Phase diagram of epidemic spreading — unimodal vs. bimodal probability distributions

Lancic, Alen; Antulov-Fantulin, Nino; Šikić, Mile; Štefančić, Hrvoje

doi:10.1016/j.physa.2010.06.024

Cited by 9 publications

(10 citation statements)

References 21 publications

(16 reference statements)

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“…We will also often use the notation P (X n = k), which denotes the probability that the infected node infects k neighbours out of total n susceptible neighbours in the limit of the time. This probability has the following analytical form [21] in the SIR model:…”

Section: Epidemic Simulation Problemmentioning

confidence: 99%

“…To that end, we will use X n , random variable of a number of directly infected susceptible nodes by the infected node of degree n [21]. It can be easily verified that …”

Section: Time and Space Complexity Analysis Of The Naive Sir Algorithmmentioning

confidence: 99%

“…For a network with cycles, it is difficult to analytically calculate the expected number of infected nodes, but we can calculate it for a regular m-arry tree. To that end, we will use X n , random variable of a number of directly infected susceptible nodes by the infected node of degree n [21]. It can be easily verified that…”

Section: Algorithm 1 the Naive Sir Algorithmmentioning

confidence: 99%

“…Looking at complexity of Algorithm 1, we can see that possible speed up of sequential version of the algorithm can be obtained only by reducing the 1/q part. Since we know how to calculate the probability distributions for the number of infected nodes [21], the idea is to choose that number from distribution. The probability that the infected node infects k neighbours out of total n susceptible neighbours in the limit of the time is:…”

Section: The Fastsir Algorithmmentioning

confidence: 99%

“…Recently, the phase diagrams of epidemic spreading with the SIR model on complex networks were introduced as a useful tool for epidemic spreading analysis [21]. To predict expected value of the number of infected nodes in epidemic spreading on arbitrary network, we should repeat simulations till standard deviation of the number of the infected nodes sufficiently reduces (in unimodal part of the epidemic phase diagram) or converges to nonzero value (in bimodal part of the epidemic phase diagram).…”

Section: Introductionmentioning

confidence: 99%

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FastSIR algorithm: A fast algorithm for the simulation of the epidemic spread in large networks by using the susceptible–infected–recovered compartment model

Antulov-Fantulin

Lancic

Štefančić

et al. 2013

Information Sciences

Self Cite

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The epidemic spreading on arbitrary complex networks is studied in SIR (Susceptible Infected Recovered) compartment model. We propose our implementation of a Naive SIR algorithm for epidemic simulation spreading on networks that uses data structures efficiently to reduce running time. The Naive SIR algorithm models full epidemic dynamics and can be easily upgraded to parallel version. We also propose novel algorithm for epidemic simulation spreading on networks called the FastSIR algorithm that has better average case running time than the Naive SIR algorithm. The FastSIR algorithm uses novel approach to reduce average case running time by constant factor by using probability distributions of the number of infected nodes. Moreover, the FastSIR algorithm does not follow epidemic dynamics in time, but still captures all infection transfers. Furthermore, we also propose an efficient recursive method for calculating probability distributions of the number of infected nodes. Average case running time of both algorithms has also been derived and experimental analysis was made on five different empirical complex networks.

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Section: Epidemic Simulation Problemmentioning

confidence: 99%

“…To that end, we will use X n , random variable of a number of directly infected susceptible nodes by the infected node of degree n [21]. It can be easily verified that …”

Section: Time and Space Complexity Analysis Of The Naive Sir Algorithmmentioning

confidence: 99%

Section: Algorithm 1 the Naive Sir Algorithmmentioning

confidence: 99%

Section: The Fastsir Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

FastSIR algorithm: A fast algorithm for the simulation of the epidemic spread in large networks by using the susceptible–infected–recovered compartment model

Antulov-Fantulin

Lancic

Štefančić

et al. 2013

Information Sciences

Self Cite

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The effect of social distancing on the reach of an epidemic in social networks

Gutin

Hirano

Hwang

et al. 2021

J Econ Interact Coord

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How does social distancing affect the reach of an epidemic in social networks? We present Monte Carlo simulation results of a susceptible–infected–removed with social distancing model. The key feature of the model is that individuals are limited in the number of acquaintances that they can interact with, thereby constraining disease transmission to an infectious subnetwork of the original social network. While increased social distancing typically reduces the spread of an infectious disease, the magnitude varies greatly depending on the topology of the network, indicating the need for policies that are network dependent. Our results also reveal the importance of coordinating policies at the ‘global’ level. In particular, the public health benefits from social distancing to a group (e.g. a country) may be completely undone if that group maintains connections with outside groups that are not following suit.

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Benchmarking Measures of Network Influence

Bramson

Vandermarliere

2016

Sci Rep

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Identifying key agents for the transmission of diseases (ideas, technology, etc.) across social networks has predominantly relied on measures of centrality on a static base network or a temporally flattened graph of agent interactions. Various measures have been proposed as the best trackers of influence, such as degree centrality, betweenness, and k-shell, depending on the structure of the connectivity. We consider SIR and SIS propagation dynamics on a temporally-extruded network of observed interactions and measure the conditional marginal spread as the change in the magnitude of the infection given the removal of each agent at each time: its temporal knockout (TKO) score. We argue that this TKO score is an effective benchmark measure for evaluating the accuracy of other, often more practical, measures of influence. We find that none of the network measures applied to the induced flat graphs are accurate predictors of network propagation influence on the systems studied; however, temporal networks and the TKO measure provide the requisite targets for the search for effective predictive measures.

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Phase diagram of epidemic spreading — unimodal vs. bimodal probability distributions

Cited by 9 publications

References 21 publications

FastSIR algorithm: A fast algorithm for the simulation of the epidemic spread in large networks by using the susceptible–infected–recovered compartment model

FastSIR algorithm: A fast algorithm for the simulation of the epidemic spread in large networks by using the susceptible–infected–recovered compartment model

The effect of social distancing on the reach of an epidemic in social networks

Benchmarking Measures of Network Influence

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