---
res:
  bibo_abstract:
  - 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.@eng
  bibo_authorlist:
  - foaf_Person:
      foaf_givenName: Arturo
      foaf_name: Gómez, Arturo
      foaf_surname: Gómez
  - foaf_Person:
      foaf_givenName: Goncalo
      foaf_name: Oliveira, Goncalo
      foaf_surname: Oliveira
      foaf_workInfoHomepage: http://www.librecat.org/personId=58abbde8-f455-11eb-a497-98c8fd71b905
  bibo_doi: 10.1038/s41598-022-19827-9
  bibo_volume: 13
  dct_date: 2023^xs_gYear
  dct_identifier:
  - UT:001003345000051
  dct_isPartOf:
  - http://id.crossref.org/issn/2045-2322
  dct_language: eng
  dct_publisher: Springer Nature@
  dct_title: New approaches to epidemic modeling on networks@
...