1.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Real-time Bayesian Data Assimilation and
Prediction for Livestock Epidemics
Chris Jewell1, Will Probert2, Mike Tildesley2
1CHICAS, Lancaster University, c.jewell@lancaster.ac.uk
2Life Sciences, University of Warwick
27th October, 2016

2.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
1 Aims of model-based analysis
2 Application: Japan foot and mouth disease 2010
3 Epidemic model
4 Inference
5 Results

3.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Aims
During an epidemic, we wish to use a model for...
Nowcasting:
What is the current extent of the epidemic?
What puts a farm at high risk?
Is our current control strategy working?
Forecasting:
Where will the disease go next?
What is the best control decision, given imperfect knowledge?

4.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Japanese foot and mouth disease, 2010
Muroga et al. (2012)
Miyazaki prefecture
First detection late March 2010
Day 0 = date of first detection
290 IPs
948 non-IP culls
10km vaccination implemented
days 60–64
DC culls mostly > day 84
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0
50000
100000
150000
200000
5e+04 1e+05
0
100
200
300
Mar Apr May Jun
Date
Detectedcases

5.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Nowcasting questions
At each stage of the epidemic:
Evaluate control policy
Vaccine efficacy
What was the true extent of the outbreak?
Where are the undetected, or occult infections?
Vaccination strategy
Cull strategy
Target surveillance

6.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Available data
I think like a statistician: data =⇒ model!
Population data (explanatory variables):
Location of each farm: centroid, UTM coordinates
Number of cattle, pigs
Date of vaccination (∞ if not vaccinated)
Epidemiological data (response variable(s)):
Detection (notification) date
Cull date
Infection date not observed =⇒ censored

7.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
SINR model
S I N R
0
Time
Infectivity
Farm as epidemiological unit
Infections determined by relationship to other infectives
Infection times are censored (unobserved)
Undetected occult infections

8.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Transmission model – quickly!
Keeling et al. 2001
Infected
Cattle
Pigs
Location
Susceptible
Cattle
Pigs
Location
Notified
Cattle
Pigs
Location
1 - θ
γ2
Vaccine
efficacy
Biosecurity
t-I > 4
Spatial SINR Model
0 5 10 15 20 25
0.00.20.40.60.81.0
Distance/km
K(i,|(j,δ))
delta=0.5
delta=1
delta=5
delta=10
Spatial transmission
(proxy for network)

9.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Model-based inference
Simulation moves forward in time
Parameters unknown
Population
Data
Parameters Model Epidemic
Prior to simulation, we need parameter inference

10.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Inference
Parameter inference looks backward in time
Done in real-time during epidemic
Inference requirements
Parameters estimated with full measurement of uncertainty
Account for censored and occult infection times
Easy to feed forward into simulation
Population
Data
Parameters Model Epidemic

11.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Bayesian Inference
1 Incorporation of prior information
2 Machinery to account for missing data
Censored infection times
occult (undetected) infections
3 Fully likelihood-based
We know what we’re getting from our model! (cf. ABC)
Likelihood fast to compute (cf. simulation)
GPU accelerated MCMC → results overnight!
4 Results provided as (posterior) probability distributions
Suitable for decision making under uncertainty
Don’t be over-confident!

12.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Vaccine efficacy
How effective was vaccination?
Vaccine efficacy: θ parameter
s(j; t, ζ, φ) = (1 − θ)[vj <t]
˜cj
φc
+ ζ ˜pj
φp
Vaccine efficacy tested 4, 8, 16 days post vaccination
Results from weekly analyses during outbreak
N.B. results from epidemic model avoids bias due to
non-independence of infections

13.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Vaccine efficacy
4 days post-vaccination
0.00
0.25
0.50
0.75
1.00
34 41 48 55 62 69 76 83 90 97 104
Day
θ
Efficacy 4 days post vaccination

14.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Vaccine efficacy
8 days post-vaccination
0.25
0.50
0.75
1.00
34 41 48 55 62 69 76 83 90 97 104
Day
θ
Efficacy 8 days post vaccination

15.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Vaccine efficacy
14 days post-vaccination
0.2
0.4
0.6
0.8
1.0
34 41 48 55 62 69 76 83 90 97 104
Day
θ
Efficacy 14 days post vaccination

16.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Vaccination timing
Was vaccination performed in time?

17.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Vaccination timing
Was vaccination performed in time?
What was the probability that herds were already infected
when they were vaccinated? (Preliminary results!)
q
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60 65 70 75
0.00.20.40.60.81.0
Day of vacc.
Pr(I<V)

18.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Extent of the epidemic
Was vaccination and/or DC culling keeping up with the
epidemic?
Nowcasting of undetected infections can tell us...
Show movie now...

19.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Conclusions
Methods
Likelihood-based inference is fast: nowcast information ≈ 1h
Suitable for epidemic management if data comes in promptly!
Work on automated data pipeline to improve this
Joint parameter posterior provides basis for forecasting
See Will Probert’s talk up next...
GPU-enabled code available at
http://fhm-chicas-code.lancs.ac.uk/groups/InFER/
Help provided to compile and/or develop the model!

20.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Conclusions
Japan 2010
Apparent vaccine efficacy highly sensitive to delay between
dose and immunity
Vaccine takes time to work – need to be ahead of the epidemic!
Eventual efficacy around 85%, but epidemic escapes vaccine
delivery.
Knowledge of spatial extent of the epidemic required
Optimise vaccine delivery, culling
Occult probabilties: prioritise active surveillance (see Jewell et
al (2012) Biostatistics)
More precise results: we need to to negative testing results as
well as positive

21.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
The end

22.
Aims of model-based analysis Japan FMD 2010 Model Inference Results
Transmission model – less quickly!
Susceptible → Infected
λij (t) = γ1q (i; ξ, ψ) s (j; ζ, φ) K(i, j; δ) i ∈ I, j ∈ S
λ∗
ij (t) = γ2βij (t) i ∈ N, j ∈ S
t =
1 if t < µ
1 2 otherwise
q(i; t, ξ, ψ) = 1[t − Ii > 4] ˜ci
ψ1
+ ξ ˜pi
ψp
s(j; t, ζ, φ) = (1 − θ)[vj <t]
˜cj
φc
+ ζ ˜pj
φp
˜c, ˜p = cattle, pigs; 2 = movt ban; γ2 = notification
v = vaccine effect date; θ = farm-level vaccine efficacy