---
_id: '12329'
abstract:
- lang: eng
  text: In this article, we develop two independent and new approaches to model epidemic
    spread in a network. Contrary to the most studied models, those developed here
    allow for contacts with different probabilities of transmitting the disease (transmissibilities).
    We then examine each of these models using some mean field type approximations.
    The first model looks at the late-stage effects of an epidemic outbreak and allows
    for the computation of the probability that a given vertex was infected. This
    computation is based on a mean field approximation and only depends on the number
    of contacts and their transmissibilities. This approach shares many similarities
    with percolation models in networks. The second model we develop is a dynamic
    model which we analyze using a mean field approximation which highly reduces the
    dimensionality of the system. In particular, the original system which individually
    analyses each vertex of the network is reduced to one with as many equations as
    different transmissibilities. Perhaps the greatest contribution of this article
    is the observation that, in both these models, the existence and size of an epidemic
    outbreak are linked to the properties of a matrix which we call the R-matrix.
    This is a generalization of the basic reproduction number which more precisely
    characterizes the main routes of infection.
acknowledgement: Gonçalo Oliveira is supported by the NOMIS Foundation, Fundação Serrapilheira
  1812-27395, by CNPq grants 428959/2018-0 and 307475/2018-2, and by FAPERJ through
  the grant Jovem Cientista do Nosso Estado E-26/202.793/2019.
article_number: '468'
article_processing_charge: No
article_type: original
author:
- first_name: Arturo
  full_name: Gómez, Arturo
  last_name: Gómez
- first_name: Goncalo
  full_name: Oliveira, Goncalo
  id: 58abbde8-f455-11eb-a497-98c8fd71b905
  last_name: Oliveira
citation:
  ama: Gómez A, Oliveira G. New approaches to epidemic modeling on networks. <i>Scientific
    Reports</i>. 2023;13. doi:<a href="https://doi.org/10.1038/s41598-022-19827-9">10.1038/s41598-022-19827-9</a>
  apa: Gómez, A., &#38; Oliveira, G. (2023). New approaches to epidemic modeling on
    networks. <i>Scientific Reports</i>. Springer Nature. <a href="https://doi.org/10.1038/s41598-022-19827-9">https://doi.org/10.1038/s41598-022-19827-9</a>
  chicago: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling
    on Networks.” <i>Scientific Reports</i>. Springer Nature, 2023. <a href="https://doi.org/10.1038/s41598-022-19827-9">https://doi.org/10.1038/s41598-022-19827-9</a>.
  ieee: A. Gómez and G. Oliveira, “New approaches to epidemic modeling on networks,”
    <i>Scientific Reports</i>, vol. 13. Springer Nature, 2023.
  ista: Gómez A, Oliveira G. 2023. New approaches to epidemic modeling on networks.
    Scientific Reports. 13, 468.
  mla: Gómez, Arturo, and Goncalo Oliveira. “New Approaches to Epidemic Modeling on
    Networks.” <i>Scientific Reports</i>, vol. 13, 468, Springer Nature, 2023, doi:<a
    href="https://doi.org/10.1038/s41598-022-19827-9">10.1038/s41598-022-19827-9</a>.
  short: A. Gómez, G. Oliveira, Scientific Reports 13 (2023).
date_created: 2023-01-22T23:00:55Z
date_published: 2023-01-10T00:00:00Z
date_updated: 2023-08-01T12:31:40Z
day: '10'
ddc:
- '510'
department:
- _id: TaHa
doi: 10.1038/s41598-022-19827-9
external_id:
  isi:
  - '001003345000051'
file:
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  creator: dernst
  date_created: 2023-01-23T07:53:23Z
  date_updated: 2023-01-23T07:53:23Z
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has_accepted_license: '1'
intvolume: '        13'
isi: 1
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
publication: Scientific Reports
publication_identifier:
  eissn:
  - 2045-2322
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: New approaches to epidemic modeling on networks
tmp:
  image: /images/cc_by.png
  legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
  name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
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type: journal_article
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volume: 13
year: '2023'
...