Master-equation analysis of accelerating networks.

In many real-world networks, the rates of node and link addition are time dependent. This observation motivates the definition of accelerating networks. There has been relatively little investigation of accelerating networks and previous efforts at analyzing their degree distributions have employed mean-field techniques. By contrast, we show that it is possible to apply a master-equation approach to such network development. We provide full time-dependent expressions for the evolution of the degree distributions for the canonical situations of random and preferential attachment in networks undergoing constant acceleration. These results are in excellent agreement with results obtained from simulations. We note that a growing nonequilibrium network undergoing constant acceleration with random attachment is equivalent to a classical random graph, bridging the gap between nonequilibrium and classical equilibrium networks.

Link-space formalism for network analysis.

We introduce the link-space formalism for analyzing network models with degree-degree correlations. The formalism is based on a statistical description of the fraction of links l(i,j) connecting nodes of degrees i and j. To demonstrate its use, we apply the framework to some pedagogical network models, namely, random attachment, Barabási-Albert preferential attachment, and the classical Erdos and Rényi random graph. For these three models the link-space matrix can be solved analytically. We apply the formalism to a simple one-parameter growing network model whose numerical solution exemplifies the effect of degree-degree correlations for the resulting degree distribution. We also employ the formalism to derive the degree distributions of two very simple network decay models, more specifically, that of random link deletion and random node deletion. The formalism allows detailed analysis of the correlations within networks and we also employ it to derive the form of a perfectly nonassortative network for arbitrary degree distribution.

Forecasted trends in vaccination coverage and correlations with socioeconomic factors: a global time-series analysis over 30 years.

BACKGROUND: Incomplete immunisation coverage causes preventable illness and death in both developing and developed countries. Identification of factors that might modulate coverage could inform effective immunisation programmes and policies. We constructed a performance indicator that could quantitatively approximate measures of the susceptibility of immunisation programmes to coverage losses, with an aim to identify correlations between trends in vaccine coverage and socioeconomic factors. METHODS: We undertook a data-driven time-series analysis to examine trends in coverage of diphtheria, tetanus, and pertussis (DTP) vaccination across 190 countries over the past 30 years. We grouped countries into six world regions according to WHO classifications. We used Gaussian process regression to forecast future coverage rates and provide a vaccine performance index: a summary measure of the strength of immunisation coverage in a country. FINDINGS: Overall vaccine coverage increased in all six world regions between 1980 and 2010, with variation in volatility and trends. Our vaccine performance index identified that 53 countries had more than a 50% chance of missing the Global Vaccine Action Plan (GVAP) target of 90% worldwide coverage with three doses of DTP (DTP3) by 2015. These countries were mostly in sub-Saharan Africa and south Asia, but Austria and Ukraine also featured. Factors associated with DTP3 immunisation coverage varied by world region: personal income (Spearman's ρ=0·66, p=0·0011) and government health spending (0·66, p<0·0001) were informative of immunisation coverage in the Eastern Mediterranean between 1980 and 2010, whereas primary school completion was informative of coverage in Africa (0·56, p<0·0001) over the same period. The proportion of births attended by skilled health staff correlated significantly with immunisation coverage across many world regions. INTERPRETATION: Our vaccine performance index highlighted countries at risk of failing to achieve the GVAP target of 90% coverage by 2015, and could aid policy makers' assessments of the strength and resilience of immunisation programmes. Weakening correlations with socioeconomic factors show a need to tackle vaccine confidence, whereas strengthening correlations point to clear factors to address. FUNDING: UK Engineering and Physical Sciences Research Council.

Measuring vaccine confidence: introducing a global vaccine confidence index.

BACKGROUND: Public confidence in vaccination is vital to the success of immunisation programmes worldwide. Understanding the dynamics of vaccine confidence is therefore of great importance for global public health. Few published studies permit global comparisons of vaccination sentiments and behaviours against a common metric. This article presents the findings of a multi-country survey of confidence in vaccines and immunisation programmes in Georgia, India, Nigeria, Pakistan, and the United Kingdom (UK) - these being the first results of a larger project to map vaccine confidence globally. METHODS: Data were collected from a sample of the general population and from those with children under 5 years old against a core set of confidence questions. All surveys were conducted in the relevant local-language in Georgia, India, Nigeria, Pakistan, and the UK. We examine confidence in immunisation programmes as compared to confidence in other government health services, the relationships between confidence in the system and levels of vaccine hesitancy, reasons for vaccine hesitancy, ultimate vaccination decisions, and their variation based on country contexts and demographic factors. RESULTS: The numbers of respondents by country were: Georgia (n=1000); India (n=1259); Pakistan (n=2609); UK (n=2055); Nigerian households (n=12554); and Nigerian health providers (n=1272). The UK respondents with children under five years of age were more likely to hesitate to vaccinate, compared to other countries. Confidence in immunisation programmes was more closely associated with confidence in the broader health system in the UK (Spearman's ρ=0.5990), compared to Nigeria (ρ=0.5477), Pakistan (ρ=0.4491), and India (ρ=0.4240), all of which ranked confidence in immunisation programmes higher than confidence in the broader health system. Georgia had the highest rate of vaccine refusals (6 %) among those who reported initial hesitation. In all other countries surveyed most respondents who reported hesitating to vaccinate went on to receive the vaccine except in Kano state, Nigeria, where the percentage of those who ultimately refused vaccination after initially hesitating was as high as 76%) Reported reasons for hesitancy in all countries were classified under the domains of "confidence," "convenience," or "complacency," and confidence issues were found to be the primary driver of hesitancy in all countries surveyed.

Understanding vaccine hesitancy around vaccines and vaccination from a global perspective: a systematic review of published literature, 2007-2012.

Vaccine "hesitancy" is an emerging term in the literature and discourse on vaccine decision-making and determinants of vaccine acceptance. It recognizes a continuum between the domains of vaccine acceptance and vaccine refusal and de-polarizes previous characterization of individuals and groups as either anti-vaccine or pro-vaccine. The primary aims of this systematic review are to: 1) identify research on vaccine hesitancy; 2) identify determinants of vaccine hesitancy in different settings including its context-specific causes, its expression and its impact; and 3) inform the development of a model for assessing determinants of vaccine hesitancy in different settings as proposed by the Strategic Advisory Group of Experts Working Group (SAGE WG) for dealing with vaccine hesitancy. A broad search strategy, built to capture multiple dimensions of public trust, confidence and hesitancy around vaccines, was applied across multiple databases. Peer-reviewed studies were selected for inclusion if they focused on childhood vaccines [≤ 7 years of age], used multivariate analyses, and were published between January 2007 and November 2012. Our results show a variety of factors as being associated with vaccine hesitancy but they do not allow for a complete classification and confirmation of their independent and relative strength of influence. Determinants of vaccine hesitancy are complex and context-specific - varying across time, place and vaccines.

Measuring vaccine confidence: analysis of data obtained by a media surveillance system used to analyse public concerns about vaccines.

BACKGROUND: The intensity, spread, and effects of public opinion about vaccines are growing as new modes of communication speed up information sharing, contributing to vaccine hesitancy, refusals, and disease outbreaks. We aimed to develop a new application of existing surveillance systems to detect and characterise early signs of vaccine issues. We also aimed to develop a typology of concerns and a way to assess the priority of each concern. METHODS: Following preliminary research by The Vaccine Confidence Project, media reports (eg, online articles, blogs, government reports) were obtained using the HealthMap automated data collection system, adapted to monitor online reports about vaccines, vaccination programmes, and vaccine-preventable diseases. Any reports that did not meet the inclusion criteria--any reference to a human vaccine or vaccination campaign or programme that was accessible online--were removed from analysis. Reports were manually analysed for content and categorised by concerns, vaccine, disease, location, and source of report, and overall positive or negative sentiment towards vaccines. They were then given a priority level depending on the seriousness of the reported event and time of event occurrence. We used descriptive statistics to analyse the data collected during a period of 1 year, after refinements to the search terms and processes had been made. FINDINGS: We analysed data from 10,380 reports (from 144 countries) obtained between May 1, 2011, and April 30, 2012. 7171 (69%) contained positive or neutral content and 3209 (31%) contained negative content. Of the negative reports, 1977 (24%) were associated with impacts on vaccine programmes and disease outbreaks; 1726 (21%) with beliefs, awareness, and perceptions; 1371 (16%) with vaccine safety; and 1336 (16%) with vaccine delivery programmes. We were able to disaggregate the data by country and vaccine type, and monitor evolution of events over time and location in specific regions where vaccine concerns were high. INTERPRETATION: Real-time monitoring and analysis of vaccine concerns over time and location could help immunisation programmes to tailor more effective and timely strategies to address specific public concerns. FUNDING: Bill & Melinda Gates Foundation.