Stripe Rust Epidemics and Control inStripe Rust Epidemics and Control in

XIANMING CHEN, David Wood, Laura Penman, Peng Ling and Meinan Wang 1USDA-ARS Wheat Genetics, Quality, Physiology and Disease Research Unit and 2Department of Plant

Pathology, Washington State University, Pullman, WA 99164-6430 (xianming@mail.wsu.edu)

Barley Stripe Rust(Puccinia striiformis f. sp. hordei)

WA

OR ID

MT

NV

WY

UT

AZ NM

OK

KS

SD WI

IA

MO

AR

LA

IL IN

MI

OH

KY

TN

MS AL GA

SC

VA

NC

WV

PA

NY

MDDE

NJ

ME

NHVT

MACT

NC

ND

MN

TX

NE

CO

2000

WA

OR

CA

ID

MT

NV

WY

UT

AZ NM

OK

KS

SD WI

IA

MO

AR

LA

IL IN

MI

OH

KY

TN

MS AL GA

FL

SC

VA

NC

WV

PA

NY

MDDE

NJ

ME

NHVT

MACT

NC

ND

MN

TX

NE

CO

2001FL

WA

OR

CA

ID

MT

NV

WY

UT

AZ NM

OK

KS

SD WI

IA

MO

AR

LA

IL IN

MI

OH

KY

TN

MS AL GA

FL

SC

VA

NC

WV

PA

NY

MDDE

NJ

ME

NHVT

MACT

NC

ND

MN

TX

NE

CO

2002

Barley Stripe Rust

1991

19921992

1992

1993

1993

1993

19941994

1995

1995

Spread in 1991-95 Distributions in 2000-2005

FLWA

OR

CA

ID

MT

NV

WY

UT

AZ NM

OK

KS

SD WI

IA

MO

AR

LA

IL IN

MI

OH

KY

TN

MS AL GA

FL

SC

VA

NC

WV

PA

NY

MDDE

NJ

ME

NHVT

MACT

NC

ND

MN

TX

NE

CO

2003 - 2005

Trace –20%

Severe (>20%)

Wheat Stripe Rust Epidemics

WA

OR

CA

ID

MT

NV

WY

UT

AZ

CO

NM

TX

OK

KS

NE

SD

NDMN

WI

IA

MO

AR

LA

IL IN

MI

OH

KYTN

MSAL GA

FL

SC

VAWV

PANY

MDDENJ

MENH

VT

MACT

NC

2000

WA

OR

CA

ID

MT

NV

WY

UT

AZ

CO

NM

TX

OK

KS

NE

SD

NDMN

WI

IA

MO

AR

LA

IL IN

MI

OH

KYTN

MSAL GA

FL

SC

VAWV

PANY

MDDENJ

MENH

VT

MACT

NC

2002

WA

CA

MT

NV

WY

UT

AZ NMOK

KS

NE

SD

IA

MO

AR

LA

ILIN

MI

OH

KYTN

MSALGA

FL

SC

VA

NC

WV

PANY

VT

MA

NC

NDMN

TX

SD

NE

CO KS

OK AR

MO

IA

LAMSAL

TNKY

IL

ID

2001

ORWI

MD NJDE

CT

ME

NH

2003WA

CA

MT

NV

WY

UT

AZ NM NC

PANY

VT

MA

CO

IDOR

MD NJDE

CT

ME

NHMI

NC

VA

FL

SC

WVIN

KSOH

KYTN

AL GA

OK

TX

AR

LA

MO

MS

SD

NDMN

WI

NE IAIL

Trace (1-20%)Severe (>20%)

Germplasm EvaluationIn every year, more than 13,000 wheat and 5,000 barley entries were evaluated in the fields and/or greenhousefor rust resistance. The data were used to determine

provided to breeders for developing resistant cultivars.genetics of and mapping genes for resistance and were

• Germplasm nurseries• Regional nurseries• Individual breeder’s nurseries• Genetic populations

• Germplasm nurseries• Regional nurseries• Individual breeder’s nurseries• Genetic populations

Wheat Stripe RustPuccinia striiformis f. sp. tritici

Wheat Stripe Rust Epidemic in 2005

Places fromwhich striperust werecollected.

Stripe rustoccurredwithin theregion.

Wheat Stripe Rust Epidemic in 2004

WA

CA

MT

NV

WY

UT

AZNM

NC

PA

NY

VT

MA

CO

IDOR

MD NJ

DE

CT

ME

NH

NC

VA

SC

WV

ND

MN

KS

OK

TX

AR

LA

MO

MS

SD

NEIA

FL

KY

GA

IN

TN

AL

IL

WI

MI

OH

Trace (1-20%)Severe (>20%)

1,3PST-31964

1,3,11PST-381987

1,3,12 PST-221981

1,3,11,12PST-421990

PST-591998 1,3,11,12,16

1,3,8,11,12,16,17,18,19,20 PST-802000

PST-972002

1,3,10,11,12,16,17,18,19,20

PST-982002

1,3,8,10,11,12,16,17,18,19,20

2003

1,3,8,9,10,11,12,14,16,17,18,19,201,3,8,9,10,11,12,14,16,17,18,19,20

PST-782000 1,3,11,12,16,17,18,19,20

1,3,9,11,12,16,17,18,19,20 PST-992002

PST-100PST-101 1,2,3,8,9,10,11,12,16,17,18,19,20

PST-102

2003

PST-1141,3,5,8,9,10,11,12,14,16,17,18,19,20

PST-113

1,3,4,8,9,10,11,12,14,16,17,18,19,20

1,3,8,9,10,11,12,16,17,18,19,20

1,3,5,8,9,10,11,12,16,17,18,19,20 PST-1111,2,3,8,9,10,11,12,14,16,17,18,19,201,2,3,8,9,10,11,12,14,16,17,18,19,20

PST-115

2003

2004

2004

2004

2004

PST-116 1,3,4,5,8,9,10,11,12,14,16,17,18,19,202005

12345678

LemhiChinese 166Heines VIIMoroPahaDruchamp

Produra9

10YamhillStephens

Yr5

1112131415

Lee Fielder TyeeTresHyak

16 Express 17 Yr818 Yr919 Clement 20 Compair

Wheat DifferentialsEvolutionary relationshipsof new racesof the wheatstripe rustpathogen

the United States From 2000 to 2004the United States From 2000 to 2004

Puccinia striiformis f. sp. tritici cDNA Library and Gene IdentificationPuccinia striiformis f. sp. tritici cDNA Library and Gene Identification

1.0E-09NeurosporacrassaRelated to stress response protein rds1pgi1837631360I14

1.0E-100Cryptococcus neoformansTransaldolasegi5722999130K8

1.0E-102NeurosporacrassaATP synthasealpha chain gbEAA36409.155E23

1.0E-124Cryptococcus neoformansH3/H4 histoneacetyltransferasegi57228180 65I3

1.0E-13SchizosaccharomycespombeTransthyretingi358190480G10

1.0E-134Aspergillus fumigatusCalnexingi45551624 60J23

1.0E-137Cryptococcus neoformansSuccinatedehydrogenaseflavoproteingi57228890 30N15

1.0E-143AlternariaalternataEnolasegi601509490H16

1.0E-149Cryptococcus neoformansUDP-glucose dehydrogenasegi4256371765M2

1.0E-160Cryptococcus neoformansGlycinehydroxymethyltransferase,gi5722934765N4

1.0E-22Cryptococcus neoformansSpermidinesynthasegi5722802258D15

1.0E-57Cryptococcus neoformansdiphosphatekinasegi57227197 65M20

1E-040Ustilagomaydisthreoninekinasereceptor EAK84204.170E5

2.0E-07Saccharomyces cerevisiaeGPI transamidasecomponentgi731758 60N1

3.0E-29UstilagomaydisRac1 GTP binding proteingi2166751680F12

3.0E-33Cryptococcus neoformansgi50255528 65G21

3.0E-35Schizosaccharomycespombegi1911577155N13

3.0E-85PneumocystiscariniiTATA binding proteingbAAA79367.158E6

3.80E-01DebaryomyceshanseniiSerine/threonine-protein kinaseCBK1gi5278270390O18

4.0E-04BlumeriagraminisgEgh7gi72715790B8

4.0E-28Aspergillusnidulanspalmitoyltransferasesubunitgi31323646 10D13

5.0E-39Cryptococcus neoformansembCAD10036.1 40F18

5.0E-51Tuber magnatumgi588195090M15

5.0E-61UstilagomaydisGlyoxaloxidase3embCAD79490.2 55J22

5E-068Uromyces Viciae-fabaeBeta-tubulinCAC83953.158H22

6.0E-35DavidiellatassianaHydrophobingi2279615335N24

6.0E-72MortierellaramannianaDiacylglycerolacyltransferasegi1509996165D3

8.0E-12Uromyces appendiculatusDifferentiation-related proteingi505941030M9

8E-056Cryptococcus neoformansAAQ98966.140H12

9.0E-53MagnaporthegriseaChainB, ApoSaccharopineReductasegi12084779 58D15

9.0E-72Cryptococcus neoformansMAPKgbAA061669.155B10

0.0E+00PucciniagraminisElongation factorgi397949 80N15

E-ValueFungal speciesGene descriptionGenBankaccession #

1.0E-09gi1837631360I14

1.0E-100gi5722999130K8

1.0E-102ATP synthasealpha chain gbEAA36409.155E23

1.0E-124H3/H4 histoneacetyltransferasegi57228180 65I3

1.0E-13gi358190480G10

1.0E-134gi45551624 60J23

1.0E-137gi57228890 30N15

1.0E-143Enolasegi601509490H16

1.0E-149UDP-glucose dehydrogenasegi4256371765M2

1.0E-160,gi5722934765N4

1.0E-22gi5722802258D15

1.0E-57Nucleoside-gi57227197 65M20

1E-040Serine/EAK84204.170E5

2.0E-07GPI transamidasecomponentgi731758 60N1

3.0E-29Rac1 GTP binding proteingi2166751680F12

3.0E-33Oxidoreductasegi50255528 65G21

3.0E-35Ubiquitin-conjugating enzyme e2-16 kdgi1911577155N13

3.0E-85TATA binding proteingbAAA79367.158E6

3.80E-01Serine/threonine-protein kinaseCBK1gi5278270390O18

4.0E-04gEgh7gi72715790B8

4.0E-28Serine palmitoyltransferasesubunitgi31323646 10D13

5.0E-39DeacetylaseembCAD10036.1 40F18

5.0E-51Mitochondrial phosphate carrier proteingi588195090M15

5.0E-61Glyoxaloxidase3embCAD79490.2 55J22

5E-068CAC83953.158H22

6.0E-35gi2279615335N24

6.0E-72gi1509996165D3

8.0E-12gi505941030M9

8E-056AAQ98966.140H12

9.0E-53ChainB, ApoSaccharopineReductasegi12084779 58D15

9.0E-72MAPKgbAA061669.155B10

0.0E+00gi397949 80N15

Clone ID

Iron-sulfur cluster isul-like protein

1.0E-09NeurosporacrassaRelated to stress response protein rds1pgi1837631360I14

1.0E-100Cryptococcus neoformansTransaldolasegi5722999130K8

1.0E-102NeurosporacrassaATP synthasealpha chain gbEAA36409.155E23

1.0E-124Cryptococcus neoformansH3/H4 histoneacetyltransferasegi57228180 65I3

1.0E-13SchizosaccharomycespombeTransthyretingi358190480G10

1.0E-134Aspergillus fumigatusCalnexingi45551624 60J23

1.0E-137Cryptococcus neoformansSuccinatedehydrogenaseflavoproteingi57228890 30N15

1.0E-143AlternariaalternataEnolasegi601509490H16

1.0E-149Cryptococcus neoformansUDP-glucose dehydrogenasegi4256371765M2

1.0E-160Cryptococcus neoformansGlycinehydroxymethyltransferase,gi5722934765N4

1.0E-22Cryptococcus neoformansSpermidinesynthasegi5722802258D15

1.0E-57Cryptococcus neoformansdiphosphatekinasegi57227197 65M20

1E-040Ustilagomaydisthreoninekinasereceptor EAK84204.170E5

2.0E-07Saccharomyces cerevisiaeGPI transamidasecomponentgi731758 60N1

3.0E-29UstilagomaydisRac1 GTP binding proteingi2166751680F12

3.0E-33Cryptococcus neoformansgi50255528 65G21

3.0E-35Schizosaccharomycespombegi1911577155N13

3.0E-85PneumocystiscariniiTATA binding proteingbAAA79367.158E6

3.80E-01DebaryomyceshanseniiSerine/threonine-protein kinaseCBK1gi5278270390O18

4.0E-04BlumeriagraminisgEgh7gi72715790B8

4.0E-28Aspergillusnidulanspalmitoyltransferasesubunitgi31323646 10D13

5.0E-39Cryptococcus neoformansembCAD10036.1 40F18

5.0E-51Tuber magnatumgi588195090M15

5.0E-61UstilagomaydisGlyoxaloxidase3embCAD79490.2 55J22

5E-068Uromyces Viciae-fabaeBeta-tubulinCAC83953.158H22

6.0E-35DavidiellatassianaHydrophobingi2279615335N24

6.0E-72MortierellaramannianaDiacylglycerolacyltransferasegi1509996165D3

8.0E-12Uromyces appendiculatusDifferentiation-related proteingi505941030M9

8E-056Cryptococcus neoformansAAQ98966.140H12

9.0E-53MagnaporthegriseaChainB, ApoSaccharopineReductasegi12084779 58D15

9.0E-72Cryptococcus neoformansMAPKgbAA061669.155B10

0.0E+00PucciniagraminisElongation factorgi397949 80N15

E-ValueFungal speciesGene descriptionGenBankaccession #

1.0E-09gi1837631360I14

1.0E-100gi5722999130K8

1.0E-102ATP synthasealpha chain gbEAA36409.155E23

1.0E-124H3/H4 histoneacetyltransferasegi57228180 65I3

1.0E-13gi358190480G10

1.0E-134gi45551624 60J23

1.0E-137gi57228890 30N15

1.0E-143Enolasegi601509490H16

1.0E-149UDP-glucose dehydrogenasegi4256371765M2

1.0E-160,gi5722934765N4

1.0E-22gi5722802258D15

1.0E-57Nucleoside-gi57227197 65M20

1E-040Serine/EAK84204.170E5

2.0E-07GPI transamidasecomponentgi731758 60N1

3.0E-29Rac1 GTP binding proteingi2166751680F12

3.0E-33Oxidoreductasegi50255528 65G21

3.0E-35Ubiquitin-conjugating enzyme e2-16 kdgi1911577155N13

3.0E-85TATA binding proteingbAAA79367.158E6

3.80E-01Serine/threonine-protein kinaseCBK1gi5278270390O18

4.0E-04gEgh7gi72715790B8

4.0E-28Serine palmitoyltransferasesubunitgi31323646 10D13

5.0E-39DeacetylaseembCAD10036.1 40F18

5.0E-51Mitochondrial phosphate carrier proteingi588195090M15

5.0E-61Glyoxaloxidase3embCAD79490.2 55J22

5E-068CAC83953.158H22

6.0E-35gi2279615335N24

6.0E-72gi1509996165D3

8.0E-12gi505941030M9

8E-056AAQ98966.140H12

9.0E-53ChainB, ApoSaccharopineReductasegi12084779 58D15

9.0E-72MAPKgbAA061669.155B10

0.0E+00gi397949 80N15

Clone ID

Iron-sulfur cluster isul-like protein

• 40,000 clones• 1.5 -2.0 kb

• Urediniospores• HindIII digestion

• 95% clones arefull length

M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 M

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 M

1 2 3 4 M

M 1 2 3 4 5 6 7 8 9 10 1 12 13 14 15 16 MPGT PST PT PH PSH

PSTc30M9: Differentiation-Related Protein

M 1 2 3 4 5 6 7 8 9 10 11 12 13 14 1516 17 1819 20 21 22 23 24 25 26 27 M

PST PSH PSP

PSTc10C13: Deacetylase

Inserts of Puccinia striiformis f. sp. tritici BAC Clones

98kb48kb

Vector

Individual BAC clones

98kb

48kb

Vector

M M

Size Frequencies of Puccinia striiformis f. sp. tritici BAC Clones

0

10

20

30

40

50

15-20 21-30 31-60 61-85 86-125

Insert Size (kb)

Nu

mb

er

of

Clo

ne

Puccinia striiformis f. sp. tritici BAC Library

•24,000 clones

•60 kb/clone in average

•Hind III digest

•17X genome coverage

Resistance Resistance

Yr18 Yr18

AlpowaAlpowa

High-TemperatureAdult-Plant

(HTAP)Resistance

Chromosomal Location of Yr Genes

12345

6

7

A B DYr3a Yr9 Yr15 Yr24 Yr3c Yr10 Yr21 Yr29YrDa1

Yr1 Yr17 Yr32

YrTr2YrHVIIYrMin YrND

YrDru YrH46

Yr5 YrSte2 Yr27 Yr7 YrV23 Yr31YrSte Yr30YrCle YrYamYrMorYr19 YrDru2

Yr4a Yr4b

Yr2 Yr6

Yr8 Yr16

Yr22 Yr28

YrDa2Yr20 YrTr1Yr23 YrTyeYr18 Yr33

Yr25

Yr26

Yr34

One gene after anotherGene rotationGene deployment

Gene pyramiding

Cultivar mixtureMultiline cultivars

All-Stage Resistance

52-513-532-4Adult

888788SeedlingWA7939

2-32-42-312Adult

888588SeedlingWA7936

1009897584337TestLine

Infection types produced by PST races

Evaluation of WA7936 and WA7939 for Resistance to Stripe Rust in the Greenhouse

WA7936 and WA7939 have HTAP resistance.

Constructing BAC Library for Cloning Yr genesConstructing BAC Library for Cloning Yr genes

0.1 0.2 0.4 0.5MHind III unit

350 kb

•410,000 clones in 1,100 384-well plates•130 kb/clone in average

•Hind III digest

•3.4X genome coverage•Primary and super pools weremade for efficient screening

P31

D6

P32

D3

P33

D8

Yr5

NIL

500 bp

E.c

oliD

NA

Y

r5 N

ILP

25

3 p

late

Pools of P253 Rows

L M N OA B C D E F G H I J K P C-1

C-3

C-2

Pools of P253 Columns

C-5

C-1

9C

-20

Yr5

NIL

C-4

C-6

C-7

C-8

C-9

C-1

0C

-11

C-1

2C

-13

C-1

4C

-15

C-1

6C

-17

C-1

8

C-2

1C

-22

C-2

3C

-24

Identification of Yr5-Marker Positive BAC Clones

L5

M5

N5

O5

5

L1

9M

19

O1

9N

19

L2

0M

20

N2

0O

20

M M M M

Disease Epidemiology and Pathogen Races Host Resistance Resistance Gene Cloning

Pathogen Genomics

Disease MonitoringDisease Monitoring

Fungicide Treatments, Hatton, Pullman, 2004

58.559.059.560.060.561.061.562.062.563.063.5

Quilt 7+14

Quilt 14

Stratego10

Tilt 4 Headline9

Headline6

No-fungicide

Test weight (1b/bu)

0

20

40

60

80

100

120

Quilt 7+14 Quilt 14 Stratego10

Tilt 4 Headline9

Headline6

No-fungicide

Yield (bu/A)58.0 57.1 53.8 52.4 51.7 50.1

0

20

40

60

80

100

120

Quilt 7+14 Quilt 14 Stratego 10 Tilt 4 Headline 9 Headline 6 No-fungicide

6/14(B-H) 6/18(M) 7/12(SD)

Str

ipe

ru

st

severi

ty (

%)

Sprayed on 6/9 (boot), 6/16 (heading)

Fungicide TestingFungicide Treatments, Hatton, Pullman, 2004

58.559.059.560.060.561.061.562.062.563.063.5

Quilt 7+14

Quilt 14

Stratego10

Tilt 4 Headline9

Headline6

No-fungicide

Test weight (1b/bu)

0

20

40

60

80

100

120

Quilt 7+14 Quilt 14 Stratego10

Tilt 4 Headline9

Headline6

No-fungicide

Yield (bu/A)58.0 57.1 53.8 52.4 51.7 50.1

0

20

40

60

80

100

120

Quilt 7+14 Quilt 14 Stratego 10 Tilt 4 Headline 9 Headline 6 No-fungicide

6/14(B-H) 6/18(M) 7/12(SD)

Str

ipe

ru

st

severi

ty (

%)

Sprayed on 6/9 (boot), 6/16 (heading)

Fungicide Testing

0 500 1000 1500 2000 2500

PS 279Hatton

BuchananWPB 470

LewjainBoundary

Rely

EdwinFinleyTubbs

EltanWA7939

Brundage 96WA7936LambertMasami

RodCashup

CodaStephens

Madsen

ChukarFinch

Bruehl

Non-spraySprayed

Stripe rustStripe rust

Stripe rust severity (AUDPC)

Winter Wheat (2004)

-10 0 10 20 30 40 50 60 70 80

PS 279Hatton

BuchananWPB 470

Lewjain

BoundaryRely

EdwinFinleyTubbs

Eltan

WA7939Brundage 96

WA7936LambertMasami

RodCashup

CodaStephens

MadsenChukar

FinchBruehl

LossIncrease

Yield loss/increase

Yield loss/increase

Yield (%)

Cultivar Response

0 500 1000 1500 2000 2500

PS 279Hatton

BuchananWPB 470

LewjainBoundary

Rely

EdwinFinleyTubbs

EltanWA7939

Brundage 96WA7936LambertMasami

RodCashup

CodaStephens

Madsen

ChukarFinch

Bruehl

Non-spraySprayed

Stripe rustStripe rust

Stripe rust severity (AUDPC)

Winter Wheat (2004)

-10 0 10 20 30 40 50 60 70 80

PS 279Hatton

BuchananWPB 470

Lewjain

BoundaryRely

EdwinFinleyTubbs

Eltan

WA7939Brundage 96

WA7936LambertMasami

RodCashup

CodaStephens

MadsenChukar

FinchBruehl

LossIncrease

Yield loss/increase

Yield loss/increase

Yield (%)

Cultivar Response

• Rust alerts and real-time situations were sent to growersfor preparing and implementing fungicide control throughe-mails and news releases.

• Advises and recommendations were provided to growers onwhether to use fungicide on certain cultivars, which one touse, and when to use fungicides.

Implementation of Fungicide Control

Losses of multimillion dollars were prevented.

Integrated Disease Management

40 104

35 9530 86

25 77

20 68

15 5910 50

5 41

0 32

-5 23-10 14

-15 5

-20 -4

Mean (29.6 oF)

Normal (1949 -2004)

Mean max. (35 oF)

Mean min. (24 oF)

Recorded low ( -29 oF)

Recorded high (57 oF)

2005

Mean (33.7 oF)Mean max. (39.6 oF)

Mean min. (27.7 oF)

Highest (56 oF)

Lowest (56 oF)

January Weather Comparison

Disease forecasting

40 104

35 9530 86

25 77

20 68

15 5910 50

5 41

0 32

-5 23-10 14

-15 5

-20 -4

Mean (29.6 oF)

Normal (1949 -2004)

Mean max. (35 oF)

Mean min. (24 oF)

Recorded low ( -29 oF)

Recorded high (57 oF)

2005

Mean (33.7 oF)Mean max. (39.6 oF)

Mean min. (27.7 oF)

Highest (56 oF)

Lowest (7 oF)

January Weather Comparison

Disease forecasting

AcknowledgementsThis rust research program is supported byUSDA-ARS, Washington Wheat Commission,Washington Barley Commission, Idaho WheatCommission, and Vogel Foundation. We thankmany working study students and part -timeworkers for their assistance. The collaborationsby many regional, national, and internationalscientists are highly appreciated.

40 104

35 95

30 86

25 77

20 68

15 59

10 50

5 41

0 32

-5 23

-10 14

-15 5

-20 -4

Spores germinate

Disease developsmost rapidly at

Sporulation

Lethal(10 days)

daily max.daily Avg.

Temperature Effecton Stripe Rust

Parameters in Models for Stripe Rust Forecasting

1. Negative Degree Days (NDD):Accumulated daily temperatureslower than 7oC from December1 to January 31.

2. Positive Degree Days (PDD):Accumulated daily temperatureshigher than 7oC from April 1 toJune 30.

3. Julian Day of Spring (JDS):The date when positive 40oC orhigher during the following 14days.

Eq. 1: DIi=ai–biNDDZ+ciJDSEq. 2: DIi=ai–biNDDZ+ciJDS–diPDDEq. 3: DIi=ai–biNDDZ

(Coakley et al. 1982, Phytopathology 72:1539-42)(Coakley et al. 1983, Phytopathology 73:1382-85)

Epidemic Models