Dynamics of epidemics from cavity master equations: Susceptible-infectious-susceptible models

Ortega, Ernesto; Machado, David; Lage-Castellanos, Alejandro

doi:10.1103/physreve.105.024308

Cited by 13 publications

(10 citation statements)

References 31 publications

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“…By invoking the assumption on v ’s independence of its neighborhood, we factorize the exact but cumbersome master equation into | V | equations in the form of eq. (6), a technique also introduced in [35, 41, 42]. This technique is called by many in the field as “one-vertex quenched mean-field theory”.…”

Section: Theoretical Resultsmentioning

confidence: 99%

Scalable parallel and distributed simulation of an epidemic on a graph

Dou

2023

Preprint

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We propose an algorithm to simulate Markovian SIS epidemics with homogeneous rates and pairwise interactions on a fixed undirected graph, assuming a distributed memory model of parallel programming and limited bandwidth. We offer an implementation of the algorithm in the form of pseudocode in the Appendix. Also, we analyze its algorithmic complexity and its induced dynamical system. Finally, we design experiments to show its scalability and faithfulness. We believe this algorithm offers a way of scaling out, allowing researchers to run simulation tasks at a scale that was not accessible before. Furthermore, we believe this algorithm lays a solid foundation for extensions to simulating more advanced epidemic processes and graph dynamics in other fields.

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Section: Theoretical Resultsmentioning

confidence: 99%

Scalable parallel and distributed simulation of an epidemic on a graph

Dou

2023

Preprint

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“…The Causal Variational Approach is very flexible and, employing sampling to perform estimates, it can be applied virtually to any dynamics for which the latter can be carried out efficiently. In particular, the method can thus be applied to inference problems involving recurrent epidemic processes, such as the SIS model 28 or other models (e.g. 29 ) where immunity decays over time.…”

Section: Discussionmentioning

confidence: 99%

Inference in conditioned dynamics through causality restoration

Braunstein

Catania

Dall’Asta

et al. 2023

Preprint

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Estimating observables from conditioned dynamics is typically computationally hard. While obtaining independent samples efficiently from unconditioned dynamics is usually feasible, most of them do not satisfy the imposed conditions and must be discarded.On the other hand, conditioning breaks the causal properties of the dynamics, which ultimately renders the sampling of the conditioned dynamics non-trivial and inefficient. In this work, a Causal Variational Approach is proposed, as an approximate method to generate independent samples from a conditioned distribution. The procedure relies on learning the parameters of a generalized dynamical model that optimally describes the conditioned distribution in a variational sense. The outcome is an effective and unconditioned dynamical model from which one can trivially obtain independent samples, effectively restoring the causality of the conditioned dynamics. The consequences are twofold: the method allows one to efficiently compute observables from the conditioned dynamics by averaging over independent samples; moreover, it provides an effective unconditioned distribution that is easy to interpret. This approximation can be applied virtually to any dynamics. The application of the method to epidemic inference is discussed in detail. The results of direct comparison with state-of-the-art inference methods, including the soft-margin approach and mean-field methods, are promising.

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“…The Causal Variational Approach is very flexible and, employing sampling to perform estimates, it can be applied virtually to any dynamics for which the latter can be carried out efficiently. In particular, the method can thus be applied to inference problems involving recurrent epidemic processes, such as the SIS model 31 or other models (e.g. 32 ) where immunity decays over time.…”

Section: Discussionmentioning

confidence: 99%

Inference in conditioned dynamics through causality restoration

Braunstein

Catania

Dall’Asta

et al. 2023

Sci Rep

View full text Add to dashboard Cite

Estimating observables from conditioned dynamics is typically computationally hard. While obtaining independent samples efficiently from unconditioned dynamics is usually feasible, most of them do not satisfy the imposed conditions and must be discarded. On the other hand, conditioning breaks the causal properties of the dynamics, which ultimately renders the sampling of the conditioned dynamics non-trivial and inefficient. In this work, a Causal Variational Approach is proposed, as an approximate method to generate independent samples from a conditioned distribution. The procedure relies on learning the parameters of a generalized dynamical model that optimally describes the conditioned distribution in a variational sense. The outcome is an effective and unconditioned dynamical model from which one can trivially obtain independent samples, effectively restoring the causality of the conditioned dynamics. The consequences are twofold: the method allows one to efficiently compute observables from the conditioned dynamics by averaging over independent samples; moreover, it provides an effective unconditioned distribution that is easy to interpret. This approximation can be applied virtually to any dynamics. The application of the method to epidemic inference is discussed in detail. The results of direct comparison with state-of-the-art inference methods, including the soft-margin approach and mean-field methods, are promising.

show abstract

Dynamics of epidemics from cavity master equations: Susceptible-infectious-susceptible models

Cited by 13 publications

References 31 publications

Scalable parallel and distributed simulation of an epidemic on a graph

Scalable parallel and distributed simulation of an epidemic on a graph

Inference in conditioned dynamics through causality restoration

Inference in conditioned dynamics through causality restoration

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