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Efficient method for comprehensive computation of agent-level epidemic dissemination in networks

Susceptible-infected (SI) and susceptible-infected-susceptible (SIS) are simple agent-based models often employed in epidemic studies. Both models describe the time evolution of infectious diseases in networks whose vertices are either susceptible (S) or infected (I) agents. Precise estimation for d...

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Autores principales: Nakamura, Gilberto M., Monteiro, Ana Carolina P., Cardoso, George C., Martinez, Alexandre S.
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5247741/
https://www.ncbi.nlm.nih.gov/pubmed/28106086
http://dx.doi.org/10.1038/srep40885
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author Nakamura, Gilberto M.
Monteiro, Ana Carolina P.
Cardoso, George C.
Martinez, Alexandre S.
author_facet Nakamura, Gilberto M.
Monteiro, Ana Carolina P.
Cardoso, George C.
Martinez, Alexandre S.
author_sort Nakamura, Gilberto M.
collection PubMed
description Susceptible-infected (SI) and susceptible-infected-susceptible (SIS) are simple agent-based models often employed in epidemic studies. Both models describe the time evolution of infectious diseases in networks whose vertices are either susceptible (S) or infected (I) agents. Precise estimation for disease spreading is one of the major goals in epidemic studies but often restricted to heavy numerical simulations. Analytic methods using operatorial content are subject to the asymmetric eigenvalue problem, limiting the use of perturbative methods. Numerical methods are limited to small populations, since the vector space increases exponentially with population size N. Here, we propose the use of the squared norm of the probability vector to obtain an algebraic equation, which permits the evaluation of stationary states in Markov processes. The equation requires the eigenvalues of symmetrized time generators and takes full advantage of symmetries, reducing the time evolution to an O(N) sparse problem. The calculation of eigenvalues employs quantum many-body techniques, while the standard perturbation theory accounts for small modifications to the network topology.
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spelling pubmed-52477412017-01-23 Efficient method for comprehensive computation of agent-level epidemic dissemination in networks Nakamura, Gilberto M. Monteiro, Ana Carolina P. Cardoso, George C. Martinez, Alexandre S. Sci Rep Article Susceptible-infected (SI) and susceptible-infected-susceptible (SIS) are simple agent-based models often employed in epidemic studies. Both models describe the time evolution of infectious diseases in networks whose vertices are either susceptible (S) or infected (I) agents. Precise estimation for disease spreading is one of the major goals in epidemic studies but often restricted to heavy numerical simulations. Analytic methods using operatorial content are subject to the asymmetric eigenvalue problem, limiting the use of perturbative methods. Numerical methods are limited to small populations, since the vector space increases exponentially with population size N. Here, we propose the use of the squared norm of the probability vector to obtain an algebraic equation, which permits the evaluation of stationary states in Markov processes. The equation requires the eigenvalues of symmetrized time generators and takes full advantage of symmetries, reducing the time evolution to an O(N) sparse problem. The calculation of eigenvalues employs quantum many-body techniques, while the standard perturbation theory accounts for small modifications to the network topology. Nature Publishing Group 2017-01-20 /pmc/articles/PMC5247741/ /pubmed/28106086 http://dx.doi.org/10.1038/srep40885 Text en Copyright © 2017, The Author(s) http://creativecommons.org/licenses/by/4.0/ This work is licensed under a Creative Commons Attribution 4.0 International License. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/
spellingShingle Article
Nakamura, Gilberto M.
Monteiro, Ana Carolina P.
Cardoso, George C.
Martinez, Alexandre S.
Efficient method for comprehensive computation of agent-level epidemic dissemination in networks
title Efficient method for comprehensive computation of agent-level epidemic dissemination in networks
title_full Efficient method for comprehensive computation of agent-level epidemic dissemination in networks
title_fullStr Efficient method for comprehensive computation of agent-level epidemic dissemination in networks
title_full_unstemmed Efficient method for comprehensive computation of agent-level epidemic dissemination in networks
title_short Efficient method for comprehensive computation of agent-level epidemic dissemination in networks
title_sort efficient method for comprehensive computation of agent-level epidemic dissemination in networks
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5247741/
https://www.ncbi.nlm.nih.gov/pubmed/28106086
http://dx.doi.org/10.1038/srep40885
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