The construction and analysis of epidemic trees with reference to the 2001 UK FMDV outbreak Dan Haydon, Dept Zoology, University of Guelph, On. Ca.

The construction and analysis of epidemic trees with reference to the 2001 UK FMDV outbreak

Dan Haydon,Dept Zoology,University of Guelph, On. Ca.

• Provide case reproduction ratios from outbreak data as it arises

• Explore the consequences of applying stricter control measures

Woolhouse, MEJ., Topping, M.C., Haydon, D.T. and 8 others. 2001. Foot-and-mouth disease under control in the UK.Nature 411, 258-259.

Haydon, D.T., Topping, M.C., Shaw, D.J., Matthews, L., Friar, J.K., Wilesmith, J., and Woolhouse, M.E.J.

2003. The construction and analysis of epidemic trees with reference to the 2001 UK foot-and-mouth outbreak. Proceedings: Biological Sciences (The Royal Society, UK) 270, 121-127.

Date

10-Feb

17-Feb

24-Feb

03-Mar

10-Mar

17-Mar

24-Mar

31-Mar

07-Apr

14-Apr

21-Apr

28-Apr

05-May

12-May

19-May

26-May

02-Jun

09-Jun

16-Jun

23-Jun

30-Jun

07-Jul

14-Jul

21-Jul

28-Jul

04-Aug

11-Aug

18-Aug

25-Aug

01-Sep

08-Sep

15-Sep

Num

bers

0

100

200

300

400

500a)

Num

ber

of in

fect

ed p

rem

ises

∞

skiing Move to Guelph

d)

Transmission distance (km's)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Furth

er

Fre

quen

cy

0.0

0.1

0.2

0.3

0.4

0.5

0.6Pre NMB contact tracingPost NMB contact tracing

Post NMB inferred

time

5 km

3 km

3 km

13 km

0.5 km

1.5 km

Reportingdate

Cullingdate

Infection date

d)

Transmission distance (km's)

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50

Furth

er

Fre

quen

cy

0.0

0.1

0.2

0.3

0.4

0.5

0.6Pre NMB contact tracingPost NMB contact tracing

Post NMB inferred

Always pick the closestPick candidates with equal probabilityPick candidates with probabiltiy weighted by distance

time

1

7

0

0

0

0

0

1

4

1

0

1

0

0

0

0

0

0 5 10 15 20 25 30

Infection week

Rt

0

1

2

3

4

5a)

47

101316

Infection week

Ca

se R

ep

rod

uct

ion

Ra

tio

0 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

Cumbria Devon Dumfries & Galloway Settle0

12

30

12

30

12

30

12

3b)

timeParent

reportingdate

Estimatedparent

infectiondate

Daughter reporting

date

Parent Infected – daughter reporting interval

c)

Parent infection to daughter reporting (IDR) interval

0 5 10 15 20 25 30

Fre

quen

cy

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

93%60%

Rt

0 2 4 6 8 10 12 14 16 18

Fre

quen

cy

0.0

0.1

0.2

0.3

0.4

0.5

Post NMB Pre NMB

20th Feb. Time

20th Feb. 23rd Feb. Time

NMB

20th Feb. 23rd Feb.

X

X

Time

NMB

20th Feb. 23rd Feb. Time

NMB

Imposing the NMB on Feb. 20th, or 21st

Epidemic size

600 800 1000 1200 1400 1600 1800 2000

Pro

ba

bili

ty

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Imposing 24 hr reporting to cull interval from Feb. 24th

Epidemic size600 800 1000 1200 1400 1600 1800 2000

Pro

babi

lity

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

a)

b)

Between 20th – evening of 23rd of February:

• 17 IPs infected at distance greater than 20km

• 16 of these IPs have positive contact tracing

• 13 were infected by animal movements from markets

time

time

time

Imposing the NMB on Feb. 20th, or 21st

Epidemic size

600 800 1000 1200 1400 1600 1800 2000

Pro

babi

lity

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.16

0.18

0.20

Imposing 24 hr reporting to cull interval from Feb. 24th

Epidemic size600 800 1000 1200 1400 1600 1800 2000

Pro

babi

lity

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

a)

b)

20th Feb. 23rd Feb. Time

NMB

20th Feb. 23rd Feb. Time

NMB

X

X

20th Feb. 23rd Feb. Time

NMB

20th Feb. Time

Distance of IP from infection source (km's)

0.01 0.1 1 10 100 1000

Tot

al n

umbe

r of

des

cend

ents

left

res

ultin

gfr

om t

rans

mis

sion

link

s <

20

km d

ista

nt

0.1

1

10

100

1000IPs infected post-NMBIPs infected pre-NMB

a)

0

0

50

100

150

200

250

300

1 3 5 7 9

11 13

15

17

19

21

23

25

27

29

31

Week

Num

ber

of n

ew in

fect

ions

The government, however, dismisses Woolhouse's figures as an overestimate. It also argues that it could not have acted any faster than it did. "A national ban was imposed as soon as it became clear that there was a national problem," a spokesman for the Department for Environment Food and Rural Affairs told New Scientist. But he did add that such a ban would be imposed immediately if any future outbreak occurred.

New Scientist vol. 176 issue 2372 (07 December 2002)

What the foot and mouth virus looks like (not actual size)

1.5% yr-1

1.0% yr-1 1.4% yr-1

1.0% yr-1

1.1% yr-1

0.4% yr-1

Wildtype virus

Mutant virus

Assume:

Simple exponential population growth

Simple Poisson mutation process (no back mutation)

Mutants are either tolerated and equally fit as wildtypeor not tolerated at all

WITHIN HOST POPULATION DYNAMICS

Haydon, D.T., Samuel, A.R., and Knowles, N.J. (2001). The generation and persistence of genetic variation in foot-and-mouth disease virus. Preventative Veterinary Medicine 51, 111-124.

Poliovirus (from Smith and Inglis, 1987)

Monoclonal Target Freq. Resistant #mutations Log freq. each Antibody Antigen Variants (log10) conferring mutation

resistance 27-4-4 VP1 -3.9 7 -4.7 25-5-5 VP1 -3.1 3 -3.6 25-4-12 VP1 -3.2 4 -3.8 I32 VP1 -3.1 1 -3.1 I34 VP1 -3.9 3 -4.4 ICJ31-10 VP1 -5.2 1 -5.2 D3 VP2 -4.6 3 -5.1 IBM55-6 VP2 -5.1 1 -5.1 ICJ27 VP3 -3.0 1 -3.0 ICJ12-9 VP3 -5.3 1 -5.3 IH8-4 VP3 -2.7 1 -2.7 IH8-25 VP3 -3.0 1 -3.0 IBA12 VP3 -2.9 1 -2.9 ICJ12 VP3 -3.6 2 -3.6

Average mutation rate at least 0.0001 per site per replication cycle i.e. at least 1 mutation per genome duplication

0 10 20 30 40 50

10-3

10-4

10-5

10-6

Viral Generations (t)

Error Rate(per base

per replicationcycle)

The fraction of mutant capsid genes in an infected animal?

• observed rates of change in the field are 0.5 - 1.5 % yr-1

• corresponding to 10 - 30 nucleotide changes in capsids genes yr-1

• plausible that the bulk of virus excreted by infected animals differs by at least one point mutation to capsid genes from that which ‘went in’

• therefore sequential chains of infection of 10 - 30 animals yr-1 could give rise to observed rates of change

Uncertainty surrounds many of the critical parameters governing the generation of genetic variation during a single infection

In particular:

• the mutation rate• the number of viral generations• the viability of variants

However, if variation is generated at the rate anticipated, then transmission networks may be traced at a much finer resolution than practiced to date

Group 1 Group 2 Group 3 Group 4

Introduceinfection

Hughes, G.J., Mioulet, V., Haydon, D.T., Kitching, P.R., Donaldson , A.I., and Woolhouse, M.E.J. (2002). Serial passage of foot-and-mouth disease virus in sheep reveals declining levels of viraemia through time. Journal of General Virology 83, 1907-1914.

07

98

83

06

97

90 82

05

96

89 81

04

95

88 80

03

94

87 79

02 86 78

85 77

Inoculum Group 1 Group 2 Group 3 Group 4

01 93

84 76 00 92

99 91

NOT DONE

NOT DONE

NOT DONE

NOT DONE

NOT DONE

NOT DONE

NOT DONE

NOT DONE

Inoculum a

Inoculum b

Ø

487

23487

231,2

487

23487577

23487

23487577

23487

23487577

231,2

487

23487577

23487577

23487577

23

231,2

4875771,2

487

487

NOT INFECTED

NOT INFECTED

NOT INFECTED

NOT INFECTED

NOT INFECTED NOT INFECTED

NOT INFECTED

NOT INFECTED

NOT INFECTED