Epidemic variability in complex networks

Crépey, Pascal; Álvarez, Francisco Blanco; Barthélemy, Marc

doi:10.1103/physreve.73.046131

Cited by 55 publications

(60 citation statements)

References 31 publications

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“…In most cases our theoretical predictions are in a good agreement with the numerical effective epidemic thresholds identified by the variability measure [28,29], which has been confirmed to be effective for identifying the SIR effective epidemic threshold [30]. Although there exist some differences between the theoretical predictions and numerical results in networks with disassortative mixing, the theoretical effective epidemic threshold displays the same trend to that of the numerical effective epidemic threshold.…”

Section: Introductionsupporting

confidence: 72%

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Recovery rate affects the effective epidemic threshold with synchronous updating

Shu

Wang

Tang

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Accurate identification of effective epidemic threshold is essential for understanding epidemic dynamics on complex networks. The existing studies on the effective epidemic threshold of the susceptible-infected-removed (SIR) model generally assume that all infected nodes immediately recover after the infection process, which more or less does not conform to the realistic situation of disease. In this paper, we systematically study the effect of arbitrary recovery rate on the SIR spreading dynamics on complex networks. We derive the theoretical effective epidemic threshold and final outbreak size based on the edge-based compartmental theory. To validate the proposed theoretical predictions, extensive numerical experiments are implemented by using asynchronous and synchronous updating methods. When asynchronous updating method is used in simulations, recovery rate does not affect the final state of spreading dynamics. But with synchronous updating, we find that the effective epidemic threshold decreases with recovery rate, and final outbreak size increases with recovery rate. A good agreement between the theoretical predictions and numerical results are observed on both synthetic and real-world networks. Our results extend the existing theoretical studies, and help us to understand the phase transition with arbitrary recovery rate. 64.60.Ht How to accurately predict the effective epidemic threshold has attracted increasing attentions. The existing studies on the epidemic threshold generally suppose the recovery process with a constant recovery rate of 1, while the investigation on the effect of recovery rate is still insufficient. Considering the difference of recovery rate between different real diseases and the accompanying effects on the human health, it is very necessary to predict the effective epidemic thresholds with different recovery rates. In this work, the effect of recovery rate on the effective threshold of epidemic outbreak is systematically studied. We first develop a novel theoretical framework based on the edge-based compartmental theory. The developed theory predicts that recovery rate does not affect the spreading dynamics with asynchronous updating, but with synchronous updating, the effective epidemic threshold decreases with the recovery rate, and the final outbreak sizes increases with the recovery rate for a given effective transmission rate. It should be noted that the SIR epidemic of synchronous updating breaks more easily than asynchronous updating. To verify the accuracy of the theoretical predictions, we numerically predict the effective epidemic threshold using the variability measure on random regular networks, where the numerical results agrees well with the theoretical predictions. Moreover, we investigate how the recovery rate affects the epidemic outbreaks with synchronous updating on scale-free networks and real-world networks, and find the same variation trend of effective epidemic threshold. * Electronic address:

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Section: Introductionsupporting

confidence: 72%

“…To numerically identify the effective epidemic threshold of the SIR model, we use the variability measure [28,29] …”

Section: Resultsmentioning

confidence: 99%

Recovery rate affects the effective epidemic threshold with synchronous updating

Shu

Wang

Tang

et al. 2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

View full text Add to dashboard Cite

show abstract

“…Both Monte Carlo simulations [14][15][16][17] and theoretical study [18] have investigated the effects of network structures on epidemic spreading velocity [19,20], epidemic variability [21,22], epidemic size [23][24][25][26][27][28], and epidemic thresholds [29][30][31][32][33][34]. Both the epidemic size and threshold can indicate the probability of an epidemic occurring [32], which seeds are influential [35][36][37][38], and how to effectively control the epidemic once it begins [39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Unification of theoretical approaches for epidemic spreading on complex networks

et al. 2017

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Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical messagepassing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.

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“…For simplicity, estimates of R 0 for infectious diseases have mostly been based on either susceptible-infectious (SI) or susceptible-infectious-recovered (SIR) models assuming a homogeneous mixing process. Recognising that these conditions are rarely met, attempts have been made to quantify the extent and direction of the bias in estimates of R 0 in disease epidemics in animal and human populations [15,23,43,50,57]. In this study, we have extended the approach of May et al [50] by introducing stochastic variation in the number of contacts and duration of infectiousness (Eq.…”

Section: Discussionmentioning

confidence: 99%

Influence of contact heterogeneity on TB reproduction ratioR₀in a free-living brushtail possumTrichosurus vulpeculapopulation

et al. 2008

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-Social network analyses were used to investigate contact patterns in a free-living possum Trichosurus vulpecula population and to estimate the influence of contact on R 0 for bovine tuberculosis (TB). Using data collected during a five-year capture-mark-recapture study of a free-living possum population, observed estimates of R 0 were computed and compared with R 0 computed from random networks of similar size that approximated a random mixing process. All networks displayed a heterogeneous pattern of contact with the average number of contacts per possum ranging from 20 to 26 per year. The networks consistently showed small-world and single-scale features. The mean estimates of R 0 for TB using the observed contact networks were 1.78, 1.53, 1.53, 1.51, and 1.52 times greater than the corresponding random networks (P < 0.05). We estimate that TB would spread if an average of between 1.94 and 1.97 infective contacts occurred per year per infected possum, which is approximately half of that expected from a random network. These results have implications for the management of TB in New Zealand where the possum is the principal wildlife reservoir host of Mycobacterium bovis, the causal agent of bovine TB. This study argues the relevance of refining epidemiological models used to inform disease management policy to account for contact heterogeneity.basic reproduction ratio / Mycobacterium bovis / small-world / social network analysis / wildlife disease

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Epidemic variability in complex networks

Cited by 55 publications

References 31 publications

Recovery rate affects the effective epidemic threshold with synchronous updating

Recovery rate affects the effective epidemic threshold with synchronous updating

Unification of theoretical approaches for epidemic spreading on complex networks

Influence of contact heterogeneity on TB reproduction ratioR₀in a free-living brushtail possumTrichosurus vulpeculapopulation

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Epidemic variability in complex networks

Cited by 55 publications

References 31 publications

Recovery rate affects the effective epidemic threshold with synchronous updating

Recovery rate affects the effective epidemic threshold with synchronous updating

Unification of theoretical approaches for epidemic spreading on complex networks

Influence of contact heterogeneity on TB reproduction ratioR0in a free-living brushtail possumTrichosurus vulpeculapopulation

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Product

Resources

About

Influence of contact heterogeneity on TB reproduction ratioR₀in a free-living brushtail possumTrichosurus vulpeculapopulation