CiteULike: sala's library [12 articles]

Attainment of quasilinkage equilibrium when gene frequencies are changing by natural selection.

M Kimura — 2008-03-20T15:36:03-00:00

Genetics, Vol. 52 (1965), pp. 875-890.

Effectiveness of realistic vaccination strategies for contact networks of various degree distributions

Fumihiko Takeuchi — 2008-03-19T15:10:53-00:00

Journal of Theoretical Biology, Vol. 243, No. 1. (7 November 2006), pp. 39-47.

A "contact network" that models infection transmission comprises nodes (or individuals) that are linked when they are in contact and can potentially transmit an infection. Through analysis and simulation, we studied the influence of the distribution of the number of contacts per node, defined as degree, on infection spreading and its control by vaccination. Three random contact networks of various degree distributions were examined. In a scale-free network, the frequency of high-degree nodes decreases as the power of the degree (the case of the third power is studied here); the decrease is exponential in an exponential network, whereas all nodes have the same degree in a constant network. Aiming for containment at a very early stage of an epidemic, we measured the sustainability of a specific network under a vaccination strategy by employing the critical transmissibility larger than which the epidemic would occur. We examined three vaccination strategies: mass, ring, and acquaintance. Irrespective of the networks, mass preventive vaccination increased the critical transmissibility inversely proportional to the unvaccinated rate of the population. Ring post-outbreak vaccination increased the critical transmissibility inversely proportional to the unvaccinated rate, which is the rate confined to the targeted ring comprising the neighbors of an infected node; however, the total number of vaccinated nodes could mostly be fewer than 100 nodes at the critical transmissibility. In combination, mass and ring vaccinations decreased the pathogen's "effective" transmissibility each by the factor of the unvaccinated rate. The amount of vaccination used in acquaintance preventive vaccination was lesser than the mass vaccination, particularly under a highly heterogeneous degree distribution; however, it was not as less as that used in ring vaccination. Consequently, our results yielded a quantitative assessment of the amount of vaccination necessary for infection containment, which is universally applicable to contact networks of various degree distributions.

Exploring complex networks.

SH Strogatz — 2004-11-22T00:17:30-00:00

Nature, Vol. 410, No. 6825. (8 March 2001), pp. 268-276.

The study of networks pervades all of science, from neurobiology to statistical physics. The most basic issues are structural: how does one characterize the wiring diagram of a food web or the Internet or the metabolic network of the bacterium Escherichia coli? Are there any unifying principles underlying their topology? From the perspective of nonlinear dynamics, we would also like to understand how an enormous network of interacting dynamical systems-be they neurons, power stations or lasers-will behave collectively, given their individual dynamics and coupling architecture. Researchers are only now beginning to unravel the structure and dynamics of complex networks.

Planetary-Scale Views on an Instant-Messaging Network

Jure Leskovec — 2008-03-10T13:29:09-00:00

(6 Mar 2008)

We present a study of anonymized data capturing a month of high-level communication activities within the whole of the Microsoft Messenger instant-messaging system. We examine characteristics and patterns that emerge from the collective dynamics of large numbers of people, rather than the actions and characteristics of individuals. The dataset contains summary properties of 30 billion conversations among 240 million people. From the data, we construct a communication graph with 180 million nodes and 1.3 billion undirected edges, creating the largest social network constructed and analyzed to date. We report on multiple aspects of the dataset and synthesized graph. We find that the graph is well-connected and robust to node removal. We investigate on a planetary-scale the oft-cited report that people are separated by “six degrees of separation” and find that the average path length among Messenger users is 6.6. We also find that people tend to communicate more with each other when they have similar age, language, and location, and that cross-gender conversations are both more frequent and of longer duration than conversations with the same gender.

Modelling disease outbreaks in realistic urban social networks

Stephen Eubank — 2007-12-29T20:55:00-00:00

Nature, Vol. 429, No. 6988. (13 May 2004), pp. 180-184.

Properties of highly clustered networks

MEJ Newman — 2008-03-12T12:55:05-00:00

(10 Mar 2003)

We propose and solve exactly a model of a network that has both a tunable degree distribution and a tunable clustering coefficient. Among other things, our results indicate that increased clustering leads to a decrease in the size of the giant component of the network. We also study SIR-type epidemic processes within the model and find that clustering decreases the size of epidemics, but also decreases the epidemic threshold, making it easier for diseases to spread. In addition, clustering causes epidemics to saturate sooner, meaning that they infect a near-maximal fraction of the network for quite low transmission rates.

A Measles Epidemic Threshold in a Highly Vaccinated Population

Jacco Wallinga — 2008-03-12T10:17:58-00:00

PLoS Medicine, Vol. 2, No. 11. (1 November 2005), e316.

Background Mass vaccination against measles has successfully lowered the incidence of the disease and has changed the epidemic pattern from a roughly biennial cycle to an irregular sequence of outbreaks. A possible explanation for this sequence of outbreaks is that the vaccinated population is protected by solid herd immunity. If so, we would expect to see the fraction of susceptible individuals remaining below an epidemic threshold. An alternative explanation is the occurrence of occasional localised lapses in herd immunity that allow for major outbreaks in areas with a low vaccine coverage. In that case, we would expect the fraction of susceptible individuals to exceed an epidemic threshold before outbreaks occur. These two explanations for the irregular sequence of measles outbreaks can be tested against observations of both the fraction of susceptible individuals and infection attack rates. Methods and Findings We have estimated both the fraction of susceptible individuals at the start of each epidemic year and the infection attack rates for each epidemic year in the Netherlands over a 28-y period. During this period the vaccine coverage averaged 93%, and there was no sustained measles transmission. Several measles outbreaks occurred in communities with low vaccine coverage, and these ended without intervention. We show that there is a clear threshold value for the fraction of susceptible individuals, below which only minor outbreaks occurred, and above which both minor and major outbreaks occurred. A precise, quantitative relationship exists between the fraction of susceptible individuals in excess of this threshold and the infection attack rate during the major outbreaks. Conclusion In populations with a high but heterogeneous vaccine coverage, measles transmission can be interrupted without establishing solid herd immunity. When infection is reintroduced, a major outbreak can occur in the communities with low vaccine coverage. During such a major outbreak, each additional susceptible individual in excess of the threshold is associated with almost two additional infections. This quantitative relationship offers potential for anticipating both the likelihood and size of future major outbreaks when measles transmission has been interrupted.

Global trends in emerging infectious diseases

Kate Jones — 2008-02-21T13:23:19-00:00

Nature, Vol. 451, No. 7181., pp. 990-993.

When individual behaviour matters: homogeneous and network models in epidemiology

Shweta Bansal — 2008-03-12T10:04:01-00:00

Journal of The Royal Society Interface, Vol. 4, No. 16. (22 October 2007), pp. 879-891.

Heterogeneity in host contact patterns profoundly shapes population-level disease dynamics. Many epidemiological models make simplifying assumptions about the patterns of disease-causing interactions among hosts. In particular, homogeneous-mixing models assume that all hosts have identical rates of disease-causing contacts. In recent years, several network-based approaches have been developed to explicitly model heterogeneity in host contact patterns. Here, we use a network perspective to quantify the extent to which real populations depart from the homogeneous-mixing assumption, in terms of both the underlying network structure and the resulting epidemiological dynamics. We find that human contact patterns are indeed more heterogeneous than assumed by homogeneous-mixing models, but are not as variable as some have speculated. We then evaluate a variety of methodologies for incorporating contact heterogeneity, including network-based models and several modifications to the simple SIR compartmental model. We conclude that the homogeneous-mixing compartmental model is appropriate when host populations are nearly homogeneous, and can be modified effectively for a few classes of non-homogeneous networks. In general, however, network models are more intuitive and accurate for predicting disease spread through heterogeneous host populations.

Network frailty and the geometry of herd immunity

Matthew Ferrari — 2008-03-12T09:52:26-00:00

Proceedings of the Royal Society B: Biological Sciences, Vol. 273, No. 1602. (7 November 2006), pp. 2743-2748.

The spread of infectious disease through communities depends fundamentally on the underlying patterns of contacts between individuals. Generally, the more contacts one individual has, the more vulnerable they are to infection during an epidemic. Thus, outbreaks disproportionately impact the most highly connected demographics. Epidemics can then lead, through immunization or removal of individuals, to sparser networks that are more resistant to future transmission of a given disease. Using several classes of contact networks—Poisson, scale-free and small-world—we characterize the structural evolution of a network due to an epidemic in terms of frailty (the degree to which highly connected individuals are more vulnerable to infection) and interference (the extent to which the epidemic cuts off connectivity among the susceptible population that remains following an epidemic). The evolution of the susceptible network over the course of an epidemic differs among the classes of networks; frailty, relative to interference, accounts for an increasing component of network evolution on networks with greater variance in contacts. The result is that immunization due to prior epidemics can provide greater community protection than random vaccination on networks with heterogeneous contact patterns, while the reverse is true for highly structured populations.

The dynamics of measles in sub-Saharan Africa

Matthew Ferrari — 2008-02-08T00:40:44-00:00

Nature, Vol. 451, No. 7179., pp. 679-684.

The implications of network structure for epidemic dynamics

Matt Keeling — 2008-03-12T09:40:39-00:00

Theoretical Population Biology, Vol. 67, No. 1. (February 2005), pp. 1-8.

It has long been realised that the standard assumptions of mass-action mixing are a crude approximation of the true mechanistic processes that govern the transmission of infection. In particular, many infections can be considered to be spread through a limited network of contacts. Yet, despite the underlying discrepancies, mass-action models continue to be used and provide a remarkably accurate description of epidemic behaviour. Here, the differences between mass-action and network-based models are investigated. This allows us to determine when mass-action models are a reliable tool, and suggest ways in which their behaviour should be refined.