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.
500
Numberspremises
Number of infected
a)
400
300
200
∞
100
skiing
Move to Guelph
0
l l l l
r r r r
ebFebFebMarMarMarMarMa-rAp-Ap-Ap-ApMayMayMayMayJunJunJunJunJun-Ju -Ju -Ju -JuAugAugAugAugSepSepSep
F
- - - - - - - 7 4 1 8 - - - - - - - - - 10 17 24 03 10 17 24 31 07 14 21 28 05 12 19 26 02 09 16 23 30 0 1 2 2 04 11 18 25 01 08 15
Date
0.6
d)
0.5
Pre NMB contact tracing
Post NMB contact tracing
Post NMB inferred
0.3
0.2
0.1
0.0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
4
Fu 58
rth 0
er
Frequency
0.4
Transmission distance (km's)
Always pick the closest
Pick candidates with equal probability
Pick candidates with probabiltiy weighted by distance
0.6
d)
0.5
Pre NMB contact tracing
Post NMB contact tracing
Post NMB inferred
Frequency
0.4
0.3
0.2
0.1
0
2
4
6
8
10
12
14
16
18
20
22
24
26
28
30
32
34
36
38
40
42
44
46
4
Fu 58
rth 0
er
0.0
Transmission distance (km's)
1.5 km
0.5 km
13 km
3 km
3 km
5 km
Reporting
date
Culling
date
Infection
date
time
1
7
0
0
0
0
0
1
4
1
0
1
0
0
0
0
0
time
16
5
13
10
7
4
4
Rt
a)
3
2
1
0
0
5
10
15
Infection week
20
25
30
C
a
s
e
R
p
r
o
d
u
c
t
i
n
R
a
o
0 1 2 30 1 2 30 1 2 30 1 2 3
b)
Cu
De
m
Du
v
b
o
r
m
i
S
n
a
f
e
0
1
2
3
4
5
6
7
8
9
1
1
1
0
1
1
1
2
1
3
1
4
1
5
1
6
1
7
2
8
2
9
2
0
2
1
2
2
2
3
2
4
2
5
2
6
2
7
3
8
3
9
0
1
In fe c ti o n
Estimated
parent
infection
date
time
Parent
reporting
date
Daughter
reporting
date
Parent Infected – daughter reporting interval
0.14
c)
60%
0.12
93%
Frequency
0.10
0.08
0.06
0.04
0.02
0.00
0
5
10
15
20
25
30
Parent infection to daughter reporting (IDR) interval
0.5
Post NMB
Pre NMB
Frequency
0.4
0.3
0.2
0.1
0.0
0
2
4
6
8
Rt
10
12
14
16
18
20th Feb.
Time
NMB
20th Feb.
23rd Feb.
Time
NMB
X
X
20th Feb.
23rd Feb.
Time
NMB
20th Feb.
23rd Feb.
Time
Imposing the NMB on Feb. 20th, or 21st
0.20
a)
0.18
Probability
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
600
800
1000
1200
1400
Epidemic size
1600
1800
2000
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 24 hr reporting to cull
interval from Feb. 24th
0.14
b)
0.12
Probability
0.10
0.08
0.06
0.04
0.02
0.00
600
800
1000
1200
1400
Epidemic size
1600
1800
2000
NMB
20th Feb.
23rd Feb.
Time
NMB
X
X
20th Feb.
23rd Feb.
Time
NMB
20th Feb.
23rd Feb.
Time
20th Feb.
Time
Total number of descendents left resulting
from transmission links < 20 km distant
a)
1000
IPs infected post-NMB
IPs infected pre-NMB
100
10
1
0
0.1
0.01
0.1
1
10
100
Distance of IP from infection source (km's)
1000
Week
31
29
27
25
23
21
19
17
15
13
11
9
7
5
3
1
Number of new infections
300
250
200
150
100
50
0
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)
Philippines
% nucleotide divergence
18
16
8
Serotype A
Serotype C
A
Serotype O
B
14
6
12
10
4
1.5% yr-1
8
1.0% yr-1
6
1.4% yr-1
2
4
2
0
Year
19
99
19
98
19
97
19
96
19
95
Year
Turkey
12
14
C
Serotype A
12
10
D
Serotype A
Serotype O
10
8
8
6
1.0% yr-1
4
1.1% yr-1
6
4
2
2
0
0.4% yr-1
Year
19
84
19
86
19
88
19
90
19
92
19
94
19
96
19
98
19
74
19
72
19
70
19
68
0
19
66
19
64
% nucleotide divergence
19
94
19
74
19
76
19
78
19
80
19
82
19
84
19
86
19
88
19
90
19
92
0
Year
WITHIN HOST POPULATION DYNAMICS
Assume:
Simple exponential population growth
Simple Poisson mutation process (no back mutation)
Mutants are either tolerated and equally fit as wildtype
or not tolerated at all
Wildtype
virus
Mutant
virus
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
Antibody
Target
Antigen
27-4-4
25-5-5
25-4-12
I32
I34
ICJ31-10
D3
IBM55-6
ICJ27
ICJ12-9
IH8-4
IH8-25
IBA12
ICJ12
VP1
VP1
VP1
VP1
VP1
VP1
VP2
VP2
VP3
VP3
VP3
VP3
VP3
VP3
Freq. Resistant #mutations
Variants (log10) conferring
resistance
-3.9
7
-3.1
3
-3.2
4
-3.1
1
-3.9
3
-5.2
1
-4.6
3
-5.1
1
-3.0
1
-5.3
1
-2.7
1
-3.0
1
-2.9
1
-3.6
2
Log freq. each
mutation
-4.7
-3.6
-3.8
-3.1
-4.4
-5.2
-5.1
-5.1
-3.0
-5.3
-2.7
-3.0
-2.9
-3.6
Average mutation rate at least 0.0001 per site per replication cycle
i.e. at least 1 mutation per genome duplication
The fraction of mutant capsid genes in an infected animal?
10-3
10-4
Error Rate
(per base
per replication
cycle)
10-5
10-6
0
10
20
30
40
Viral Generations (t)
50
• 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
Introduce
infection
Group 1
Group 2
Group 3
Group 4
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.
Inoculum
Group 1
Group 2
99
07
23
487
Group 3
91
NOT DONE
06
98
NOT DONE
05
97
23
487
577
23
487
Ø
Inoculum b
NOT DONE
03
487
23
487
577
95
89
02
01
231,2
487
487
00
NOT DONE
81
94
23
487
NOT DONE
88
80
NOT INFECTED
NOT INFECTED
87
231,2
487
79
23
487
577
78
NOT INFECTED
487
23
NOT DONE
NOT DONE
96
04
23
487
577
83
82
90
NOT DONE
Inoculum a
23
487
577
Group 4
86
231,2
487
5771,2
NOT INFECTED
93
85
77
NOT INFECTED
NOT INFECTED
NOT INFECTED
92
84
76
NOT INFECTED
23
487
577
NOT INFECTED