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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Nature Publishing Group
2017
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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. |
format | Online Article Text |
id | pubmed-5247741 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2017 |
publisher | Nature Publishing Group |
record_format | MEDLINE/PubMed |
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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