Large-scale properties of clustered networks: implications for disease dynamics

We consider previously proposed procedures for generating clustered networks and investigate how these procedures lead to differences in network properties other than clustering. We interpret our findings in terms of the effect of the network structure on the disease outbreak threshold and disease dynamics. To generate null-model networks for comparison, we implement an assortativity-conserving rewiring algorithm that alters the level of clustering while causing minimal impact on other properties. We show that many theoretical network models used to generate networks with a particular property often lead to significant changes in network properties other than that of interest. For high levels of clustering, different procedures lead to networks that differ in degree heterogeneity and assortativity, and in broader scale measures such as ?(0) and the distribution of shortest path lengths. Hence, care must be taken when investigating the implications of network properties for disease transmission or other dynamic process that the network supports.     

Capturing escape in infectious disease dynamics

Identifying the causes of interannual variability in disease dynamics is important for understanding and managing epidemics. Traditionally, these causes have been classified as intrinsic (e.g. immunity fluctuations) or extrinsic (e.g. climate forcing); ecologists determine the relative contributions of these factors by applying statistical models to time series of cases. Here we address the problem of isolating the drivers of pathogen dynamics that are influenced by antigenic evolution. Recent findings indicate that many pathogens escape immunity in a punctuated manner; for them, we argue that time series of cases alone will be insufficient to isolate causal drivers. We detail observations that can reveal the presence of punctuated immune escape, and which can be used in new statistical approaches to identify extrinsic and intrinsic regulators of disease.     

Transient dynamics and early diagnostics in infectious disease

To date, mathematical models of the dynamics of infectious disease have consistently focused on understanding the long-term behavior of the interacting components, where the steady state solutions are paramount. However for most acute infections, the long-term behavior of the pathogen population is of little importance to the host and population health. We introduce the notion of transient pathology, where the short-term dynamics of interaction between the immune system and pathogens is the principal focus. We identify the amplifying effect of the absence of a fully operative immune system on the pathogenesis of the initial inoculum, and its implication for the acute severity of the infection. We then formalize the underlying dynamics, and derive two measures of transient pathogenicity: the peak of infection (maximum pathogenic load) and the time to peak of infection, both crucial to understanding the early dynamics of infection and its consequences for early intervention. Received: 25 January 2000 / Revised version: 30 November 2000 / Published online: 12 October 2001     

Social contact patterns in Vietnam and implications for the control of infectious diseases

Background

The spread of infectious diseases from person to person is determined by the frequency and nature of contacts between infected and susceptible members of the population. Although there is a long history of using mathematical models to understand these transmission dynamics, there are still remarkably little empirical data on contact behaviors with which to parameterize these models. Even starker is the almost complete absence of data from developing countries. We sought to address this knowledge gap by conducting a household based social contact diary in rural Vietnam.

Methods and Findings

A diary based survey of social contact patterns was conducted in a household-structured community cohort in North Vietnam in 2007. We used generalized estimating equations to model the number of contacts while taking into account the household sampling design, and used weighting to balance the household size and age distribution towards the Vietnamese population. We recorded 6675 contacts from 865 participants in 264 different households and found that mixing patterns were assortative by age but were more homogenous than observed in a recent European study. We also observed that physical contacts were more concentrated in the home setting in Vietnam than in Europe but the overall level of physical contact was lower. A model of individual versus household vaccination strategies revealed no difference between strategies in the impact on R ₀.

Conclusions and Significance

This work is the first to estimate contact patterns relevant to the spread of infections transmitted from person to person by non-sexual routes in a developing country setting. The results show interesting similarities and differences from European data and demonstrate the importance of context specific data.     

Perspective: human contact patterns and the spread of airborne infectious diseases.

Networks of social contacts channel the transmission of airborne infections. Emerging insights from fields of science as diverse as mathematics, population biology and the social sciences are beginning to reveal how the contact pattern of the hosts determines the spread and evolution of airborne infectious agents.     

Modeling immune response and its effect on infectious disease outbreak dynamics

Background

In recent epidemiological models, immunity is incorporated as a simplified value that determines the capacity of an individual to become infected or to transmit the disease. Moreover, the quality of the immune response determines the chances of infection and the length of time an individual is capable to infect others. We present a model that incorporates individuals’ immune responses to, further, examine the role of the collective immune response of individuals in a population during an infectious outbreak.

Methods

We constructed a contagion model that incorporates the collective immune response of individuals represented by the superposition of individual immune responses (PIR). Multiple probability distributions are used to represent the immunocompetence of different age groups, thereby modeling the concept of Population Immune Response (PIR). Multiple experiments were conducted in which the population is divided in different age groups for which each group has a unique immune response quality and thus a different length for its immune periods. Finally, we explored the effects of implementing different vaccination strategies in the population.

Results

The experiments displayed important variations in the outbreak dynamics as a consequence of incorporating PIR in homogeneous and mixed populations. The experiments showed that individuals with weak immune responses and those who are immune to the pathogen play a significant role in shaping the outbreak dynamics. Finally, after implementing different vaccination strategies, the results suggest that if vaccination resources are limited, the vaccination should be targeted towards individuals that spread the disease for a longer period of time.

Conclusions

Our results suggest that it is essential for the public health establishment to increase their understanding of the characteristics of regional demographics that could impact the quality of the immune response of the individuals. The results indicate that it is necessary to further investigate mitigation strategies to limit the capacity to transmit the disease by individuals that spread the pathogen for extended periods of time. Ultimately, this study suggests that it is crucial for public health researchers to identify appropriate targeted vaccination regimes and to explore the link between PIR and outbreak dynamics to improve the monitoring and mitigating efforts of ongoing and future epidemics.

     

Revealing mechanisms of infectious disease spread through empirical contact networks

The spread of pathogens fundamentally depends on the underlying contacts between individuals. Modeling the dynamics of infectious disease spread through contact networks, however, can be challenging due to limited knowledge of how an infectious disease spreads and its transmission rate. We developed a novel statistical tool, INoDS (Identifying contact Networks of infectious Disease Spread) that estimates the transmission rate of an infectious disease outbreak, establishes epidemiological relevance of a contact network in explaining the observed pattern of infectious disease spread and enables model comparison between different contact network hypotheses. We show that our tool is robust to incomplete data and can be easily applied to datasets where infection timings of individuals are unknown. We tested the reliability of INoDS using simulation experiments of disease spread on a synthetic contact network and find that it is robust to incomplete data and is reliable under different settings of network dynamics and disease contagiousness compared with previous approaches. We demonstrate the applicability of our method in two host-pathogen systems: Crithidia bombi in bumblebee colonies and Salmonella in wild Australian sleepy lizard populations. INoDS thus provides a novel and reliable statistical tool for identifying transmission pathways of infectious disease spread. In addition, application of INoDS extends to understanding the spread of novel or emerging infectious disease, an alternative approach to laboratory transmission experiments, and overcoming common data-collection constraints.     

Non-linear transmission rates and the dynamics of infectious disease.

This study considers how non-linearities in the transmission of microparasitic infections affect the population dynamics of host-parasite systems in which the disease is potentially lethal to the host. Non-linearities can either lead to a locally stable or unstable host-parasite equilibrium point, depending on the respective contributions of healthy and infected hosts to the functional form of the transmission rate. Analysis of the non-linear transmission model results in a revealing pair of local stability criteria. Specifically, stability requires sufficient total levels of intrinsic growth of the host population and total levels of density-dependent transmission. The most stable systems occur when increases in the density of healthy hosts result in increases in transmission efficiency, and increases in the number of infected hosts result in small decreases in transmission efficiency. These appear to be very reasonable relationships for directly transmitted microparasites.     

Disease contact tracing in random and clustered networks

The efficacy of contact tracing, be it between individuals (e.g. sexually transmitted diseases or severe acute respiratory syndrome) or between groups of individuals (e.g. foot-and-mouth disease; FMD), is difficult to evaluate without precise knowledge of the underlying contact structure; i.e. who is connected to whom? Motivated by the 2001 FMD epidemic in the UK, we determine, using stochastic simulations and deterministic 'moment closure' models of disease transmission on networks of premises (nodes), network and disease properties that are important for contact tracing efficiency. For random networks with a high average number of connections per node, little clustering of connections and short latency periods, contact tracing is typically ineffective. In this case, isolation of infected nodes is the dominant factor in determining disease epidemic size and duration. If the latency period is longer and the average number of connections per node small, or if the network is spatially clustered, then the contact tracing performs better and an overall reduction in the proportion of nodes that are removed during an epidemic is observed.     

The dynamic nature of contact networks in infectious disease epidemiology

Although contact network models have yielded important insights into infectious disease transmission and control throughout the last decade, researchers have just begun to explore the dynamic nature of contact patterns and their epidemiological significance. Most network models have assumed that contacts are static through time. Developing more realistic models of the social interactions that underlie the spread of infectious diseases thus remains an important challenge for both data gatherers and modelers. In this article, we review some recent data-driven and process-driven approaches that capture the dynamics of human contact, and discuss future challenges for the field.     

Observations on clustered synaptic plasticity and highly structured input patterns

In this issue of Neuron, Makino and Malinow and Kleindienst et?al. present evidence of a behaviorally induced form of synaptic plasticity that would encourage the development of fine-scale structured input patterns and?the binding of features within single neurons.     

Modelling the spatio-temporal dynamics of multi-species host-parasitoid interactions: heterogeneous patterns and ecological implications

A mathematical model of the spatio-temporal dynamics of a two host, two parasitoid system is presented. There is a coupling of the four species through parasitism of both hosts by one of the parasitoids. The model comprises a system of four reaction-diffusion equations. The underlying system of ordinary differential equations, modelling the host-parasitoid population dynamics, has a unique positive steady state and is shown to be capable of undergoing Hopf bifurcations, leading to limit cycle kinetics which give rise to oscillatory temporal dynamics. The stability of the positive steady state has a fundamental impact on the spatio-temporal dynamics: stable travelling waves of parasitoid invasion exhibit increasingly irregular periodic travelling wave behaviour when key parameter values are increased beyond their Hopf bifurcation point. These irregular periodic travelling waves give rise to heterogeneous spatio-temporal patterns of host and parasitoid abundance. The generation of heterogeneous patterns has ecological implications and the concepts of temporary host refuge and niche formation are considered.     

Host resource supplies influence the dynamics and outcome of infectious disease

Pathogens and their host organisms share a wide range of resourceneeds that are required to support normal metabolism and growth.Because the development of infectious disease on or within thehost involves the processes of invasion and resource consumption,competition for growth-limiting resources potentially may occurbetween pathogens and cellular or sub-cellular components ofthe host ecosystem. Examples from the plant, animal, and microbiologicalliterature provide unambiguous evidence that external resourcesupplies to the host organism can have profound effects on theoutcome of infection by a broad diversity of bacterial, fungal,metazoan, protozoan, and viral pathogens.     

The dynamics of sexual contact networks: effects on disease spread and control

Sexually transmitted pathogens persist in populations despite the availability of biomedical interventions and knowledge of behavioural changes that would reduce individual-level risk. While behavioural risk factors are shared between many sexually transmitted infections, the prevalence of these diseases across different risk groups varies. Understanding this heterogeneity and identifying better control strategies depends on an improved understanding of the complex social contact networks over which pathogens spread. To date, most efforts to study the impact of sexual network structure on disease dynamics have focused on static networks. However, the interaction between the dynamics of partnership formation and dissolution and the dynamics of transmission plays a role, both in restricting the effective network accessible to the pathogen, and in modulating the transmission dynamics. We present a simple method to simulate dynamical networks of sexual partnerships. We inform the model using survey data on sexual attitudes and lifestyles, and investigate how the duration of infectiousness changes the effective contact network over which disease may spread. We then simulate several control strategies: screening, vaccination and behavioural interventions. Previous theory and research has advanced the importance of core groups for spread and control of STD. Our work is consistent with the importance of core groups, but extends this idea to consider how the duration of infectiousness associated with a particular pathogen interacts with host behaviours to define these high risk subpopulations. Characteristics of the parts of the network accessible to the pathogen, which represent the network structure of sexual contacts from the “point of view” of the pathogen, are substantially different from those of the network as a whole. The pathogen itself plays an important role in determining this effective network structure; specifically, we find that if the pathogen’s duration of infectiousness is short, infection is more concentrated in high-activity, high-concurrency individuals even when all other factors are held constant. Widespread screening programmes would be enhanced by follow-up interventions targeting higher-risk individuals, because screening shortens the expected duration of infectiousness and causes a greater relative decrease in prevalence among lower-activity than in higher-activity individuals. Even for pathogens with longer durations of infectiousness, our findings suggest that targeting vaccination and behavioural interventions towards high-activity individuals provides comparable benefits to population-wide interventions.     

Using network properties to predict disease dynamics on human contact networks

Recent studies have increasingly turned to graph theory to model more realistic contact structures that characterize disease spread. Because of the computational demands of these methods, many researchers have sought to use measures of network structure to modify analytically tractable differential equation models. Several of these studies have focused on the degree distribution of the contact network as the basis for their modifications. We show that although degree distribution is sufficient to predict disease behaviour on very sparse or very dense human contact networks, for intermediate density networks we must include information on clustering and path length to accurately predict disease behaviour. Using these three metrics, we were able to explain more than 98 per cent of the variation in endemic disease levels in our stochastic simulations.     

Effects of patch number and dispersal patterns on population dynamics and synchrony

In this paper, we examine the effects of patch number and different dispersal patterns on dynamics of local populations and on the level of synchrony between them. Local population renewal is governed by the Ricker model and we also consider asymmetrical dispersal as well as the presence of environmental heterogeneity. Our results show that both population dynamics and the level of synchrony differ markedly between two and a larger number of local populations. For two patches different dispersal rules give very versatile dynamics. However, for a larger number of local populations the dynamics are similar irrespective of the dispersal rule. For example, for the parameter values yielding stable or periodic dynamics in a single population, the dynamics do not change when the patches are coupled with dispersal. High intensity of dispersal does not guarantee synchrony between local populations. The level of synchrony depends also on dispersal rule, the number of local populations, and the intrinsic rate of increase. In our study, the effects of density-independent and density-dependent dispersal rules do not show any consistent difference. The results call for caution when drawing general conclusions from models of only two interacting populations and question the applicability of a large number of theoretical papers dealing with two local populations.     

Geographic variation in seasonality and its influence on the dynamics of an infectious disease

Seasonal changes in environmental drivers – such as temperature, rainfall, and resource availability – have the potential to shape infection dynamics through their reverberating effects on biological processes including host abundance and susceptibility to infection. However, seasonality varies geographically. We therefore expect marked differences in infection dynamics between regions with different seasonal patterns. By pairing extensive Avian Influenza Virus (AIV) surveillance data – 65 358 individual bird samples from 12 species of dabbling ducks sampled at 174 locations across North America – with quantification of seasonality using remote sensed data indicative for primary productivity (normalised differenced vegetation index, NDVI), we provide evidence that seasonal dynamics influence infection dynamics across a continent. More pronounced epidemics were seen to occur in regions experiencing a higher degree of seasonality, and epidemics of lower amplitude and longer duration occurred in regions with a more protracted and lower seasonal amplitude. These results demonstrate the potential importance of geographic variation in seasonality for explaining geographic variation in the dynamics of infectious diseases in wildlife.     

有色环境噪音对空间异质种群动态同步性的影响

随着种群动态和空间结构研究兴趣的增加,激发了大量的有关空间同步性的理论和实验的研究工作。空间种群的同步波动现象在自然界广泛存在,它的影响和原因引起了很多生态学家的兴趣。Moran定理是一个非常重要的解释。但以往的研究大多假设环境变化为空间相关的白噪音。越来越多的研究表明很多环境变化的时间序列具有正的时间自相关性,也就是说用红噪音来描述更加合理。因此,推广经典的Moran效应来处理空间相关红噪音的情形很有必要。利用线性的二阶自回归过程的种群模型,推导了两种群空间同步性与种群动态异质性和环境变化的时间相关性(即环境噪音的颜色)之间的关系。深入分析了种群异质性和噪音颜色对空间同步性的影响。结果表明种群动态异质性不利于空间同步性,但详细的关系比较复杂。而红色噪音的同步能力体现在两方面:一方面,本身的相关性对同步性有贡献;另一方面,环境变化时间相关性可以通过改变种群密度依赖来影响同步性,但对同步性的影响并无一致性的结论,依赖于种群的平均动态等因素。这些结果对理解同步性的机理、利用同步机理来制定物种保护策略和害虫防治都有重要的意义。