Spreading dynamics on complex networks: a general stochastic approach

Noël, Pierre-André; Allard, Antoine; Marceau, Vincent; Dubé, Louis J.

doi:10.1007/s00285-013-0744-9

Cited by 8 publications

(16 citation statements)

References 36 publications

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“…A mean-field description of the time evolution can be written in the spirit of existing formalisms (18,29). Here we give a brief description of how the mean-field equations are obtained and provide the full system in SI Appendix.…”

Section: Network Structure and Epidemic Dynamicsmentioning

confidence: 99%

Complex dynamics of synergistic coinfections on realistically clustered networks

Hébert‐Dufresne

Althouse

2015

Proc. Natl. Acad. Sci. U.S.A.

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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-infectioussusceptible 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.interacting coinfections | epidemiology | network theory | influenza | discontinuous transitions I ndividuals are at constant attack from infectious pathogens. Coinfection with two or more pathogens is common and can seriously alter the course of each infection from its own natural history. Infection with HIV increases susceptibility to many pathogens, especially tuberculosis, where coinfection worsens outcomes and increases transmission of both pathogens (1). Recent studies have examined epidemiological case counts to highlight the importance of upper respiratory infections (e.g., rhinovirus, influenza virus, respiratory syncytial virus [RSV]) and Streptococcus pneumoniae carriage leading to increased risk of pneumococcal pneumonia (2-5), although there are few dynamic transmission models of pneumococcus (PC) and other viral infections.Models of disease transmission in structured populations have remained a main focus of network theory for over a decade as realistic descriptions of contact structures are necessary to understand how diseases are transmitted between individuals (6-11). Typically, specific structural properties (average degree, network size, clustering) are explored in isolation. It remains a strong (and potentially dangerous) assumption that results obtained with different models exploring distinct structural properties will give the same results when combined with other models exploring different properties. Disease transmission is a nonlinear problem with features of the propagation itself interacting in complex ways. In this paper, we focus on combining two much studied phenomena-realistic clustering of contact structure and the interaction of respiratory pathogens (influenza and PC pneumonia)-and show that a combination of these two phenomena leads to behavio...

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Section: Network Structure and Epidemic Dynamicsmentioning

confidence: 99%

Complex dynamics of synergistic coinfections on realistically clustered networks

Hébert‐Dufresne

Althouse

2015

Proc. Natl. Acad. Sci. U.S.A.

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“…We follow the system through a heterogeneous mean-field approximation, where individuals are distinguished by their states (S or I) and by their number of connections (degree k ). This formalism allows us to describe the evolution of both the epidemics and the underlying network even in the presence of significant heterogeneity [ 14 – 18 ]. The mean-field approximation is given by and where Θ si and Θ is are mean-field quantities giving the average probability that a link stemming from a susceptible (infectious) node leads to an infectious (susceptible) node, respectively.…”

Section: Resultsmentioning

confidence: 99%

Epidemic cycles driven by host behaviour

Althouse

Hébert‐Dufresne

2014

J. R. Soc. Interface.

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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.

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“…Connectivity patterns beyond edges are commonly described in terms of small subgraphs called motifs (or graphlets). There is increasing interest in algorithmic methods to count motifs [6,7,8,9,10], or the relation between motifs and network functions, like the spread of epidemics [11,12,13,14,15,16]. Motifs can describe the tendency for clustering and other forms of network organization [17,18,19].…”

Section: Introductionmentioning

confidence: 99%

Variational principle for scale-free network motifs

Stegehuis¹,

Hofstad²,

Leeuwaarden³

2019

Sci Rep

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For scale-free networks with degrees following a power law with an exponent τ ∈ (2, 3), the structures of motifs (small subgraphs) are not yet well understood. We introduce a method designed to identify the dominant structure of any given motif as the solution of an optimization problem. The unique optimizer describes the degrees of the vertices that together span the most likely motif, resulting in explicit asymptotic formulas for the motif count and its fluctuations. We then classify all motifs into two categories: motifs with small and large fluctuations.

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Spreading dynamics on complex networks: a general stochastic approach

Cited by 8 publications

References 36 publications

Complex dynamics of synergistic coinfections on realistically clustered networks

Complex dynamics of synergistic coinfections on realistically clustered networks

Epidemic cycles driven by host behaviour

Variational principle for scale-free network motifs

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