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
May 11, 2015
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
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 26 51 760
10
20
30
40
50
60
70
80
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 26 51 760
5
10
15
20
25
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1 26 51 760
10
20
30
40
50
60
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1 51 101 151 2010
5
10
15
20
25
30
35
40
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
pro
babi
lity
of in
fect
ion
acro
ss a
ll no
des
iteration iteration
% n
odes
with
pro
babi
lity
of in
fect
ion
> 0.
01
from: Pautasso & Jeger (in press) Ecological Complexity
0.00
0.25
0.50
0.75
1.00
0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45
probability of transmission
prob
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
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 25 50 75 1000.0
0.5
1.0
1.5
2.0
2.5
3.0
0 25 50 75 100
0.0
0.5
1.0
1.5
2.0
2.5
0 25 50 75 1000.0
0.5
1.0
1.5
2.0
0 25 50 75 100
Fina
l siz
e of
epi
dem
ic (s
um o
f in
fect
ion
prob
abili
ty a
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
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8 10 12
0.0
0.5
1.0
1.5
2.0
0 1 2 3 4 5 6
sum
at e
quili
briu
m o
f pro
babi
lity
of in
fect
ion
acro
ss a
ll no
des
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
0.0
1.0
2.0
3.0
4.0
5.0
6.0
0 20 40 60 80 100
scale-free
n of links from starting node n of links from starting node
0.0
0.5
1.0
1.5
2.0
2.5
3.0
0 2 4 6 8
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
ReferencesDehnen-Schmutz K, Holdenrieder O, Jeger MJ & Pautasso M (2010) Structural change in the international horticultural industry: some implications for plant health. Scientia Horticulturae 125: 1-15Harwood TD, Xu XM, Pautasso M, Jeger MJ & Shaw M (2009) Epidemiological risk assessment using linked network and grid based modelling: Phytophthora ramorum and P. kernoviae in the UK. Ecological Modelling 220: 3353-3361 Jeger MJ & Pautasso M (2008) Comparative epidemiology of zoosporic plant pathogens. European Journal of Plant Pathology 122: 111-126Jeger MJ, Pautasso M, Holdenrieder O & Shaw MW (2007) Modelling disease spread and control in networks: implications for plant sciences. New Phytologist 174: 179-197 Lonsdale D, Pautasso M & Holdenrieder O (2008) Wood-decaying fungi in the forest: conservation needs and management options. European Journal of Forest Research 127: 1-22 MacLeod A, Pautasso M, Jeger MJ & Haines-Young R (2010) Evolution of the international regulation of plant pests and challenges for future plant health. Food Security 2: 49-70 Moslonka-Lefebvre M, Pautasso M & Jeger MJ (2009) Disease spread in small-size directed networks: epidemic threshold, correlation between links to and from nodes, and clustering. J Theor Biol 260: 402-411Moslonka-Lefebvre M, Finley A, Dorigatti I, Dehnen-Schmutz K, Harwood T, Jeger MJ, Xu XM, Holdenrieder O & Pautasso M (2011) Networks in plant epidemiology: from genes to landscapes, countries and continents. Phytopathology 101: 392-403Pautasso M (2009) Geographical genetics and the conservation of forest trees. Perspectives in Plant Ecology, Systematics & Evolution 11: 157-189Pautasso M (2010) Worsening file-drawer problem in the abstracts of natural, medical and social science databases. Scientometrics 85: 193-202Pautasso M & Jeger MJ (2008) Epidemic threshold and network structure: the interplay of probability of transmission and of persistence in directed networks. Ecological Complexity 5: 1-8Pautasso M et al (2010) Plant health and global change – some implications for landscape management. Biological Reviews 85: 729-755Pautasso M, Moslonka-Lefebvre M & Jeger MJ (2010) The number of links to and from the starting node as a predictor of epidemic size in small-size directed networks. Ecological Complexity 7: 424-432 Pautasso M, Xu XM, Jeger MJ, Harwood T, Moslonka-Lefebvre M & Pellis L (2010) Disease spread in small-size directed trade networks: the role of hierarchical categories. Journal of Applied Ecology 47: 1300-1309Xu XM, Harwood TD, Pautasso M & Jeger MJ (2009) Spatio-temporal analysis of an invasive plant pathogen (Phytophthora ramorum) in England and Wales. Ecography 32: 504-516