Rejection-Based Simulation of Stochastic Spreading Processes on Complex Networks

Complex Networks and Their Applications VIII

Bortolussi

Wolf

2019

Self Cite

Stochastic models in which agents interact with their neighborhood according to a network topology are a powerful modeling framework to study the emergence of complex dynamic patterns in real-world systems. Stochastic simulations are often the preferred-sometimes the only feasible-way to investigate such systems. Previous research focused primarily on Markovian models where the random time until an interaction happens follows an exponential distribution. In this work, we study a general framework to model systems where each agent is in one of several states. Agents can change their state at random, influenced by their complete neighborhood, while the time to the next event can follow an arbitrary probability distribution. Classically, these simulations are hindered by high computational costs of updating the rates of interconnected agents and sampling the random residence times from arbitrary distributions. We propose a rejection-based, event-driven simulation algorithm to overcome these limitations. Our method over-approximates the instantaneous rates corresponding to inter-event times while rejection events counterbalance these over-approximations. We demonstrate the effectiveness of our approach on models of epidemic and information spreading.Here, c i , c r ∈ R ≥0 denote the infection and recovery rate constants, respectively. Note that the infection rate is proportional to the number of infected neighbors whereas the rate of recovery is independent from neighboring agents. Moreover,

Section: Event Queuementioning

confidence: 89%

Section: Our Methodsmentioning

confidence: 99%

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Rejection-Based Simulation of Non-Markovian Agents on Complex Networks

Complex Networks and Their Applications VIII

Bortolussi

Wolf

2019

Self Cite

“…Explicitly computing the evolution of the probability of x ∈ X over time with an ODE solver, using numerical integration, is only possible for very small contact networks, since the state space grows exponentially with the number of nodes. Alternative approaches include sampling the CTMC, which can be done reasonably efficiently even for comparably large networks [20,8,43] but is subject to statistical inaccuracies and is mostly used to estimate global properties.…”

Section: Ctmc Semanticsmentioning

confidence: 99%

Reducing Spreading Processes on Networks to Markov Population Models

Quantitative Evaluation of Systems

Bortolussi

2019

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Stochastic processes on complex networks, where each node is in one of several compartments, and neighboring nodes interact with each other, can be used to describe a variety of real-world spreading phenomena. However, computational analysis of such processes is hindered by the enormous size of their underlying state space. In this work, we demonstrate that lumping can be used to reduce any epidemic model to a Markov Population Model (MPM). Therefore, we propose a novel lumping scheme based on a partitioning of the nodes. By imposing different types of counting abstractions, we obtain coarsegrained Markov models with a natural MPM representation that approximate the original systems. This makes it possible to transfer the rich pool of approximation techniques developed for MPMs to the computational analysis of complex networks' dynamics. We present numerical examples to investigate the relationship between the accuracy of the MPMs, the size of the lumped state space, and the type of counting abstraction.

“…Here, we propose Simba, (Simulation-based vaccine allocation), which is a method that makes use of recent developments in fast simulation of epidemic processes using a rejection-based approach [6]. This allows performing a large number of simulation runs of networks with millions of nodes and edges in the order of minutes on a standard desktop PC.…”

Section: Introductionmentioning

confidence: 99%

Learning Vaccine Allocation from Simulations

Studies in Computational Intelligence

Backenköhler

Klesen

et al. 2020

Self Cite

We address the problem of reducing the spread of an epidemic over a contact network by vaccinating a limited number of nodes that represent individuals or agents.We propose a Sim-ulation-based vaccine allocation method (Simba), a combination of (i) numerous repetitions of an efficient Monte-Carlo simulation, (ii) a PageRank-type influence analysis on an empirical transmission graph which is learned from the simulations, and (iii) discrete stochastic optimization.Our method scales very well with the size of the network and is suitable for networks with millions of nodes. Moreover, in contrast to most approaches that are model-agnostic approaches and solely perform graph-analysis on the contact graph, the stochastic simulations explicitly take the exact diffusion dynamics of the epidemic into account. Thereby, we make our vaccination strategy sensitive to the specific clinical and transmission parameters of the epidemic.