Modelling the Spread of Infectious Diseases in Complex Metapopulations

J. Saldaña

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 5, Issue: 6, page 22-37
  • ISSN: 0973-5348

Abstract

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Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially, and, in the second one, both processes occur simultaneously. Here we follow the second approach and give a necessary and sufficient condition for the instability of the disease-free equilibrium in generic networks under the assumption of limited (or frequency-dependent) transmission. Moreover, for uncorrelated networks and under the assumption of non-limited (or density-dependent) transmission, we give a bounding interval for the dominant eigenvalue of the Jacobian matrix of the model equations around the disease-free equilibrium. Finally, for this latter case, we study numerically the prevalence of the infection across the metapopulation as a function of the patch connectivity.

How to cite

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Saldaña, J.. "Modelling the Spread of Infectious Diseases in Complex Metapopulations." Mathematical Modelling of Natural Phenomena 5.6 (2010): 22-37. <http://eudml.org/doc/197644>.

@article{Saldaña2010,
abstract = {Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially, and, in the second one, both processes occur simultaneously. Here we follow the second approach and give a necessary and sufficient condition for the instability of the disease-free equilibrium in generic networks under the assumption of limited (or frequency-dependent) transmission. Moreover, for uncorrelated networks and under the assumption of non-limited (or density-dependent) transmission, we give a bounding interval for the dominant eigenvalue of the Jacobian matrix of the model equations around the disease-free equilibrium. Finally, for this latter case, we study numerically the prevalence of the infection across the metapopulation as a function of the patch connectivity.},
author = {Saldaña, J.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {metapopulations; infectious diseases; reaction-diffusion processes},
language = {eng},
month = {4},
number = {6},
pages = {22-37},
publisher = {EDP Sciences},
title = {Modelling the Spread of Infectious Diseases in Complex Metapopulations},
url = {http://eudml.org/doc/197644},
volume = {5},
year = {2010},
}

TY - JOUR
AU - Saldaña, J.
TI - Modelling the Spread of Infectious Diseases in Complex Metapopulations
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/4//
PB - EDP Sciences
VL - 5
IS - 6
SP - 22
EP - 37
AB - Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially, and, in the second one, both processes occur simultaneously. Here we follow the second approach and give a necessary and sufficient condition for the instability of the disease-free equilibrium in generic networks under the assumption of limited (or frequency-dependent) transmission. Moreover, for uncorrelated networks and under the assumption of non-limited (or density-dependent) transmission, we give a bounding interval for the dominant eigenvalue of the Jacobian matrix of the model equations around the disease-free equilibrium. Finally, for this latter case, we study numerically the prevalence of the infection across the metapopulation as a function of the patch connectivity.
LA - eng
KW - metapopulations; infectious diseases; reaction-diffusion processes
UR - http://eudml.org/doc/197644
ER -

References

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