Modelling the spread of Phytophthora ramorum

in complex directed networks

Marco Pautasso,Division of Biology,

Imperial College London, Wye Campus, Kent, UK

Wye, 14 Jul 2007

Sudden Oak Death

from Desprez-Loustau et multi al. (in press) Trends in Ecology & Evolution

Source: United States Department of Agriculture, Animal and Plant Health Inspection Service, Plant Protection and Quarantine

Trace forward/back zipcode

Positive (Phytophthora ramorum) site

Hold released

Trace-forwards and positive detections across the USA, July 2004

Simulation of disease spread in four basic types of directed networks of small size

SIS-modelN nodes = 100 constant n of linksdirected networks

probability of infection for the node x at time t+1 = Σ px,y iy where px,y is the probability of connection between node x and y, and iy is the infection status of the node y at time t

local small-world

random scale-free

from: Pautasso & Jeger (in press) Ecological Complexity

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Examples of epidemic development in four kinds of directed networks (at threshold conditions)

random network nr 8;starting node = nr 80

scale-free network nr 2; starting node = nr 11

local network nr 6; starting node = nr 100

small-world network nr 4;starting node = nr 14

sum

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lity

of in

fect

ion

acro

ss a

ll no

des

iteration iteration

% n

odes

with

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babi

lity

of in

fect

ion

> 0.

01

from: Pautasso & Jeger (in press) Ecological Complexity

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probability of transmission

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abili

ty o

f per

sist

ence

localsmall-worldrandomscale-free

epidemic develops

no epidemic

Linear epidemic threshold on a plot of p(persistence) f p(transmission)

from: Pautasso & Jeger (in press) Ecological Complexity

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Fina

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um o

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cros

s al

l nod

es)

Starting node of epidemic

local small-world

random scale-free

from: Pautasso & Jeger (in review) Journal of Theoretical Biology

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Marked variations in epidemic final size at threshold conditionsdepend on the number of links of the starting node

local

random

from: Pautasso & Jeger (in review) Journal of Theoretical Biology

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n of links from starting node n of links from starting node

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small-world

Local Trade

Heathland

Woodland

Spatially-explicit modelling framework

Long-distance tradeClimate suitability

from: Hufnagel, Brockmann & Geisel (2004) PNAS

number of passengers per day

Network epidemiology

Nature's guide for mentors

NATURAL

TECHNOLOGICAL SOCIAL

food webs

airport networks

cell metabolism

neural networks

railway networks

ant nests

WWWInternet

electrical power grids

software mapscomputing

gridsE-mail

patterns

innovation flows

telephone calls

co-authorship nets

family networks

committees

sexual partnerships DISEASE

SPREAD

Food web of Little Rock Lake, Wisconsin, US

Internet structure

Network pictures from: Newman (2003) SIAM Review

HIV spread

network

Epidemiology is just one of the many applications of network theory

urban road networks

Modified from: Jeger, Pautasso, Holdenrieder & Shaw (2007) New Phytologist

Acknowledgements

Ottmar Holdenrieder,

ETHZ, CH

Mike Jeger, Imperial College,

WyeMike Shaw,

Univ. of Reading

Kevin Gaston, Univ. of

SheffieldKatrin

Boehning-Gaese,

Univ. Mainz, Germany

Emanuele Della Valle, Politecnico di

Milano, Italy

Peter Weisberg, Univ. of Nevada,

Reno, US

Mike McKinney, Univ. of Tennessee, US

Chris Gilligan, Univ. of Cambridge

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