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Perturbative solution to susceptible-infected-susceptible epidemics on networks.

Sanders, Lloyd LU ; Söderberg, Bo LU ; Brockmann, Dirk and Ambjörnsson, Tobias LU (2013) In Physical Review E (Statistical, Nonlinear, and Soft Matter Physics) 88(3).
Abstract
Herein we provide a closed form perturbative solution to a general M-node network susceptible-infected-susceptible (SIS) model using the transport rates between nodes as a perturbation parameter. We separate the dynamics into a short-time regime and a medium-to-long-time regime. We solve the short-time dynamics of the system and provide a limit before which our explicit, analytical result of the first-order perturbation for the medium-to-long-time regime is to be employed. These stitched calculations provide an approximation to the full temporal dynamics for rather general initial conditions. To further corroborate our results, we solve the mean-field equations numerically for an infectious SIS outbreak in New Zealand (NZ, Aotearoa)... (More)
Herein we provide a closed form perturbative solution to a general M-node network susceptible-infected-susceptible (SIS) model using the transport rates between nodes as a perturbation parameter. We separate the dynamics into a short-time regime and a medium-to-long-time regime. We solve the short-time dynamics of the system and provide a limit before which our explicit, analytical result of the first-order perturbation for the medium-to-long-time regime is to be employed. These stitched calculations provide an approximation to the full temporal dynamics for rather general initial conditions. To further corroborate our results, we solve the mean-field equations numerically for an infectious SIS outbreak in New Zealand (NZ, Aotearoa) recomposed into 23 subpopulations where the virus is spread to different subpopulations via (documented) air traffic data, and the country is internationally quarantined. We demonstrate that our analytical predictions compare well to the numerical solution. (Less)
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)
volume
88
issue
3
publisher
American Physical Society
external identifiers
  • wos:000324692200010
  • pmid:24125300
  • scopus:84885138096
ISSN
1539-3755
DOI
10.1103/PhysRevE.88.032713
language
English
LU publication?
yes
id
86e913b2-2c1c-40ed-9e29-32e3774f30e4 (old id 4143253)
date added to LUP
2013-11-08 13:51:42
date last changed
2019-02-20 02:11:33
@article{86e913b2-2c1c-40ed-9e29-32e3774f30e4,
  abstract     = {Herein we provide a closed form perturbative solution to a general M-node network susceptible-infected-susceptible (SIS) model using the transport rates between nodes as a perturbation parameter. We separate the dynamics into a short-time regime and a medium-to-long-time regime. We solve the short-time dynamics of the system and provide a limit before which our explicit, analytical result of the first-order perturbation for the medium-to-long-time regime is to be employed. These stitched calculations provide an approximation to the full temporal dynamics for rather general initial conditions. To further corroborate our results, we solve the mean-field equations numerically for an infectious SIS outbreak in New Zealand (NZ, Aotearoa) recomposed into 23 subpopulations where the virus is spread to different subpopulations via (documented) air traffic data, and the country is internationally quarantined. We demonstrate that our analytical predictions compare well to the numerical solution.},
  articleno    = {032713},
  author       = {Sanders, Lloyd and Söderberg, Bo and Brockmann, Dirk and Ambjörnsson, Tobias},
  issn         = {1539-3755},
  language     = {eng},
  number       = {3},
  publisher    = {American Physical Society},
  series       = {Physical Review E (Statistical, Nonlinear, and Soft Matter Physics)},
  title        = {Perturbative solution to susceptible-infected-susceptible epidemics on networks.},
  url          = {http://dx.doi.org/10.1103/PhysRevE.88.032713},
  volume       = {88},
  year         = {2013},
}