# The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

Igor Sazonov; Mark Kelbert; Michael B. Gravenor

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 4, page 28-47
- ISSN: 0973-5348

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topSazonov, Igor, Kelbert, Mark, and Gravenor, Michael B.. "The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models." Mathematical Modelling of Natural Phenomena 3.4 (2008): 28-47. <http://eudml.org/doc/222322>.

@article{Sazonov2008,

abstract = {A one-dimensional lattice of SIR (susceptible/infected/removed) epidemic centres is
considered numerically and analytically. The limiting solutions describing the behaviour of the
standard SIR model with a small number of initially infected individuals are derived, and expressions
found for the duration of an outbreak. We study a model for a weakly mixed population
distributed between the interacting centres. The centres are modelled as SIR nodes with interaction
between sites determined by a diffusion-type migration process. Under the assumption of fast
migration, a one-dimensional lattice of SIR nodes is studied numerically with deterministic and
random coupling, and travelling wave-like solutions are found in both cases. For weak coupling,
the main part of the travelling wave is well approximated by the limiting SIR solution. Explicit
formulae are found for the speed of the travelling waves and compared with results of numerical
simulation. Approximate formulae for the epidemic propagation speed are also derived when
coupling coefficients are randomly distributed, they allow us to estimate how the average speed in
random media is slowed down.
},

author = {Sazonov, Igor, Kelbert, Mark, Gravenor, Michael B.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {spatial epidemic models; dynamic systems; travelling waves},

language = {eng},

month = {12},

number = {4},

pages = {28-47},

publisher = {EDP Sciences},

title = {The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models},

url = {http://eudml.org/doc/222322},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Sazonov, Igor

AU - Kelbert, Mark

AU - Gravenor, Michael B.

TI - The Speed of Epidemic Waves in a One-Dimensional Lattice of SIR Models

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/12//

PB - EDP Sciences

VL - 3

IS - 4

SP - 28

EP - 47

AB - A one-dimensional lattice of SIR (susceptible/infected/removed) epidemic centres is
considered numerically and analytically. The limiting solutions describing the behaviour of the
standard SIR model with a small number of initially infected individuals are derived, and expressions
found for the duration of an outbreak. We study a model for a weakly mixed population
distributed between the interacting centres. The centres are modelled as SIR nodes with interaction
between sites determined by a diffusion-type migration process. Under the assumption of fast
migration, a one-dimensional lattice of SIR nodes is studied numerically with deterministic and
random coupling, and travelling wave-like solutions are found in both cases. For weak coupling,
the main part of the travelling wave is well approximated by the limiting SIR solution. Explicit
formulae are found for the speed of the travelling waves and compared with results of numerical
simulation. Approximate formulae for the epidemic propagation speed are also derived when
coupling coefficients are randomly distributed, they allow us to estimate how the average speed in
random media is slowed down.

LA - eng

KW - spatial epidemic models; dynamic systems; travelling waves

UR - http://eudml.org/doc/222322

ER -

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