Please use this identifier to cite or link to this item: doi:10.22028/D291-31042
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Title: Lumping of degree-based mean-field and pair-approximation equations for multistate contact processes
Author(s): Kyriakopoulos, Charalampos
Grossmann, Gerrit
Wolf, Verena
Bortolussi, Luca
Language: English
Title: Physical review
Volume: 97
Issue: 1
Pages: 15
Publisher/Platform: APS
Year of Publication: 2018
Publikation type: Journal Article
Abstract: Contact processes form a large and highly interesting class of dynamic processes on networks, including epidemic and information-spreading networks. While devising stochastic models of such processes is relatively easy, analyzing them is very challenging from a computational point of view, particularly for large networks appearing in real applications. One strategy to reduce the complexity of their analysis is to rely on approximations, often in terms of a set of differential equations capturing the evolution of a random node, distinguishing nodes with different topological contexts (i.e., different degrees of different neighborhoods), such as degree-based mean-field (DBMF), approximate-master-equation (AME), or pair-approximation (PA) approaches. The number of differential equations so obtained is typically proportional to the maximum degree k_{max} of the network, which is much smaller than the size of the master equation of the underlying stochastic model, yet numerically solving these equations can still be problematic for large k_{max}. In this paper, we consider AME and PA, extended to cope with multiple local states, and we provide an aggregation procedure that clusters together nodes having similar degrees, treating those in the same cluster as indistinguishable, thus reducing the number of equations while preserving an accurate description of global observables of interest. We also provide an automatic way to build such equations and to identify a small number of degree clusters that give accurate results. The method is tested on several case studies, where it shows a high level of compression and a reduction of computational time of several orders of magnitude for large networks, with minimal loss in accuracy.
DOI of the first publication: 10.1103/PhysRevE.97.012301
URL of the first publication: https://journals.aps.org/pre/abstract/10.1103/PhysRevE.97.012301
Link to this record: hdl:20.500.11880/29193
http://dx.doi.org/10.22028/D291-31042
ISSN: 2470-0045
2470-0053
Date of registration: 28-May-2020
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Informatik
Professorship: MI - Prof. Dr. Verena Wolf
Collections:UniBib – Die Universitätsbibliographie

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