathways of virus transmission between farms and between infected areas. In addition, we investigated the evolutionary processes shaping viral genetic diversity, and assess how they could have affected our phylogenetic analyses. Our results show that the H7N7 virus was characterized by a high level of genetic diversity driven mainly by a high neutral substitution rate, purifying selection and limited positive selection. We also identified potential reassortment in the three genes that we have tested, but they had only a limited effect on the resolution of the inter-farm transmission network. Clonal sequencing analyses performed on six farm samples showed that at least one farm sample presented very complex virus diversity and was probably at the origin of chronological anomalies in the transmission network. However, most virus sequences could be grouped within clearly defined and chronologically sound clusters of infection and some likely transmission events between farms located 0.8-13 Km apart were identified. In addition, three farms were found as most likely source of virus introduction in distantly located new areas. These long distance transmission events were likely facilitated by human-mediated transport, underlining the need for strict enforcement of biosafety measures during outbreaks. This study shows that in-depth genetic analysis of virus outbreaks at multiple scales can provide critical information on virus transmission dynamics and can be used to increase our capacity to efficiently control epidemics.     

Credit or debit? Resource input changes population dynamics of city-slicker birds

The underlying evolutionary mechanisms of urban bird populations have hardly been studied. High food density and low predation risk serve to explain the global pattern of extremely high urban bird population densities. Both these bottom-up and top-down effects are paradoxical since the per capita amount of food is small due to competition, and domestic predator density is high in cities. The bottom-up paradox can be resolved by taking into account the high food resource-predictability in cities. Concerning the top-down effect, recent studies suggest that at least when it comes to nest predation the effect of cats is minor. I suggest that the combination of high food predictability and low predation risk in cities alter bird foraging behaviour, which in turn affects population dynamics. In terms of density, the result is that bird populations exceed the carrying capacity of the urban environment, costing heavily on body condition and/or life span. Under such conditions the population should consist of a few winners and many losers. Only the winners have sufficient access to food resources and the opportunity to reproduce. The highly predictable continuous input of food in the urban environment allows them to "live on their credit". They may trade off between offspring body condition and clutch size. In the lack of predation, the losers among the fledglings may survive for a relatively long period, getting just enough energy to survive. Though they may never become healthy enough to reproduce, they will have a major contribution to the observed population density. Results of several case studies seem to support the credit card hypothesis and suggest that it can serve as a general rule for the evolution of animal populations and communities in highly predictable human managed environments.     

Network structure and city size

Network structure varies across cities. This variation may yield important knowledge about how the internal structure of the city affects its performance. This paper systematically compares a set of surface transportation network structure variables (connectivity, hierarchy, circuity, treeness, entropy, accessibility) across the 50 largest metropolitan areas in the United States. A set of scaling parameters are discovered to show how network size and structure vary with city size. These results suggest that larger cities are physically more inter-connected. Hypotheses are presented as to why this might obtain. This paper then consistently measures and ranks access to jobs across 50 US metropolitan areas. It uses that accessibility measure, along with network structure variables and city size to help explain journey-to-work time and auto mode share in those cities. A 1 percent increase in accessibility reduces average metropolitan commute times by about 90 seconds each way. A 1 percent increase in network connectivity reduces commute time by 0.1 percent. A 1 percent increase in accessibility results in a 0.0575 percent drop in auto mode share, while a 1 percent increase in treeness reduces auto mode share by 0.061 percent. Use of accessibility and network structure measures is important for planning and evaluating the performance of network investments and land use changes.     

What would it take to describe the global diversity of parasites?

How many parasites are there on Earth? Here, we use helminth parasites to highlight how little is known about parasite diversity, and how insufficient our current approach will be to describe the full scope of life on Earth. Using the largest database of host–parasite associations and one of the world’s largest parasite collections, we estimate a global total of roughly 100 000–350 000 species of helminth endoparasites of vertebrates, of which 85–95% are unknown to science. The parasites of amphibians and reptiles remain the most poorly described, but the majority of undescribed species are probably parasites of birds and bony fish. Missing species are disproportionately likely to be smaller parasites of smaller hosts in undersampled countries. At current rates, it would take centuries to comprehensively sample, collect and name vertebrate helminths. While some have suggested that macroecology can work around existing data limitations, we argue that patterns described from a small, biased sample of diversity aren’t necessarily reliable, especially as host–parasite networks are increasingly altered by global change. In the spirit of moonshots like the Human Genome Project and the Global Virome Project, we consider the idea of a Global Parasite Project: a global effort to transform parasitology and inventory parasite diversity at an unprecedented pace.     

Identifying Communities and Key Vertices by Reconstructing Networks from Samples

Sampling techniques such as Respondent-Driven Sampling (RDS) are widely used in epidemiology to sample “hidden” populations, such that properties of the network can be deduced from the sample. We consider how similar techniques can be designed that allow the discovery of the structure, especially the community structure, of networks. Our method involves collecting samples of a network by random walks and reconstructing the network by probabilistically coalescing vertices, using vertex attributes to determine the probabilities. Even though our method can only approximately reconstruct a part of the original network, it can recover its community structure relatively well. Moreover, it can find the key vertices which, when immunized, can effectively reduce the spread of an infection through the original network.     

Aerosol influenza transmission risk contours: A study of humid tropics versus winter temperate zone

Background

In recent years, much attention has been given to the spread of influenza around the world. With the continuing human outbreak of H5N1 beginning in 2003 and the H1N1 pandemic in 2009, focus on influenza and other respiratory viruses has been increased. It has been accepted for decades that international travel via jet aircraft is a major vector for global spread of influenza, and epidemiological differences between tropical and temperate regions observed. Thus we wanted to study how indoor environmental conditions (enclosed locations) in the tropics and winter temperate zones contribute to the aerosol spread of influenza by travelers. To this end, a survey consisting of 632 readings of temperature (T) versus relative humidity (RH) in 389 different enclosed locations air travelers are likely to visit in 8 tropical nations were compared to 102 such readings in 2 Australian cities, including ground transport, hotels, shops, offices and other publicly accessible locations, along with 586 time course readings from aircraft.

Results

An influenza transmission risk contour map was developed for T versus RH. Empirical equations were created for estimating: 1. risk relative to temperature and RH, and 2. time parameterized influenza transmission risk. Using the transmission risk contours and equations, transmission risk for each country's locations was compared with influenza reports from the countries. Higher risk enclosed locations in the tropics included new automobile transport, luxury buses, luxury hotels, and bank branches. Most temperate locations were high risk.

Conclusion

Environmental control is recommended for public health mitigation focused on higher risk enclosed locations. Public health can make use of the methods developed to track potential vulnerability to aerosol influenza. The methods presented can also be used in influenza modeling. Accounting for differential aerosol transmission using T and RH can potentially explain anomalies of influenza epidemiology in addition to seasonality in temperate climates.     

The limits of elaboration: curved allometries reveal the constraints on mandible size in stag beetles

Many studies have demonstrated the adaptive advantage of elaborate secondary sexual traits, but few if any have shown compelling evidence for the limits to the elaboration of these traits that must exist. We describe such evidence in the exaggerated mandibles of stag beetles. In 1932, Huxley showed that the slope of the allometric relationship between mandible length and body size in some stag beetles declines in the largest males. We show that this curvature is most pronounced in species with relatively long mandibles, consistent with the hypothesis that the decrease in slope is caused by the increasing costs of large mandibles, which ultimately limit their size. Increasing depletion of resources in the prepupa and pupa by the rapidly growing mandibles is the most likely way in which these costs are manifested. The curved allometries have two components: intraspecific mandible allometry is steepest among small males of the species with the longest mandibles, but shallowest among the largest males of those same species. These patterns suggest that selection continues to favour positive allometry in species that invest relatively more in weaponry despite the limits to mandible exaggeration being reached in the largest males.     

Unifying Viral Genetics and Human Transportation Data to Predict the Global Transmission Dynamics of Human Influenza H3N2

Information on global human movement patterns is central to spatial epidemiological models used to predict the behavior of influenza and other infectious diseases. Yet it remains difficult to test which modes of dispersal drive pathogen spread at various geographic scales using standard epidemiological data alone. Evolutionary analyses of pathogen genome sequences increasingly provide insights into the spatial dynamics of influenza viruses, but to date they have largely neglected the wealth of information on human mobility, mainly because no statistical framework exists within which viral gene sequences and empirical data on host movement can be combined. Here, we address this problem by applying a phylogeographic approach to elucidate the global spread of human influenza subtype H3N2 and assess its ability to predict the spatial spread of human influenza A viruses worldwide. Using a framework that estimates the migration history of human influenza while simultaneously testing and quantifying a range of potential predictive variables of spatial spread, we show that the global dynamics of influenza H3N2 are driven by air passenger flows, whereas at more local scales spread is also determined by processes that correlate with geographic distance. Our analyses further confirm a central role for mainland China and Southeast Asia in maintaining a source population for global influenza diversity. By comparing model output with the known pandemic expansion of H1N1 during 2009, we demonstrate that predictions of influenza spatial spread are most accurate when data on human mobility and viral evolution are integrated. In conclusion, the global dynamics of influenza viruses are best explained by combining human mobility data with the spatial information inherent in sampled viral genomes. The integrated approach introduced here offers great potential for epidemiological surveillance through phylogeographic reconstructions and for improving predictive models of disease control.     

Spatial Transmission of 2009 Pandemic Influenza in the US

The 2009 H1N1 influenza pandemic provides a unique opportunity for detailed examination of the spatial dynamics of an emerging pathogen. In the US, the pandemic was characterized by substantial geographical heterogeneity: the 2009 spring wave was limited mainly to northeastern cities while the larger fall wave affected the whole country. Here we use finely resolved spatial and temporal influenza disease data based on electronic medical claims to explore the spread of the fall pandemic wave across 271 US cities and associated suburban areas. We document a clear spatial pattern in the timing of onset of the fall wave, starting in southeastern cities and spreading outwards over a period of three months. We use mechanistic models to tease apart the external factors associated with the timing of the fall wave arrival: differential seeding events linked to demographic factors, school opening dates, absolute humidity, prior immunity from the spring wave, spatial diffusion, and their interactions. Although the onset of the fall wave was correlated with school openings as previously reported, models including spatial spread alone resulted in better fit. The best model had a combination of the two. Absolute humidity or prior exposure during the spring wave did not improve the fit and population size only played a weak role. In conclusion, the protracted spread of pandemic influenza in fall 2009 in the US was dominated by short-distance spatial spread partially catalysed by school openings rather than long-distance transmission events. This is in contrast to the rapid hierarchical transmission patterns previously described for seasonal influenza. The findings underline the critical role that school-age children play in facilitating the geographic spread of pandemic influenza and highlight the need for further information on the movement and mixing patterns of this age group.     

New approaches to quantifying the spread of infection

Recent major disease outbreaks, such as severe acute respiratory syndrome and foot-and-mouth disease in the UK, coupled with fears of emergence of human-to-human transmissible variants of avian influenza, have highlighted the importance of accurate quantification of disease threat when relatively few cases have occurred. Traditional approaches to mathematical modelling of infectious diseases deal most effectively with large outbreaks in large populations. The desire to elucidate the highly variable dynamics of disease spread amongst small numbers of individuals has fuelled the development of models that depend more directly on surveillance and contact-tracing data. This signals a move towards a closer interplay between epidemiological modelling, surveillance and disease-management strategies.     

A Few Bad Apples: A Model of Disease Influenced Agent Behaviour in a Heterogeneous Contact Environment

For diseases that infect humans or livestock, transmission dynamics are at least partially dependent on human activity and therefore human behaviour. However, the impact of human behaviour on disease transmission is relatively understudied, especially in the context of heterogeneous contact structures such as described by a social network. Here, we use a strategic game, coupled with a simple disease model, to investigate how strategic agent choices impact the spread of disease over a contact network. Using beliefs that are based on disease status and that build up over time, agents choose actions that stochastically determine disease spread on the network. An agent’s disease status is therefore a function of both his own and his neighbours actions. The effect of disease on agents is modelled by a heterogeneous payoff structure. We find that the combination of network shape and distribution of payoffs has a non-trivial impact on disease prevalence, even if the mean payoff remains the same. An important scenario occurs when a small percentage (called noncooperators) have little incentive to avoid disease. For diseases that are easily acquired when taking a risk, then even when good behavior can lead to disease eradication, a small increase in the percentage of noncooperators (less than 5%) can yield a large (up to 25%) increase in prevalence.     

A Bayesian Approach for Modeling Cattle Movements in the United States: Scaling up a Partially Observed Network

Networks are rarely completely observed and prediction of unobserved edges is an important problem, especially in disease spread modeling where networks are used to represent the pattern of contacts. We focus on a partially observed cattle movement network in the U.S. and present a method for scaling up to a full network based on Bayesian inference, with the aim of informing epidemic disease spread models in the United States. The observed network is a 10% state stratified sample of Interstate Certificates of Veterinary Inspection that are required for interstate movement; describing approximately 20,000 movements from 47 of the contiguous states, with origins and destinations aggregated at the county level. We address how to scale up the 10% sample and predict unobserved intrastate movements based on observed movement distances. Edge prediction based on a distance kernel is not straightforward because the probability of movement does not always decline monotonically with distance due to underlying industry infrastructure. Hence, we propose a spatially explicit model where the probability of movement depends on distance, number of premises per county and historical imports of animals. Our model performs well in recapturing overall metrics of the observed network at the node level (U.S. counties), including degree centrality and betweenness; and performs better compared to randomized networks. Kernel generated movement networks also recapture observed global network metrics, including network size, transitivity, reciprocity, and assortativity better than randomized networks. In addition, predicted movements are similar to observed when aggregated at the state level (a broader geographic level relevant for policy) and are concentrated around states where key infrastructures, such as feedlots, are common. We conclude that the method generally performs well in predicting both coarse geographical patterns and network structure and is a promising method to generate full networks that incorporate the uncertainty of sampled and unobserved contacts.