Laurent Hébert-Dufresne

Adaptive networks: Coevolution of disease and topology

Adaptive networks have been recently introduced in the context of disease propagation on complex networks. They account for the mutual interaction between the network topology and the states of the nodes. Until now, existing models have been analyzed using low complexity analytical formalisms, revealing nevertheless some novel dynamical features. However, current methods have failed to reproduce with accuracy the simultaneous time evolution of the disease and the underlying network topology. In the framework of the adaptive susceptible-infectious-susceptible (SIS) model of Gross [Phys. Rev. Lett. 96, 208701 (2006)]10.1103/PhysRevLett.96.208701, we introduce an improved compartmental formalism able to handle this coevolutionary task successfully. With this approach, we analyze the interplay and outcomes of both dynamical elements, process and structure, on adaptive networks featuring different degree distributions at the initial stage.

Modeling the dynamical interaction between epidemics on overlay networks.

Epidemics seldom occur as isolated phenomena. Typically, two or more viral agents spread within the same host population and may interact dynamically with each other. We present a general model where two viral agents interact via an immunity mechanism as they propagate simultaneously on two networks connecting the same set of nodes. By exploiting a correspondence between the propagation dynamics and a dynamical process performing progressive network generation, we develop an analytical approach that accurately captures the dynamical interaction between epidemics on overlay networks. The formalism allows for overlay networks with arbitrary joint degree distribution and overlap. To illustrate the versatility of our approach, we consider a hypothetical delayed intervention scenario in which an immunizing agent is disseminated in a host population to hinder the propagation of an undesirable agent (e.g., the spread of preventive information in the context of an emerging infectious disease).

Enhancing disease surveillance with novel data streams: challenges and opportunities

Novel data streams (NDS), such as web search data or social media updates, hold promise for enhancing the capabilities of public health surveillance. In this paper, we outline a conceptual framework for integrating NDS into current public health surveillance. Our approach focuses on two key questions: What are the opportunities for using NDS and what are the minimal tests of validity and utility that must be applied when using NDS? Identifying these opportunities will necessitate the involvement of public health authorities and an appreciation of the diversity of objectives and scales across agencies at different levels (local, state, national, international). We present the case that clearly articulating surveillance objectives and systematically evaluating NDS and comparing the performance of NDS to existing surveillance data and alternative NDS data is critical and has not sufficiently been addressed in many applications of NDS currently in the literature.

Global efficiency of local immunization on complex networks

Epidemics occur in all shapes and forms: infections propagating in our sparse sexual networks, rumours and diseases spreading through our much denser social interactions, or viruses circulating on the Internet. With the advent of large databases and efficient analysis algorithms, these processes can be better predicted and controlled. In this study, we use different characteristics of network organization to identify the influential spreaders in 17 empirical networks of diverse nature using 2 epidemic models. We find that a judicious choice of local measures, based either on the networks connectivity at a microscopic scale or on its community structure at a mesoscopic scale, compares favorably to global measures, such as betweenness centrality, in terms of efficiency, practicality and robustness. We also develop an analytical framework that highlights a transition in the characteristic scale of different epidemic regimes. This allows to decide which local measure should govern immunization in a given scenario.

Complex dynamics of synergistic coinfections on realistically clustered networks

Significance Concurrent infection with multiple pathogens is an important factor for human disease. For example, rates of Streptococcus pneumoniae carriage (a leading cause of pneumonia) in children under five years can exceed 80%, and coinfection with other respiratory infections (e.g., influenza) can increase mortality drastically; despite this, examination of interacting coinfections on realistic human contact structures remains an understudied problem in epidemiology and network science. Here we show that clustering of contacts, which usually hinders disease spread, can speed up spread of both diseases by keeping synergistic infections together and that a microscopic change in transmission rates can cause a macroscopic change in expected epidemic size, such that clustered networks can sustain diseases that would otherwise die in random networks. We investigate the impact of contact structure clustering on the dynamics of multiple diseases interacting through coinfection of a single individual, two problems typically studied independently. We highlight how clustering, which is well known to hinder propagation of diseases, can actually speed up epidemic propagation in the context of synergistic coinfections if the strength of the coupling matches that of the clustering. We also show that such dynamics lead to a first-order transition in endemic states, where small changes in transmissibility of the diseases can lead to explosive outbreaks and regions where these explosive outbreaks can only happen on clustered networks. We develop a mean-field model of coinfection of two diseases following susceptible-infectious-susceptible dynamics, which is allowed to interact on a general class of modular networks. We also introduce a criterion based on tertiary infections that yields precise analytical estimates of when clustering will lead to faster propagation than nonclustered networks. Our results carry importance for epidemiology, mathematical modeling, and the propagation of interacting phenomena in general. We make a call for more detailed epidemiological data of interacting coinfections.

The effect of a prudent adaptive behaviour on disease transmission

Infectious diseases often spread faster near their peak than would be predicted given early data on transmission . Despite the commonality of this phenomena, there are no known general mechanisms able to cause an exponentially spreading disease to begin spreading faster. Indeed most features of real world social networks, e.g. clustering1,2 and community structure3, and of human behaviour, e.g. social distancing4 and increased hygiene5, will slow disease spread. Here, we consider a model where individuals with essential societal roles–e.g. teachers, first responders, health-care workers, etc.– who fall ill are replaced with healthy individuals. We refer to this process as relational exchange. Relational exchange is also a behavioural process, but one whose effect on disease transmission is less obvious. By incorporating this behaviour into a dynamic network model, we demonstrate that replacing individuals can accelerate disease transmission. Furthermore, we find that the effects of this process are trivial when considering a standard mass-action model, but dramatic when considering network structure. This result highlights another critical shortcoming in mass-action models, namely their inability to account for behavioural processes. Lastly, using empirical data, we find that this mechanism parsimoniously explains observed patterns across more than seventeen years of influenza and dengue virus data. We anticipate that our findings will advance the emerging field of disease forecasting and will better inform public health decision making during outbreaks.

Propagation dynamics on networks featuring complex topologies

Analytical description of propagation phenomena on random networks has flourished in recent years, yet more complex systems have mainly been studied through numerical means. In this paper, a mean-field description is used to coherently couple the dynamics of the network elements (such as nodes, vertices, individuals, etc.) on the one hand and their recurrent topological patterns (such as subgraphs, groups, etc.) on the other hand. In a susceptible-infectious-susceptible (SIS) model of epidemic spread on social networks with community structure, this approach yields a set of ordinary differential equations for the time evolution of the system, as well as analytical solutions for the epidemic threshold and equilibria. The results obtained are in good agreement with numerical simulations and reproduce the behavior of random networks in the appropriate limits which highlights the influence of topology on the processes. Finally, it is demonstrated that our model predicts higher epidemic thresholds for clustered structures than for equivalent random topologies in the case of networks with zero degree correlation.

Epidemic cycles driven by host behaviour

Host immunity and demographics (the recruitment of susceptibles via birthrate) have been demonstrated to be a key determinant of the periodicity of measles, pertussis and dengue epidemics. However, not all epidemic cycles are from pathogens inducing sterilizing immunity or are driven by demographics. Many sexually transmitted infections are driven by sexual behaviour. We present a mathematical model of disease transmission where individuals can disconnect and reconnect depending on the infectious status of their contacts. We fit the model to historic syphilis (Treponema pallidum) and gonorrhea (Neisseria gonorrhoeae) incidence in the USA and explore potential intervention strategies against syphilis. We find that cycles in syphilis incidence can be driven solely by changing sexual behaviour in structured populations. Our model also explains the lack of similar cycles in gonorrhea incidence even if the two infections share the same propagation pathways. Our model similarly illustrates how sudden epidemic outbreaks can occur on time scales smaller than the characteristic demographic time scale of the population and that weaker infections can lead to more violent outbreaks. Behaviour also appears to be critical for control strategies as we found a bigger sensitivity to behavioural interventions than antibiotic treatment. Thus, behavioural interventions may play a larger role than previously thought, especially in the face of antibiotic resistance and low intervention efficacies.

Bond percolation on a class of correlated and clustered random graphs

We introduce a formalism for computing bond percolation properties of a class of correlated and clustered random graphs. This class of graphs is a generalization of the configuration model where nodes of different types are connected via different types of hyperedges, edges that can link more than two nodes. We argue that the multitype approach coupled with the use of clustered hyperedges can reproduce a wide spectrum of complex patterns, and thus enhances our capability to model real complex networks. As an illustration of this claim, we use our formalism to highlight unusual behaviours of the size and composition of the components (small and giant) in a synthetic, albeit realistic, social network.

Structural preferential attachment: network organization beyond the link.

We introduce a mechanism which models the emergence of the universal properties of complex networks, such as scale independence, modularity and self-similarity, and unifies them under a scale-free organization beyond the link. This brings a new perspective on network organization where communities, instead of links, are the fundamental building blocks of complex systems. We show how our simple model can reproduce social and information networks by predicting their community structure and more importantly, how their nodes or communities are interconnected, often in a self-similar manner.