Approaches to modeling, parameter
estimation, and policy guidance
during the endgame
Dr Isobel Blake
Research Fellow
Dr Kath O’Reilly
MRC Research Fellow
Vaccine Epidemiology Research Group
MRC Centre for Outbreak Analysis and Modelling
Imperial College London
Policy guidance
For modelling to be useful it must be
• In collaboration with experts, policy makers, program managers, field
staff
• Timely
• Appropriate
• Interpretable
Examples provided:
• Age and geographic targeting vaccination during outbreaks
• Global risk assessment
• Role of tOPV in cVDPV emergence
• Papers with other examples provided at the end
18+ papers
27 GPEI staff
- CDC, WHO HQ and WHO incountry staff
Targeting immunisation campaigns
•
Are there benefits from increasing the upper age-limit of vaccination campaigns even in the
absence of cases in older ages?
•
What is the impact of campaigns in accessible areas in stopping transmission in
inaccessible areas?
•
Need to understand contribution to transmission by different groups
Dynamic transmission model and parameter estimation
• Based on stochastic SEIR
framework
• Realistic incubation period of 16
days (Erlang distribution)
• Random process of case detection
(1:200)
• Allow different transmission rates
between ages (+ geographic areas)
Incubation period
(16 d)
Latent
period
(4 d)
S E
1:200 reported polio
cases
Infectious period (? d)
I
Parameter estimation:
Maximum likelihood through iterated particle filtering
• Ionides et al. 2006 PNAS 103(49)
• R package ‘pomp’ (Partially observed Markov process)
• Fit of different patterns of mixing by age compared using the likelihood
(AIC)
R
Tajikistan and Republic of Congo model fit
bOPV
outbreak suspected by local
physicians
Blake IM, Martin R, Goel A, Khetsuriani N,
Everts J, et al. (2014) PNAS 111: 1060410609
Contribution to transmission by age
Parameter
Tajikistan
Reproduction number for children 0-5 2.18 (2.06 – 2.45)
Republic of Congo
1.57 (1.53 – 3.39)
years old at the start of the outbreak
Reproduction number for older
0.46 (0.42-0.52)
1.85(1.83 – 4.00)
children and adults at the start of the
outbreak
Blake et al, 2014 PNAS
Policy guidance
•Contribution of adults and older children to transmission is likely to depend on
setting
•No support for expanding age range for vaccination campaigns in absence of adult
cases
•Late detection of outbreak, limited impact of response, need to enhance
surveillance to detect earlier
Impact of SIAs on inaccessible areas: Somalia
Divide Southern and Central Somalia into 3
areas (meta-population model)
Evidence for a higher transmission rate
within Banadir over homogeneous mixing
ΔAIC = 105
Estimate
199 confirmed cases
96% cases in Southern and Central Somalia
90% of these in children <5 yrs
Effective reproduction
for Banadir
5.9 (4.8 – 8.3)
Effective reproduction
number for Accessible
and inaccessible areas
2.1 (1.8 – 2.8)
Duration of
infectiousness (days)
9.6 (6.4 – 12.1)
Reported case to
infection ratio in
inaccessible areas
1:902 (1:1538 –
1:606)
Somalia outbreak: Impact of response
tOPV campaign
bOPV campaign
+ Date outbreak
confirmed
Best fit model
Prediction in absence
of response
Prediction of impact if first
early campaign
missed
Campaigns prevented 345 (67%)
cases
Strong herd effect inaccessible
areas – 60 (58%) cases
prevented
Early response important
Marga Pons Salort
Preventing VDPV emergence after OPV withdrawal
-
There is a trade-off between OPV use and risk of
VDPV outbreak
The risk is greatest at low to intermediate levels
of SIA coverage or when the number of SIA is
small
Model without routine immunisation
Sabin-R0=0.5, VDPV-R0=5, OPV-take=55%
In a setting with low RI,
how many OPV campaigns are
needed to reduce the risk of
VDPV outbreak?
1 or 2 SIA could increase the risk
compared to doing nothing
Marga Pons Salort
Risk factors for VDPV2 emergence in Nigeria (2004-2014)
29 emergence events
Case-control analysis of risk of VDPV2 emergence
comparing districts where first VDPV2 detected within a
genetic cluster (cases) with districts with no emergence
(controls) for data in 6 month periods
Matching on time-period (6 months) & zone (NE, NW, NC, SE, SW, SC)
Univariate analyses
Multivariate analyses
Variable
OR
(95% CI)
P
OR
(95% CI)
Type 2 population immunity
0.34
(0.02,6.86)
0.478
Routine immunisation (DTP)
0.05
(0.00,1.74)
0.096 0.02 (0.00,1.02)
No. tOPV SIA in the last 6 months
5.59
(0.85,36.73) 0.073 6.34 (0.87,46.01)
No. tOPV SIA in the last year
5.57
(0.90,34.50) 0.065
No. days since last tOPV SIA
1.00
(0.99,1.01)
0.982
No. births (log)
2.64
(1.11,6.28)
0.027 3.60 (1.39,9.31)
Population density (log)
1.29
(0.98,1.70)
0.071
Mean number of household members 1.41
(0.39,5.13)
0.601
P
0.051
0.068
0.008
Strategy for tOPV SIA
preceding serotype 2 OPV
withdrawal:
sufficient number to
achieve high serotype 2
population immunity and
high coverage
Global risk assessment of outbreak risk
•
Outbreak RA important for immunization
planning
• Analysis of risk in collaboration with
WHO HQ began in 2009
• Regional RA also being made
• RATT initiated in 2012
•
•
•
CDC, WHO, Unicef, IDM and (recently)
Imperial
Feeds into SIA options and immunisation
Zambia, Rwanda, and Cameroon. As of 12 July 2011, five
planning
countries had reported outbreaks: Côte d’Ivoire, Guinea, Gabon,
Mali, and Niger [27].
Joint WHO/Imperial model
Figure 2. Distribution of the risk of poliomyelitis outbreaks in Africa. (A) The number of poliomyelitis outbreaks reported for each co
Africa between 1 July 2004 and 31 December 2010. (B) The expected number of poliomyelitis outbreaks for each country in Africa based on t
the Poisson mixed effects model. (C) The temporal fit of the Poisson mixed effects model, where error bars show the 95% CIs, and the r
number of outbreaks for each 6-mo period.
doi:10.1371/journal.pmed.1001109.g002
rate greater than two cases per 100,000 children under 15
was associated with smaller outbreaks (Table 3).
Discussion
Factors Associated with the Duration and Size of an
Outbreak
In this paper we demonstrate a clear link between vacc
coverage and population movement from endemic regions
risk of outbreaks of poliomyelitis in Africa. Significant te
and geographic variation in the number of reported outb
explained by changes in population immunity and expo
wild poliovirus imported by travellers from affected co
Notably, a model incorporating population movement
tional to the number of permanent migrants was found to
data better than models based on physical distance, tour
flight data. The identified risk factors are sufficient to desc
scale and geographic distribution polio outbreaks in Africa
Of the 137 outbreaks recorded prior to 1 July 2010, 133 (97%)
were fully observed and the remainder were right censored (i.e.,
were regarded as ongoing outbreaks). The hazard ratio of a Cox
proportional-hazards model represents the effect of a unit change
in the explanatory variable on the frequency of the outcome,
which in this case is the last case of an outbreak. Higher
vaccination coverage in the 6 mo prior to an outbreak and sharing
a border with Nigeria were both associated with shorter and
smaller outbreaks (Tables 3 and 4). In addition, an annual AFP
PLoS Medicine | www.plosmedicine.org
5
October 2011 | Volume 8 | Issue 10 | e
A rapid assessment of risk, based on data
•
•
•
Rather than include everything in RA,
test everything
Output must be easily interpretable
Flexible enough to include expert
assessment
Risk assessment made from data on;
• Population immunity
• Previous importations in <4 years
• Migrants from polio affected countries
• % in-country population displaced
Comparing 6 month ahead predictions
Model
Predictive
ability (%)
Full WHO score model
77.8
Reduced WHO score model
80.0
Regression model
81.5
Regression model
(+refugees+mig)
83.3
60
40
% observations with outbreaks
20
Risk Score
Key
low (2−3)
medium (4)
medium high (5)
high (6+)
outbreak on−going
Endemic / not included
Note: VDPVs in South Sudan and Madagascar not included in the colour-scheme
8
7
6
5
4
3
2
0
WHO score (2015)
80
100
WHO score assessment
Other examples
OPV & IPV vaccination efficacy (not complete list)
Jafari H, Deshpande JM, Sutter RW, Bahl S, Verma H, Ahmad M, Kunwar A, Vishwakarma R, Agarwal A, Jain
S, Estivariz C, Sethi R, Molodecky NA, Grassly NC, Pallansch MA, Chatterjee A, Aylward RB. Polio
eradication. Efficacy of inactivated poliovirus vaccine in India. Science. 2014 Aug 22;345(6199):922-5.
O'Reilly KM, Durry E, ul Islam O, Quddus A, Abid N, Mir TP, Tangermann RH, Aylward RB, Grassly NC. The
effect of mass immunisation campaigns and new oral poliovirus vaccines on the incidence of poliomyelitis
in Pakistan and Afghanistan, 2001-11: a retrospective analysis. Lancet. 2012 Aug 4;380(9840):491-8.
Silent transmission
Mangal TD, Aylward RB, Grassly NC. The potential impact of routine immunization with inactivated poliovirus
vaccine on wild-type or vaccine-derived poliovirus outbreaks in a posteradication setting. Am J Epidemiol.
2013 Nov 15;178(10):1579-87.
Waning immunity
Grassly NC, Jafari H, Bahl S, Sethi R, Deshpande JM, Wolff C, Sutter RW, Aylward RB. Waning intestinal
immunity after vaccination with oral poliovirus vaccines in India. J Infect Dis. 2012 May 15;205(10):155461.
Acknowledgements
Imperial College Nick Grassly, Marga Pons Salort, Tara Mangal, George
Sherriff, Lucy Li, Natalia Molodecky, Ed Parker
GPEI staff involved in recent polio outbreak investigations
WHO Ajay Goel, (Chris Wolff), Bruce Aylward, Ravi Shankar, Paul
Chenoweth
CDC Rebecca Martin, Nino Khetsuriani, Steve Wassilak, Abdirahman
Mahamud, Cara Burns, Steve Oberste
BMGF Ananda Bandyopadhyay, Chris Wolff
Funding