Avalanche outbreaks emerging in cooperative contagions

Cai, Weiran; Chen, Li; Ghanbarnejad, Fakhteh; Grassberger, Peter

doi:10.1038/nphys3457

Cited by 158 publications

(187 citation statements)

References 25 publications

Supporting

Mentioning

169

Contrasting

Order By: Relevance

“…The last two thresholds correspond to the contributions to T (1) c and T (2) c that involve exclusively the homosexual male or heterosexual subpopulations, respectively. They are the solutions of α 0|0 k e T (5) c = 1 and α 4|5 α 5|4 [ k e T (6) c ] 2 /a = 1, respectively, where nodes of type zero, four, and five correspond to homosexual males, heterosexual males, and heterosexual females, respectively. These results, therefore, support the interpretation that the first threshold corresponds to the invasion of the MSM subpopulation [with T (3) c and T (5) c acting as lower and upper bounds, respectively] and that the second threshold is caused by the invasion of the remaining population [with T (4) c and T (6) c acting as lower and upper bounds, respectively].…”

Section: Resultsmentioning

confidence: 99%

“…They are the solutions of α 0|0 k e T (5) c = 1 and α 4|5 α 5|4 [ k e T (6) c ] 2 /a = 1, respectively, where nodes of type zero, four, and five correspond to homosexual males, heterosexual males, and heterosexual females, respectively. These results, therefore, support the interpretation that the first threshold corresponds to the invasion of the MSM subpopulation [with T (3) c and T (5) c acting as lower and upper bounds, respectively] and that the second threshold is caused by the invasion of the remaining population [with T (4) c and T (6) c acting as lower and upper bounds, respectively]. Inset shows the growing separation of the two main thresholds as asymmetry increases to values close to what we expect for ZIKV.…”

Section: Resultsmentioning

confidence: 99%

See 1 more Smart Citation

Asymmetric percolation drives a double transition in sexual contact networks

Allard

Althouse

Scarpino

2017

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

View full text Add to dashboard Cite

Zika virus (ZIKV) exhibits unique transmission dynamics in that itis concurrently spread by a mosquito vector and through sexual contact. Due to the highly asymmetric durations of infectiousness between males and females-it is estimated that males are infectious for periods up to 10 times longer than females-we show that this sexual component of ZIKV transmission behaves akin to an asymmetric percolation process on the network of sexual contacts. We exactly solve the properties of this asymmetric percolation on random sexual contact networks and show that this process exhibits two epidemic transitions corresponding to a core-periphery structure. This structure is not present in the underlying contact networks, which are not distinguishable from random networks, and emerges because of the asymmetric percolation. We provide an exact analytical description of this double transition and discuss the implications of our results in the context of ZIKV epidemics. Most importantly, our study suggests a bias in our current ZIKV surveillance, because the community most at risk is also one of the least likely to get tested.A bstract modeling of epidemics on networks remains an active field, because some of the most basic features of epidemics are still misunderstood. The classic model is quite simple (1): disease spreads stochastically with a fixed transmission probability, T , through contacts around a given patient zero. The outbreak dies quickly if T is too small but spreads to a macroscopic fraction S of the entire population if T is larger than a threshold Tc. At Tc, most of the typical insights from phase transition theory are valuable. For instance, the sizes of microscopic outbreaks follow a power law distribution, such that the expected size of microscopic outbreaks, s , indicates the position of a phase transition. Indeed, as T increases, s monotonically increases, diverges exactly at Tc, and then monotonically goes down; meanwhile, the expected macroscopic epidemic size, S , starts increasing monotonically at Tc.However, simple modifications to this model can dramatically alter its phenomenology. The epidemic threshold can vanish in networks with a scale-free degree distribution (2) or in growing networks (3). The phase transition can be discontinuous in the case of complex contagions with threshold exposition or reinforcement (4), interacting epidemics (5, 6), or adaptive networks (7-9). Recently, a unique phenomenon of double-phase transitions has also been observed numerically when networks have a very heterogeneous and clustered structure (10, 11).The current Zika virus (ZIKV) epidemic exhibits two unique properties. First, while the main transmission pathway for ZIKV is through a mosquito vector [predominantly Aedes aegypti or Aedes albopictus (13, 14)], a feature which has its own type of well-studied model and behavior (14-16), it can also spread through sexual contacts (17, 18). Second, the probability of sexual transmission is highly asymmetric between males and females. Although this is also true for ot...

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Asymmetric percolation drives a double transition in sexual contact networks

Allard

Althouse

Scarpino

2017

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

View full text Add to dashboard Cite

show abstract

“…The DMCGC model could provide therefore an ideal setting to extend models of cooperative contagion studied on single networks [48] to multilayer networks.…”

Section: Introductionmentioning

confidence: 99%

Message passing theory for percolation models on multiplex networks with link overlap

2016

View full text Add to dashboard Cite

Multiplex networks describe a large variety of complex systems, including infrastructures, transportation networks, and biological systems. Most of these networks feature a significant link overlap. It is therefore of particular importance to characterize the mutually connected giant component in these networks. Here we provide a message passing theory for characterizing the percolation transition in multiplex networks with link overlap and an arbitrary number of layers M. Specifically we propose and compare two message passing algorithms that generalize the algorithm widely used to study the percolation transition in multiplex networks without link overlap. The first algorithm describes a directed percolation transition and admits an epidemic spreading interpretation. The second algorithm describes the emergence of the mutually connected giant component, that is the percolation transition, but does not preserve the epidemic spreading interpretation. We obtain the phase diagrams for the percolation and directed percolation transition in simple representative cases. We demonstrate that for the same multiplex network structure, in which the directed percolation transition has nontrivial tricritical points, the percolation transition has a discontinuous phase transition, with the exception of the trivial case in which all the layers completely overlap.

show abstract

“…The authors have argued that their model can fall into one of three universal classes, due to the behavior of fixed point curves. Also, in [38][39][40], the authors consider "implicit memory" by applying asynchronous adapting in disease propagation. They show that this type of memory can lead to a first-order phase transition in outbreaks, thus hysteresis can arise in such models [40].…”

Section: Introductionmentioning

confidence: 99%

Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

et al. 2017

View full text Add to dashboard Cite

Memory has a great impact on the evolution of every process related to human societies. Among them, the evolution of an epidemic is directly related to the individuals' experiences. Indeed, any real epidemic process is clearly sustained by a non-Markovian dynamics: memory effects play an essential role in the spreading of diseases. Including memory effects in the susceptible-infected-recovered (SIR) epidemic model seems very appropriate for such an investigation. Thus, the memory prone SIR model dynamics is investigated using fractional derivatives. The decay of long-range memory, taken as a power-law function, is directly controlled by the order of the fractional derivatives in the corresponding nonlinear fractional differential evolution equations. Here we assume "fully mixed" approximation and show that the epidemic threshold is shifted to higher values than those for the memoryless system, depending on this memory "length" decay exponent. We also consider the SIR model on structured networks and study the effect of topology on threshold points in a non-Markovian dynamics. Furthermore, the lack of access to the precise information about the initial conditions or the past events plays a very relevant role in the correct estimation or prediction of the epidemic evolution. Such a "constraint" is analyzed and discussed.

show abstract

Avalanche outbreaks emerging in cooperative contagions

Cited by 158 publications

References 25 publications

Asymmetric percolation drives a double transition in sexual contact networks

Asymmetric percolation drives a double transition in sexual contact networks

Message passing theory for percolation models on multiplex networks with link overlap

Memory effects on epidemic evolution: The susceptible-infected-recovered epidemic model

Contact Info

Product

Resources

About