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Modelling – progress update
Stephen Catterall, BioSS
28th November 2007
Contents
• Sheep flock model
– Refinements
• JSRV infection model
– Progression to clinical disease
– Transmission
• Conclusion
Sheep flock model
•
•
•
•
Status: it has now been implemented in ‘C’
Very fast!
Three versions: hill, upland, lowland
Refinements:
– Lamb mortality modelling
– Incorporate variability between farms
1200
sample output for lowland farm
600
400
200
0
sheep
800
1000
sheep
lambs
hoggs
breeding ewes
240
250
260
270
time
280
290
300
500
1000
sheep
lambs
hoggs
breeding ewes
0
sheep
1500
sample output for upland farm
240
250
260
270
time
280
290
300
sample output for hill farm
1000
500
0
sheep
1500
2000
sheep
lambs
hoggs
breeding ewes
240
250
260
270
time
280
290
300
JSRV infection dynamics
• Status: the JSRV infection model has been
implemented in ‘C’
• However, more data is needed so as to better estimate
some of the parameters
• Assume:
–
–
–
–
All sheep initially susceptible
Some sheep acquire infection (without being infectious)
At some point later on, the sheep becomes infectious
After some time the sheep then develops clinical symptoms
JSRV infection dynamics
S
Not
infected
E
Infected
Not
infectious
Not
clinical
STANDARD MORTALITY
voluntary/involuntary culling
I
Infected
Infectious
Not
clinical
CLINICAL
removal from
flock
JSRV infection dynamics
• Modes of transmission
– Horizontal transmission
– Vertical transmission? close contact between the ewe and
her lamb
– Indirect transmission via the environment?? not very
important but cannot be excluded?
• All three modes of transmission have been
implemented within the model
JSRV infection dynamics
• Simulation of transmission…
– When initialising a susceptible sheep, take U
from U (0,1)
– and compute
H max   ln U
– set H=0
JSRV infection dynamics
• At each discrete timestep…
– Increment H by
 direct ( I  R)   indirect
tn
 f (c(t ))dt
t n 1
– the sheep acquires infection when
H  H max
1000
1200
sample model output
600
400
200
E
I
R
0
sheep
800
Sheep
300
320
340
360
time
380
400
420
In summary
• Sheep flock model
– Complete subject to a few refinements
– A paper describing the model is being written
• JSRV infection transmission model
– This has been implemented in ‘C’
– Three modes of transmission modelled
– ‘Estimation’ of key parameters is still required