# Modelling the Spread of Infectious Diseases in Complex Metapopulations

Mathematical Modelling of Natural Phenomena (2010)

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

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topSaldaña, 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 -

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