Transcript Emergence and re-emergence of whooping cough

Some challenges to make current datadriven (‘statistical’) models even more
relevant to public health
Ottar Bjornstad
Center for Infectious Disease Dynamics,
Penn State University
Focus on time series analysis of incidence analysis
400k
0-1y
1-3y
3-5y
350k
5-10y
10-15y
15- y
300k
250k
200k
150k
100k
50k
0
‘44
‘55
Quarterly measles incidence 44-55
Outline:
~ 1993
then –> now
current challenges
mostly anecdotal personal reflections
~ 1993
~1993 maturing* mathematical formalism incorporating:
(cf yesterdays talks by Mick and Val)
– Seasonal forcing
– Age-structure & non-homogenous mixing
– Spatial diffusion & metapopulation dynamics
– Plausible scenarios of scaling of transmission with pop size
– Stochasticity
But, early days w.r.t. letting these general models loose on data …
* for directly transmitted persistent (SI), fully
immunizing (SIR) or fully non-immunizing (SIS)
~1993 Early days w.r.t. letting these general models loose on data …
… because of many challenges
The obvious:
– Absence of data on key state variables (eg susceptible)
– Disparity between key state variables and observed quantities
(eg incidence is not prevalence)
The less obvious:
– Weariness regarding whether a detailed quantitative match to
data should be a critical characteristic of mathematical models
then –> now
Today’s expectation for match (1)
eg TSIR forecast for E&W measles (E&W)
Incidence
TSIR forecast
TSIR: Discrete time ‘piecewise constant’ B-D process (cf Chain-binomial)
If l is small relative to S, then the chain can be approximated by an unconstrained
B-D process; The conditional distribution of It+1 is the sum of It Geometric
distributions -> NegBin with clumping It
Host dynamics
Transmission dynamics
Stochasticity
St 1  S t  Bt  I t
t 1   t St I t

I t 1 ~ NegBin(t , I t )
S - Susceptibles, B - Births , I - Infected and Infective,  - epidemic intensity,  - correction for time
discretization, β - seasonal transmission rate
Today’s expectation for match (2)
eg age-structured TSIR forecast for rubella (South Africa)
*
* difference in heat intensity is due to underreporting
Metcalf et al 2013
Yesteryear’s expectations
Kot and Schaffer (1985) JTB:
“One way of resolving the problem is to view the motion in phase space,
i.e. in a vector space whose axes are the state independent variables.
However, for most real world ecological and epidemiological systems, this
requirement is not easily met. It is often difficult even to enumerate all of
the state variables, much less to follow their magnitudes over time.
Put another way, the variables studied in nature are generally
embedded in more complex systems. As a practical matter, it is
unlikely that population dynamicists will ever be able to write down
the complete governing equations for any natural system.”
ID complexities: age-structured mixing, age-specific seasonality in
transmission, spatial heterogeneity, heterogeneities in susceptibility, etc,
etc
Journey from there to here (1)
-> Many ‘Obvious’ challenges were painstakingly resolved along the way
Journey from there to here (1)
-> Many ‘Obvious’ challenges were painstakingly resolved along the way
1) Perhaps models may have some qualitative relevance?
- Nonparametric forecasting to distinguish cycles from chaos
(Suigihara &c).
- Nonparametric Lyapunov exponent estimators (Ellner &c).
Journey from there to here (1)
-> Many ‘Obvious’ challenges were painstakingly resolved along the way
1) Perhaps models may have some qualitative relevance?
- Nonparametric forecasting to distinguish cycles from chaos
(Suigihara &c).
- Nonparametric Lyapunov exponent estimators (Ellner &c).
2) If we can somehow reconstruct the unobserved susceptible class, would
it be egregiously ambitious to compare model simulations and data?
- Semiparametric models with smart embedding (Ellner &c)
- Susceptible reconstruction (Bobashev &c; Finkenstadt &c)
Journey from there to here (1)
-> Many ‘Obvious’ challenges were painstakingly resolved along the way
1) Perhaps models may have some qualitative relevance?
- Nonparametric forecasting to distinguish cycles from chaos
(Suigihara &c).
- Nonparametric Lyapunov exponent estimators (Ellner &c).
2) If we can somehow reconstruct the unobserved susceptible class, would
it be egregiously ambitious to compare model simulations and data?
- Semiparametric models with smart embedding (Ellner &c)
- Susceptible reconstruction (Bobashev &c; Finkenstadt &c)
3) A seasonal chain-binomial model can in fact be recast as a nonautonomous autoregressive regression: I dear you!
- Time-series SIR ver 1 (Finkenstadt & Grenfell) and TSIR ver 2
Journey from there to here (1)
-> Many ‘Obvious’ challenges were painstakingly resolved along the way
1) Perhaps models may have some qualitative relevance?
- Nonparametric forecasting to distinguish cycles from chaos
(Suigihara &c).
- Nonparametric Lyapunov exponent estimators (Ellner &c).
2) If we can somehow reconstruct the unobserved susceptible class, would
it be egregiously ambitious to compare model simulations and data?
- Semiparametric models with smart embedding (Ellner &c)
- Susceptible reconstruction (Bobashev &c; Finkenstadt &c)
3) A seasonal chain-binomial model can in fact be recast as a nonautonomous autoregressive regression: I dear you!
- Time-series SIR ver 1 (Finkenstadt & Grenfell) and TSIR ver 2
4) Why in the world does the TSIR seem to fit measles in E&W?
- ‘Emergent simplicity’ (Grenfell); Dynamic homogeneity (Earn &c)
Journey from there to here (2)
5) We believe! Real dynamics can be predicted by simple mechanistic
models (that incorporates key idiosyncrasies)
- POMP et al (King &c)
- Hierarchical models with observation process (Cauchemez &c).
- Age-structured TSIR (Metcalf &c).
….. (cf Simon’s talk)
Journey from there to here (2)
5) We believe! Real dynamics can be predicted by simple mechanistic
models (that incorporates key idiosyncrasies)
- POMP et al (King &c)
- Hierarchical models with observation process (Cauchemez &c).
- Age-structured TSIR (Metcalf &c).
….. (cf Simon’s talk)
Lessons from last 20 years:
- ‘All models are wrong …’ Some much less than we expected.
- Emergent simplicity once key idiosyncrasies are identified
- ?Tactical/strategical? models may be more relevant than we expected.
[The prevailing notion that computation was the important driver in the field
is wrong (Cambridge MRCs BUGS has been around since 20 years)]
Some current challenges
Some critical issues are:
(i) use nonlinear stochastic modeling to identify all potentially undesirable
side effects of intervention-induced reduction in circulation.
- Rubella and CRS (cf Jess’ talk)
- Chikenpox vaccine and increased shingles incidence
- Whooping cough and the role of natural antigen circulation in maintaining
immune memory. The possibility of long-term vaccine failure.
More case law!
Mass-vaccination introduced in most rich countries in mid ‘40s - early ’50s
10000
Vaccine introduced
Recent cases
200
Cases (/mo.)
400
1000
100
10
Reported pertussis cases (/ yr.)
Pertussis in Massachusetts
1990
1995
1920
2000
1940
2005
1960
1980
2000
Years
The first decades of vaccine induced control was
extremely successful …
Mass-vaccination introduced in most rich countries in mid ‘40s - early ’50s
10000
Vaccine introduced
Recent cases
200
Cases (/mo.)
400
1000
100
10
Reported pertussis cases (/ yr.)
Pertussis in Massachusetts
1990
1995
1920
2000
1940
2005
1960
1980
2000
Years
The first decades of vaccine induced control was
extremely successful …
… Then even in very high cover areas throughout the
developed world (e.g. Massachusetts with consistent
>95% cover) the disease re-emerged!
vaccine era
0.00
density
0.05
0.10
0.00
density
0.05
0.10
pre-vaccine era
0.15
0.15
Massachusets age-incidence patterns
0-1
5-6
10-15
age class
15-60
0-1
5-6
12-13
20-21
30-31
40-41
50-51
age class
Re-emergence is associated with a completely different core group
Lavine, King and Bjornstad. 2011. PNAS
The ‘anamnestic’ 4 compartment SIR model –
re-exposure helps maintain immune memory
S – suceptible
 - force of infection
I – Infected
 - boosting coeffiecient
R – Highly immune
 - recovery rate
W – Waning: resistant to infection and
will get boosted or loose immunity
depending on competing rates
- rate of loss of immunity
 - rate of loss of immunity
Lavine, King and Bjornstad. 2011. PNAS
As long as the anamnestic response is at least 10x greater than the naïve
response:
Pre-vaccination prediction
Age
Post-vaccination prediction:
Lavine, King and Bjornstad. 2011. PNAS
0.0014
Total incidence
Incidence
0.0011

?  0.5
?  20

?  5000
‘SIS’
0.0008
Proportion infected
Natural immune boosting in pertussis dynamics and the
potential for long-term vaccine failure
‘SIR’
0.0
0.2
0.4
0.6
Vaccine
Vaccinecoverage
coverage
0.8
1.0
0.01
0.02
0.03
Boost at 15
No boost
0.00
Proportion cases
0.04
Predicted public health consequences of a
boosterEffvaccine
at age
15 …
ect of booster
v accine
at a ge 15
1
3
5
7
9
11
13
15
17
19
21
… The booster may push circulation towards
adults of childbearing age and increase perinatal
infection and increase severe disease.
(cf CRS but different mechanism)
23
Some critical issues are:
(ii) robust forecasting in the face of rapidly changing demographies and
vaccination schedules
(ii) robust forecasting in the face of rapidly changing demographies and
vaccination schedules
e.g. Measles Incidence in China: 3 provinces
From Matt Ferrari
(ii) robust forecasting in the face of rapidly changing demographies and
vaccination schedules; *
* Perreti et al PNAS 2013 110:5253-5257 (‘Model-free forecasting outperforms the correct
mechanistic model for simulated and experimental data’) is not the way to go
(iii) probabilistically projecting possible/probable build-up of ‘susceptible
pockets’ in the face of imperfect vaccination programs
(iii) probabilistically projecting possible/probable build-up of ‘susceptible
pockets’ in the face of imperfect vaccination programs
Eg Measles (from Matt Ferrari)
Reported Measles Cases: Burkina Faso 1996-2009
Sao Paolo: 1997
4000
200
2000
4000
3000
2000
400
0
6000
reported cases
8000
600
0
1998
Jul-98
1997
Jul-97
1996
Jul-96
1995
Jul-95
1994
Jul-94
1993
Jul-93
1992
Jul-92
1991
Jul-91
1990
Jul-90
1989
Jul-89
1988
Jul-88
1987
Jul-87
1986
0
Jul-86
CASOS 1986-96
CAMPAÑA JUNIO 92
M-M-R 1 - 10 A
CAMPAÑA MAYO 87
SARAMPIÓN 9M - 14 A
CASOS 1997-98
10000
1000
800
Burkina Faso:
2009
12000
1000
1200
1996
1997
1998
1999
2000
2001
2002
2003
2004
MES / AÑO
Malawi: 2010
• >135,000 cases
following 10
years of low
incidence
France, 2011
2005
2006
2007
2008
2009
(iv) Important challenge:
We need accurate parametric anchoring of mechanistic models
Log-likelihood
1 e-03
-1000
8 e-04
-2000
-3000
6 e-04
inter.beta
Interstage β
Inference for mechanistic models usually
reveal severe multicollinearity among
parameters:
- Various parameter combinations can fit
observed data equally well,
- but will not make the same out of sample
predictions
-4000
4 e-04
-5000
2 e-04
-6000
-7000
2 e-04
4 e-04
6 e-04
8 e-04
1 e-03
intra.beta
Intrastage β
Eg 2-stage PDV model
(cf Klepac et al. 2009)
- ‘All models are wrong …’ Some much less than we expected.
- Emergent simplicity once key idiosyncrasies are identified.
- ?Tactical/strategical? models may be more relevant than we expected.
- We have an enormous arsenal of model fitting tools.
- Multicollinearity makes anchoring of estimates a critical challenge.
Current modeling challenges:
- Study unanticipated Public health consequences
- Consequences of rapidly changing demographics
- Understand build-up of susceptible pockets
Thank you!