Networks and Epidemiology

Marco Pautasso,Division of Biology,

Imperial College London, Wye Campus, Kent, UK

Wye, 8 June 2007number of passengers per day

from: Hufnagel et al. (2004) Forecast and control of epidemics in a globalized world. PNAS 101: 15124-15129

from: Riley (2007) Large-scale spatial-transmission models of infectious disease. Science 316: 1298-1301

Relative concentration of infectious individuals in case

of an influenza pandemic

Infections in case of a smallpox outbreak starting from London (5*5 km cells)

t = 75 days in

both cases

Web of susceptible genera connected by Phytophthora ramorum (based on genus co-existence in 2788 positive findings in England & Wales, 2003-2005)

NATURAL

TECHNOLOGICAL SOCIAL

food webs

airport networks

cell metabolism

neural networks

railway networks

ant nests

WWWInternetelectrical

power grids

software mapscomputing

grids

E-mail patterns

innovation flows

telephone callsco-authorship

nets

family networks

committees

sexual partnerships DISEASE

SPREAD

Food web of Little Rock Lake, Wisconsin, US

Internet structure

Network pictures from: Newman (2003) The structure and function of complex networks. SIAM Review 45: 167-256

HIV spread

network

Epidemiology is just one of the many applications of network theory

urban road networks

Epidemic spread of studies applying network theory

2001

2004

2002

2004

2005

20052006

2005

200520052003

2004

2003

2003

2006

20052004

2005

20062005

2005 2005

200520052005

2004

2005

Networks and Epidemiology

1. Introduction: interconnected world, growing interest in network theory and disease spread in networks

2. Examples of recent work modellingdisease (i) spread and (ii) control in networks of various kinds

4. Conclusion: further potential work applying network theory in plant sciences

3. Case study: Phytophthora ramorum and epidemiological simulations in networks of small size

Different types of networks

Modified from: Keeling & Eames (2005) Networks and epidemic models. Interface 2: 295-307

random scale-free

local small-world

Epidemic development in different types of networks

scale-freerandom2-D lattice rewired2-D lattice1-D lattice rewired1-D lattice

From: Shirley & Rushton (2005) The impacts of network topology on disease spread. Ecological Complexity 2: 287-299

N of nodes of networks = 500;p of infection = 0.1;

latent period = 2 time steps;infectious period = 10 time steps

From: Shirley & Rushton (2005) Where diseases and networks collide: lessons to be learnt from a study of the 2001 foot-and-mouth disease

epidemic. Epidemiology & Infection 133: 1023-1032

Super-connected individuals in scale-free networks

A reconstruction of the recent UK foot-and-mouth disease

epidemic (20 Feb–15 Mar 2001).

Vertices marked with a label are livestock markets,

unmarked vertices are farms.

Only confirmed infected premises are included.

Arrows indicate route of infection.

From: Shirley & Rushton (2005) Where diseases and networks collide: lessons to be learnt from a study of the 2001 foot-and-mouth disease

epidemic. Epidemiology & Infection 133: 1023-1032

Degree distribution of nodes in a scale-free network

based on a reconstruction of the UK foot-and mouth

disease network.Fitted line:

y= 118.5x -1.6, R2 = 0.87

From: May (2006) Network structure and the biology of populations. Trends in Ecology & Evolution 21, 7: 394-399

uniform degree distribution

scale-free network with P(i) ≈ i-3

Fraction of population infected (l) as a function of ρ0

ρ0 is coincident with R0

for a uniform degree distribution;

for a scale-free network, theory says that

R0 = ρ0 + [1 + (CV)2], where CV is the

coefficient of variation of the degree distribution

Networks and Epidemiology

1. Introduction: interconnected world, growing interest in network theory and disease spread in networks

2. Examples of recent work modelling disease (i) spread and (ii) control in networks of various kinds

4. Conclusion: further potential work applying network theory in plant sciences

3. Case study: Phytophthora ramorumand epidemiological simulations in networks of small size

From Desprez-Loustau et al. (2007) The fungal dimension of biological invasions. Trends in Ecology & Evolution, in press

Sudden Oak Death in California

Map courtesy of Ross Meentemeyer

Sudden Oak Death ground surveys, Northern California, 2004

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

England and Wales: records positive to Phytophthora ramorum

n = 2788

Jan 2003-Dec 2005

Data source: Department for Environment, Food and Rural Affairs, UK

Own epidemiological investigations 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

0.0

0.2

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1 26 51 760

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0.0

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0.6

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1 26 51 760

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25

0.0

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1 26 51 760

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1 51 101 151 2010

5

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30

35

40

Examples of epidemic development in four kinds of directed networks of small size (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

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 graph of the probability of persistence and of transmission

Temporal development; England & Wales, 2003-2005; n = 2788

R ecords positive to P. ram orum

0

50

100

150

200

250

Jan-03Apr-0

3Ju

l-03

Oct-03

Jan-04Apr-0

4Ju

l-04

Oct-04

Jan-05Apr-0

5Ju

l-05

Oct-05

n of

reco

rds

unclear which

estates/environm ent

nurseries/gardencentres

Data source: Department for Environment, Food and Rural Affairs, UK

Local Trade

Heathland

Woodland

Spatially-explicit modelling framework

Long-distance tradeClimate suitability

Networks and Epidemiology

1. Introduction: interconnected world, growing interest in network theory and disease spread in networks

2. Examples of recent work modelling disease spread and control in networks of various kinds

4. Conclusion: further potential work applying network theory in plant sciences

3. Case study: Phytophthora ramorum and epidemiological investigations in networks of small size

PLANT

HUMAN ANIMAL

HIVMycoplasmapneumoniae

avian fluDengueSARS

foot and mouth disease

fish diseases

bovine tuberculosisRotavirus

Where are the applications to plant pathology?

Neisseriagonorrhoeae

raccoon rabies

computer viruses

(rumor propagation)

(plant-pollinator

interactions)

(plant meta-populations)

(plant-frugivore

interactions)(bats in networks of

hollow trees)

(mycorrhiza) (plant metabolomics –

cellular pathways)

[plant-vector interactions e.g. viruses]

[nursery networks]

[quarantine][epiphytoticsmanagement

& control]

[recreation/ amenities landscape]

LEGEND:

no brackets = application existing

(…) = application existing, but not strictly involving disease

[…] = would involve plant pathology, but application of network theory lacking

Further potential work applying network theory in plant sciences

• conservation biology (e.g. meta-populations, reserve networks, botanical gardens)

• invasion ecology (for exotic organisms particularly when spread by the nursery trade)

• gene-for-gene interactions?

Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in

Xanthomonas oryzae pv. oryzae

Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

MSSHRSRHRHRRHRMRHRMSMS10JXOIII

SSHRMRRSMRMRMRSMSSMS9PX099

SSHRMRRSMRMRMRSMSSMS8PXO99 (PUFR034)

HRHRHRMRMRRHRMRHRMSSMSMS7PXO99 (p71)

SSHRSRSRMSMRSSHRS6PXO99 (p65)

RRRRRHRRHRHRMRRHRR5PXO99 (p58)

SSRSRMSRHRRMSSSMS4PXO99 (p56)

MSSRMRMRSRMSMRSHRMRS3PXO99 (p54)

HRHRHRRRHRHRRHRHRHRHRHR2PX099 (p51)

HRMRHRHRMRMSRRHRHRRRMR1PXO99 (p41)

mlkjihgfedcba

IR24

Tetep

IRBB21

IRBB14

IRBB13IRBB11IRBB10IRBB8IRBB7IRBB4IRBB3IRBB2IRBB1

HR: High Resistance; R: Resistance; MR: Medium Resistance; MS: Medium Susceptibility; S: Susceptibility

Near isogenic lines of riceAvrgene clones

Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae

(based on coexistence of High Resistance in the same isogenic lines of rice for different gene clones; the number in the matrix is the number

of isogenic lines with HR in the two gene clones connected)

Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae

(based on coexistence of High Resistance in the same isogenic lines of rice for different gene clones; the strength of the lines reflects the

number of connections)

PXO99 (p65)

PXO99 (p41)

PXO99 (p51)

PXO99 (p54)PXO99 (p58)

PXO99 (p56)

Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

PXO99 (p71)

PXO99 (pUFRO34)PXO99JXOIII

1N of links:

2 3 4 5

Frequency distribution of the number of links for isogenic lines of rice (based on coexistence of High

Resistance in the same pathogen gene clone for different isogenic lines of rice)

Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

0123

4567

0-5 6-15 16-25num ber of connections

num

ber o

f gen

e cl

ones

Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae (based on coexistence of High Resistance in the same gene clone for different isogenic lines of rice; the number in the matrix is the number of gene

clones with HR in the two isogenic lines of rice connected)

Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

Network of gene-for-gene relationships between rice and diverse avrBs3/pthA avirulence genes in Xanthomonas oryzae pv. oryzae

(based on coexistence of High Resistance in the same gene clone for different isogenic lines of rice; the strength of the lines reflects the

number of connections)

Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

1N of links:

2 3 4

IRBB11

IRBB2

IRBB4

IRBB7

IRBB10IRBB8

IRBB13

IRBB21

TetepIRBB1

IRBB3IRBB14

IR24

Frequency distribution of the number of links for Avrgene clones (based on coexistence of High Resistance

in the same isogenic lines of rice for different pathogen gene clones)

Data source: Wu et al. (2007) Plant Pathology 56, 1: 26-34

012345678

0-5 6-15 16-25num ber of connections

num

ber o

f iso

geni

c lin

es o

f ric

e

AcknowledgementsMike Jeger, Imperial College, Wye Campus

Mike Shaw & Tom Harwood, Univ. of Reading

Xiangming Xu, East Malling Research

Ottmar Holdenrieder, ETHZ, CH

Sandra Denman, Forest Research, Alice Holt

Judith Turner, Central Science Laboratory, York

Department for Environment, Food and Rural Affairs

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