Disease spread in small-size directed networks: epidemic threshold, correlation between links to and from nodes, and clustering

Landscape simplification shapes pathogen prevalence in plant-pollinator networks

Species interaction networks, which play an important role in determining pathogen transmission and spread in ecological communities, can shift in response to agricultural landscape simplification. However, we know surprisingly little about how landscape simplification-driven changes in network structure impact epidemiological patterns. Here, we combine mathematical modelling and data from eleven bipartite plant-pollinator networks observed along a landscape simplification gradient to elucidate how changes in network structure shape disease dynamics. Our empirical data show that landscape simplification reduces pathogen prevalence in bee communities via increased diet breadth of the dominant species. Furthermore, our empirical data and theoretical model indicate that increased connectance reduces the likelihood of a disease outbreak and decreases variance in prevalence among bee species in the community, resulting in a dilution effect. Because infectious diseases are implicated in pollinator declines worldwide, a better understanding of how land use change impacts species interactions is therefore critical for conserving pollinator health.

Reducing Spreading Processes on Networks to Markov Population Models

Stochastic processes on complex networks, where each node is in one of several compartments, and neighboring nodes interact with each other, can be used to describe a variety of real-world spreading phenomena. However, computational analysis of such processes is hindered by the enormous size of their underlying state space.

In this work, we demonstrate that lumping can be used to reduce any epidemic model to a Markov Population Model (MPM). Therefore, we propose a novel lumping scheme based on a partitioning of the nodes. By imposing different types of counting abstractions, we obtain coarse-grained Markov models with a natural MPM representation that approximate the original systems. This makes it possible to transfer the rich pool of approximation techniques developed for MPMs to the computational analysis of complex networks’ dynamics.

We present numerical examples to investigate the relationship between the accuracy of the MPMs, the size of the lumped state space, and the type of counting abstraction.

Disease spreading in complex networks: A numerical study with Principal Component Analysis

Disease spreading models need a population model to organize how individuals are distributed over space and how they are connected. Usually, disease agent (bacteria, virus) passes between individuals through these connections and an epidemic outbreak may occur. Here, complex networks models, like Erdös-Rényi, Small-World, Scale-Free and Barábasi-Albert will be used for modeling a population, since they are used for social networks; and the disease will be modeled by a SIR (Susceptible-Infected-Recovered) model. The objective of this work is, regardless of the network/population model, analyze which topological parameters are more relevant for a disease success or failure. Therefore, the SIR model is simulated in a wide range of each network model and a first analysis is done. By using data from all simulations, an investigation with Principal Component Analysis (PCA) is done in order to find the most relevant topological and disease parameters.

Pest risk assessment of Radopholus similis for the EU territory

The Panel on Plant Health performed a pest risk assessment on Radopholus similis, the burrowing nematode for the EU. The quantitative assessment focused on entry, establishment, spread and impact on tropical and subtropical ornamental host plants, the main pathways for entry of R. similis into the EU. Infested consignments are expected to enter the risk assessment area on ornamentals under all scenarios. For citrus, which is a closed pathway for entry, outdoor establishment was assessed. Establishment may only take place after successful transfer from ornamental plants to citrus production systems. This event is called ‘shift’ in this assessment, to indicate that this is an unusual transfer. It has been estimated that establishment of this nematode in the open field in the EU citrus production areas under current temperatures is possible in most parts of the citrus production area in the EU. Temperature conditions will prevent the nematode from establishing only in the northernmost citrus areas and at higher altitudes in the south. Host plants for planting originating from infested places of production (greenhouses) within the risk assessment area are considered the main pathway for spread within the risk assessment area. Under current climatic conditions, the population of R. similis is not expected to reach damaging population levels in the open field. In case of increased temperatures due to global warming, the nematode population may reach damaging levels in very few places outdoors. Currently, main impact is considered for ornamental greenhouse production in the risk assessment area. Impact will be either caused by direct plant growth reductions or loss due to phytosanitary measures applied on regulated plants. Despite the fact that R. similis is globally considered as one of the most destructive plant parasitic nematodes, the impact in the risk assessment area is considered low.

The role of global trade and transport network topology in the human-mediated dispersal of alien species

More people and goods are moving further and more frequently via many different trade and transport networks under current trends of globalisation. These networks can play a major role in the unintended introduction of exotic species to new locations. With the continuing rise in global trade, more research attention is being focused on the role of networks in the spread of invasive species. This represents an emerging field of research in invasion science and the substantial knowledge being generated within other disciplines can provide ecologists with new tools with which to study invasions. For the first time, we synthesise studies from several perspectives, approaches and disciplines to derive the fundamental characteristics of network topology determining the likelihood of spread of organisms via trade and transport networks. These characteristics can be used to identify critical points of vulnerability within these networks and enable the development of more effective strategies to prevent invasions.

Replicating disease spread in empirical cattle networks by adjusting the probability of infection in random networks

Comparisons between mass-action or "random" network models and empirical networks have produced mixed results. Here we seek to discover whether a simulated disease spread through randomly constructed networks can be coerced to model the spread in empirical networks by altering a single disease parameter - the probability of infection. A stochastic model for disease spread through herds of cattle is utilised to model the passage of an SEIR (susceptible-latent-infected-resistant) through five networks. The first network is an empirical network of recorded contacts, from four datasets available, and the other four networks are constructed from randomly distributed contacts based on increasing amounts of information from the recorded network. A numerical study on adjusting the value of the probability of infection was conducted for the four random network models. We found that relative percentage reductions in the probability of infection, between 5.6% and 39.4% in the random network models, produced results that most closely mirrored the results from the empirical contact networks. In all cases tested, to reduce the differences between the two models, required a reduction in the probability of infection in the random network.

Network epidemiology and plant trade networks

Models of epidemics in complex networks are improving our predictive understanding of infectious disease outbreaks. Nonetheless, applying network theory to plant pathology is still a challenge. This overview summarizes some key developments in network epidemiology that are likely to facilitate its application in the study and management of plant diseases. Recent surveys have provided much-needed datasets on contact patterns and human mobility in social networks, but plant trade networks are still understudied. Human (and plant) mobility levels across the planet are unprecedented-there is thus much potential in the use of network theory by plant health authorities and researchers. Given the directed and hierarchical nature of plant trade networks, there is a need for plant epidemiologists to further develop models based on undirected and homogeneous networks. More realistic plant health scenarios would also be obtained by developing epidemic models in dynamic, rather than static, networks. For plant diseases spread by the horticultural and ornamental trade, there is the challenge of developing spatio-temporal epidemic simulations integrating network data. The use of network theory in plant epidemiology is a promising avenue and could contribute to anticipating and preventing plant health emergencies such as European ash dieback.

Highly dynamic animal contact network and implications on disease transmission

Contact patterns among hosts are considered as one of the most critical factors contributing to unequal pathogen transmission. Consequently, networks have been widely applied in infectious disease modeling. However most studies assume static network structure due to lack of accurate observation and appropriate analytic tools. In this study we used high temporal and spatial resolution animal position data to construct a high-resolution contact network relevant to infectious disease transmission. The animal contact network aggregated at hourly level was highly variable and dynamic within and between days, for both network structure (network degree distribution) and individual rank of degree distribution in the network (degree order). We integrated network degree distribution and degree order heterogeneities with a commonly used contact-based, directly transmitted disease model to quantify the effect of these two sources of heterogeneity on the infectious disease dynamics. Four conditions were simulated based on the combination of these two heterogeneities. Simulation results indicated that disease dynamics and individual contribution to new infections varied substantially among these four conditions under both parameter settings. Changes in the contact network had a greater effect on disease dynamics for pathogens with smaller basic reproduction number (i.e. R₀ < 2).

Networks and plant disease management: concepts and applications

A network is a natural structure with which to describe many aspects of a plant pathosystem. The article seeks to set out in a nonmathematical way some of the network concepts that promise to be useful in managing plant disease. The field has been stimulated by developments designed to help understand and manage animal and human disease, and by technical infrastructures, such as the internet. It overlaps partly with landscape ecology. The study of networks has helped identify likely ways to reduce the flow of disease in traded plants, to find the best sites to monitor as warning sites for annually reinvading diseases, and to understand the fundamentals of how a pathogen spreads in different structures. A tension between the free flow of goods or species down communication channels and free flow of pathogens down the same pathways is highlighted.

Endemic infections are always possible on regular networks

We study the dependence of the largest component in regular networks on the clustering coefficient, showing that its size changes smoothly without undergoing a phase transition. We explain this behavior via an analytical approach based on the network structure, and provide an exact equation describing the numerical results. Our work indicates that intrinsic structural properties always allow the spread of epidemics on regular networks.

Modeling epidemic spread with awareness and heterogeneous transmission rates in networks

During an epidemic outbreak in a human population, susceptibility to infection can be reduced by raising awareness of the disease. In this paper, we investigate the effects of three forms of awareness (i.e., contact, local, and global) on the spread of a disease in a random network. Connectivity-correlated transmission rates are assumed. By using the mean-field theory and numerical simulation, we show that both local and contact awareness can raise the epidemic thresholds while the global awareness cannot, which mirrors the recent results of Wu et al. The obtained results point out that individual behaviors in the presence of an infectious disease has a great influence on the epidemic dynamics. Our method enriches mean-field analysis in epidemic models.

A new scale-free network model for simulating and predicting epidemics

The course of epidemics often resembles a scale-free network, but some specific elements should be considered in developing a new model. This study introduces a time-shifting and discontinuous forcing function H into the scale-free network model to fit the specific period and intensity of the infection, and redefines the probability p as abortive infection rate. For the non-human vectors or hosts, three new factors (new connectivity K(i)(t), new links M, and time delay τ) were introduced in the proposed model of this study. The simulation results of six types of epidemic transmissions show that the proposed Scale-Free Epidemic Models, SFE-1 and SFE-2, are accurate. SFE-1 model and SFE-2 model are useful for the transmission categories from human and insects/vertebrates, respectively. Further comparisons of different races/ethnicities and different transmission categories of AIDS cases in the United States were also analyzed. Both SFE models can be used to predict epidemics and can suggest the results more clearly, irrespective of whether the epidemics are under control. Therefore, the proposed SFE models can help the government determine the level of caution required and predict the results of policy decisions, thus helping to balance socioeconomic and health concerns.

Disease transmission on fragmented contact networks: livestock-associated Methicillin-resistant Staphylococcus aureus in the Danish pig-industry

Animal trade in industrialised livestock-production systems creates a complex, heterogeneous, contact network that shapes between-herd transmission of infectious diseases. We report the results of a simple mathematical model that explores patterns of spread and persistence of livestock-associated Methicillin-resistant Staphylococcus aureus (LA-MRSA) in the Danish pig-industry associated with this trade network. Simulations show that LA-MRSA can become endemic sustained by animal movements alone. Despite the extremely low predicted endemic prevalence, eradication may be difficult, and decreasing within-farm prevalence, or the time it takes a LA-MRSA positive farm to recover a negative status, fails to break long-term persistence. Our results suggest that a low level of non-movement induced transmission strongly affects MRSA dynamics, increasing endemic prevalence and probability of persistence. We also compare the model-predicted risk of 291 individual farms becoming MRSA positive, with results from a recent Europe-wide survey of LA-MRSA in holdings with breeding pigs, and find a significant correlation between contact-network connectivity properties and the model-estimated risk measure.

Social encounter networks: collective properties and disease transmission

A fundamental challenge of modern infectious disease epidemiology is to quantify the networks of social and physical contacts through which transmission can occur. Understanding the collective properties of these interactions is critical for both accurate prediction of the spread of infection and determining optimal control measures. However, even the basic properties of such networks are poorly quantified, forcing predictions to be made based on strong assumptions concerning network structure. Here, we report on the results of a large-scale survey of social encounters mainly conducted in Great Britain. First, we characterize the distribution of contacts, which possesses a lognormal body and a power-law tail with an exponent of −2.45; we provide a plausible mechanistic model that captures this form. Analysis of the high level of local clustering of contacts reveals additional structure within the network, implying that social contacts are degree assortative. Finally, we describe the epidemiological implications of this local network structure: these contradict the usual predictions from networks with heavy-tailed degree distributions and contain public-health messages about control. Our findings help us to determine the types of realistic network structure that should be assumed in future population level studies of infection transmission, leading to better interpretations of epidemiological data and more appropriate policy decisions.

Is network clustering detectable in transmission trees?

Networks are often used to model the contact processes that allow pathogens to spread between hosts but it remains unclear which models best describe these networks. One question is whether clustering in networks, roughly defined as the propensity for triangles to form, affects the dynamics of disease spread. We perform a simulation study to see if there is a signal in epidemic transmission trees of clustering. We simulate susceptible-exposed-infectious-removed (SEIR) epidemics (with no re-infection) over networks with fixed degree sequences but different levels of clustering and compare trees from networks with the same degree sequence and different clustering levels. We find that the variation of such trees simulated on networks with different levels of clustering is barely greater than those simulated on networks with the same level of clustering, suggesting that clustering can not be detected in transmission data when re-infection does not occur.

Integrating natural and social science perspectives on plant disease risk, management and policy formulation

Plant diseases threaten both food security and the botanical diversity of natural ecosystems. Substantial research effort is focused on pathogen detection and control, with detailed risk management available for many plant diseases. Risk can be assessed using analytical techniques that account for disease pressure both spatially and temporally. We suggest that such technical assessments of disease risk may not provide an adequate guide to the strategies undertaken by growers and government to manage plant disease. Instead, risk-management strategies need to account more fully for intuitive and normative responses that act to balance conflicting interests between stakeholder organizations concerned with plant diseases within the managed and natural environments. Modes of effective engagement between policy makers and stakeholders are explored in the paper, together with an assessment of such engagement in two case studies of contemporary non-indigenous diseases in one food and in one non-food sector. Finally, a model is proposed for greater integration of stakeholders in policy decisions.

Networks in plant epidemiology: from genes to landscapes, countries, and continents

There is increasing use of networks in ecology and epidemiology, but still relatively little application in phytopathology. Networks are sets of elements (nodes) connected in various ways by links (edges). Network analysis aims to understand system dynamics and outcomes in relation to network characteristics. Many existing natural, social, and technological networks have been shown to have small-world (local connectivity with short-cuts) and scale-free (presence of super-connected nodes) properties. In this review, we discuss how network concepts can be applied in plant pathology from the molecular to the landscape and global level. Wherever disease spread occurs not just because of passive/natural dispersion but also due to artificial movements, it makes sense to superimpose realistic models of the trade in plants on spatially explicit models of epidemic development. We provide an example of an emerging pathosystem (Phytophthora ramorum) where a theoretical network approach has proven particularly fruitful in analyzing the spread of disease in the UK plant trade. These studies can help in assessing the future threat posed by similar emerging pathogens. Networks have much potential in plant epidemiology and should become part of the standard curriculum.

Identifying potential survival strategies of HIV-1 through virus-host protein interaction networks

Background

The National Institute of Allergy and Infectious Diseases has launched the HIV-1 Human Protein Interaction Database in an effort to catalogue all published interactions between HIV-1 and human proteins. In order to systematically investigate these interactions functionally and dynamically, we have constructed an HIV-1 human protein interaction network. This network was analyzed for important proteins and processes that are specific for the HIV life-cycle. In order to expose viral strategies, network motif analysis was carried out showing reoccurring patterns in virus-host dynamics.

Results

Our analyses show that human proteins interacting with HIV form a densely connected and central sub-network within the total human protein interaction network. The evaluation of this sub-network for connectivity and centrality resulted in a set of proteins essential for the HIV life-cycle. Remarkably, we were able to associate proteins involved in RNA polymerase II transcription with hubs and proteasome formation with bottlenecks. Inferred network motifs show significant over-representation of positive and negative feedback patterns between virus and host. Strikingly, such patterns have never been reported in combined virus-host systems.

Conclusions

HIV infection results in a reprioritization of cellular processes reflected by an increase in the relative importance of transcriptional machinery and proteasome formation. We conclude that during the evolution of HIV, some patterns of interaction have been selected for resulting in a system where virus proteins preferably interact with central human proteins for direct control and with proteasomal proteins for indirect control over the cellular processes. Finally, the patterns described by network motifs illustrate how virus and host interact with one another.

Estimating animal movement contacts between holdings of different production types

Animal movement poses a great risk for disease transmission between holdings. Heterogeneous contact patterns are known to influence the dynamics of disease transmission and should be included in modeling. Using pig movement data from Sweden as an example, we present a method for quantification of between holding contact probabilities based on different production types. The data contained seven production types: Sow pool center, Sow pool satellite, Farrow-to-finish, Nucleus herd, Piglet producer, Multiplying herd and Fattening herd. The method also estimates how much different production types will determine the contact pattern of holdings that have more than one type. The method is based on Bayesian analysis and uses data from central databases of animal movement. Holdings with different production types are estimated to vary in the frequency of contacts as well as in what type of holding they have contact with, and the direction of the contacts. Movements from Multiplying herds to Sow pool centers, Nucleus herds to other Nucleus herds, Sow pool centers to Sow pool satellites, Sow pool satellites to Sow pool centers and Nucleus herds to Multiplying herds were estimated to be most common relative to the abundance of the production types. We show with a simulation study that these contact patterns may also be expected to result in substantial differences in disease transmission via animal movements, depending on the index holding. Simulating transmission for a 1 year period showed that the median number of infected holdings was 1 (i.e. only the index holding infected) if the infection started at a Fattening herd and 2161 if the infection started on a Nucleus herd. We conclude that it is valuable to include production types in models of disease transmission and the method presented in this paper may be used for such models when appropriate data is available. We also argue that keeping records of production types is of great value since it may be helpful in risk assessments.