Bayesian Inference of Epidemics on Networks via Belief Propagation

Altarelli, Fabrizio; Braunstein, Alfredo; Dall’Asta, Luca; Lage-Castellanos, Alejandro; Zecchina, Riccardo

doi:10.1103/physrevlett.112.118701

Cited by 173 publications

(147 citation statements)

References 16 publications

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“…In order to understand the of underlying structure in the evolution of collective behaviors, different network models are usually borrowed to simulate the mobility patterns and the interaction patterns [16,17,18,19,20,21,22]. The existing network models can be classified into two families: the network with a single layer, including regular network, random network and scale-free network [23,24,25,26,27], and the network with multiple-layers [28,29,30,31,32], which consists of two or more sub-networks. S. V. Buldyrev et al have studied the properties of two interdependent networks [33], a broader degree distribution is found to increase the vulnerability of the interdependent networks.…”

Section: Introductionmentioning

confidence: 99%

Coupled effects of local movement and global interaction on contagion

Liu

Chen

et al. 2015

Physica A: Statistical Mechanics and its Applications

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By incorporating segregated spatial domain and individual-based linkage into the SIS (susceptible-infected-susceptible) model, we propose a generalized epidemic model which can change from the territorial epidemic model to the networked epidemic model. The role of the individual-based linkage between different spatial domains is investigated. As we adjust the timescale parameter τ from 0 to unity, which represents the degree of activation of the individual-based linkage, three regions are found. Within the region of 0 < τ < 0.02, the epidemic is determined by local movement and is sensitive to the timescale τ . Within the region of 0.02 < τ < 0.5, the epidemic is insensitive to the timescale τ . Within the region of 0.5 < τ < 1, the outbreak of the epidemic is determined by the structure of the individualbased linkage. As we keep an eye on the first region, the role of activating the individual-based linkage in the present model is similar to the role of the shortcuts in the two-dimensional small world network. Only activating a small number of the individual-based linkage can prompt the outbreak of the epidemic globally. The role of narrowing segregated spatial domain and reducing mobility in epidemic control is checked. These two measures are found to be conducive to curbing the spread of infectious disease only when the global interaction is suppressed. A log-log relation between the change in the number of infected individuals and the timescale τ is found.By calculating the epidemic threshold and the mean first encounter time, we heuristically analyze the microscopic characteristics of the propagation of the epidemic in the present model.

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Section: Introductionmentioning

confidence: 99%

Coupled effects of local movement and global interaction on contagion

Liu

Chen

et al. 2015

Physica A: Statistical Mechanics and its Applications

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“…We also note that there are many aspects of the problem we have not yet considered, such as cases of incomplete or noisy information, 7 dynamics of multi-state diffusion, and even multi-source diffusion [12,13,15,16,20,21].…”

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“…Furthermore, the performance of our algorithm can be enhanced by extending what we have done with 2-body correlations to n-body correlations or time dependent correlations to calculate path integrals based on Bayesian inference (e.g. [12] for one specific model). However, generalizing such approaches for any forward model and any network topology is offset by the huge number of simulations required to resolve the correlations to within a useful error margin, and will be very costly.…”

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confidence: 99%

“…However, this is only feasible for small networks. Message-passing algorithms can approximate the marginals efficiently [12,[14][15][16], however these algorithms are model specific: for every M , one must invent new approximations, heuristic assumptions and analytic calculations.In contrast, the second class of methods works independent of the forward model [14,[17][18][19]. These presuppose that s should be approximately equidistant to all other nodes in C, and therefore, nodes with high "centrality" values should have a higher likelihood of being s. This assumption breaks down if the spread reaches "boundaries", or if the spread self-interacts (i.e.…”

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confidence: 99%

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Morphological inversion of complex diffusion

Nguyen

Vural

2017

Phys. Rev. E

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Epidemics, neural cascades, power failures, and many other phenomena can be described by a diffusion process on a network. To identify the causal origins of a spread, it is often necessary to identify the triggering initial node. Here we define a new morphological operator and use it to detect the origin of a diffusive front, given the final state of a complex network. Our method performs better than algorithms based on distance (closeness) and Jordan centrality. More importantly, our method is applicable regardless of the specifics of the forward model, and therefore can be applied to a wide range of systems such as identifying the patient zero in an epidemic, pinpointing the neuron that triggers a cascade, identifying the original malfunction that causes a catastrophic infrastructure failure, and inferring the ancestral species from which a heterogeneous population evolves.A sugar piece placed in tea will erode and eventually dissolve. Given the initial shape of the piece, it is trivial to predict its final distribution. However, the opposite problem of determining the initial state, given a final one is extremely difficult. Problems of the latter kind are referred as ill-posed inverse problems [1][2][3].Diffusion taking place on networks, in the forward direction, is well studied. One class of models originally used to describe epidemics is the Susceptible-InfectedRecovered (SIR) model [4,5]. Variations include SI, SIS, SIRS, etc. Others include more realistic delay conditions, such as an incubation period for the infection [6]. Similar models are used to describe neural cascades [7], traffic jams [8] and infrastructure failures [9].Accordingly, a successful method of inverting diffusion on complex networks can help identify patient zero in an epidemic outbreak, pinpoint neurons that trigger a cognitive cascades, remedy the parts of the road network that initiate congestion, and determine malfunctions that lead to cascading failures. In the weak selection limit, evolution can be thought as diffusion on a genotype network [10,11], so diffusion inversion may be used to identify ancestral species.Here we address the problem of identifying the origin of a diffusive process taking place on a complex network, given the its final state. We refer to the influenced nodes as the candidate set C. Any member of C may be the node from which the diffusion originated. We refer to this node as the seed, s, and to the forward model as M .Presently, there are two approaches to identify s. The first uses probability marginals from Bayesian methods [12][13][14][15][16][17][18][19][20][21]. In some cases, it is possible to sample the state space using Monte Carlo simulations [13]. However, this is only feasible for small networks. Message-passing algorithms can approximate the marginals efficiently [12,[14][15][16], however these algorithms are model specific: for every M , one must invent new approximations, heuristic assumptions and analytic calculations.In contrast, the second class of methods works independent of the forward ...

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A probability distribution function for investigating node infection and removal times

Tafazzoli

Sadeghiyan

2019

Trans Emerging Tel Tech

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Considering the important issue of computer infections by worms spread via networks, the theme of source identification has been a prominent research field that aims at investigating infection propagation including acquiring knowledge about the infection and the node removal times when a worm infection happens. This information helps in identifying the patient zero in the worm attack and may be used by computer forensic investigators and network administrators to spot the culprits and to identify related network vulnerabilities. In this paper, we tackle this problem by developing new probabilistic models based on Bayesian networks. We learn a probability distribution to calculate, at every time step, the probability that each node is infected by a scanning worm, using historical data and features extracted from the network and application layers. With the mentioned probability distribution, the node infection status can be inferred using feature values at each time step. We propose a four‐step method to investigate the time of infection and removal of each node probabilistically. First, features are extracted and derived from network traffic data. There are no suitable training and test datasets publicly available for our tests; therefore, we developed the training and test datasets using simulations of the Code Red II worm. Second, a prior model is built using training data. Third, the probabilistic model is built by the estimation of distribution algorithm. Fourth, the infection probability of nodes is inferred given the probability distribution and feature values at each time step. It has already been shown that the number of infectious nodes can be probabilistically approximated backward in time through the stochastic Back‐to‐Origin Markov model. We combine our first model with the prior stochastic Back‐to‐Origin Markov model to develop our second model. To evaluate our first and second models, we conducted experiments that show that these models can pinpoint the source node and the infection time of nodes with acceptable accuracy. It should be noted that our method could be employed with other propagating worm types including ransomware worms.

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Bayesian Inference of Epidemics on Networks via Belief Propagation

Cited by 173 publications

References 16 publications

Coupled effects of local movement and global interaction on contagion

Coupled effects of local movement and global interaction on contagion

Morphological inversion of complex diffusion

A probability distribution function for investigating node infection and removal times

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