Determinants of Silent Polio Circulation during the
Eradication Endgame
Joon Ha Park, Christopher J. Henry, Edward L. Ionides, Marisa C.
Eisenberg, David W. Hutton, Joseph N. Eisenberg, James S.
Koopman
University of Michigan
Jul 1, 2015
Introduction
I
During the endgame of polio eradication, it becomes more
important to consider chains of WPV transmissions of tiny
scale, which might go undetected by the polio survelliance
system.
I
Careful assessment of the conditions for and the possibility of
silent circulation of WPV needs to be performed before any
large-scale policy changes.
I
But, making policy inferences is challenging because of
ignorance about poliovirus immunology.
I
Assessing robustness of inferences and estimating key
parameters are paramount to theoretical advancements.
Our work
I
As a first step to pursuing Inference Robustness Assessment
(IRA), we sought to understand the dynamic properties of
vaccination effects from a very simplified model.
I
We investigated the interaction among the basic reproduction
number (R0 ), immunity waning parameters, time to ramp up
vaccination level, and the final vaccination rate (and a few
other parameters) with regard to the chance of prolonged
silent circulation.
I
Our results showed that under the presence of moderate long
term waning, high transmission conditions, and long time to
ramp up vaccination efforts, there may be a significant
possibility of prolonged silent WPV circulation.
I
This may be the case in India and the remaining endemic
countries.
Our simplifying assumptions
I
A large uniform population with homogeneous mixing.
I
Birth rates equal to death rates, which are constant across
age.
I
Immunity wanes in a single step to a single level of immunity.
I
WPV and OPV infections induce the same level of immunity
that wanes identically.
I
Susceptibility to reinfection and duration and contagiousness
of reinfection wane at the same rate.
I
No maternal immunity.
Waning of immunity
see that even in the presence of reinfections that cut the waning time short, this sm
waning can boost transmissions from reinfections significantly.
Fraction of Immunity Lost
0.3
0.25
Average Age of First
Infection = 2.25
Average Age of First
Infection = 2.5
0.2
0.15
0.1
0.05
0
0 5 10 15 20 25 30 35 40 45 50 0 5 10 15 20 25 30 35 40 4
Years Since Last Infection
Years Since Last Infection
Figure 2: The four rising lines are from the one step waning model analyzed in thi
waning depths from top to bottom are 50%, 37.5%, 25%, and 12.5%. The two line
out are from the Kid Risk waning model and represent immunity lost after first infe
and after subsequent infections (green). All lines represent the fraction of immunit
cohort of individuals who recover from infection at time zero divided by the transm
potential of a fully susceptible population. All four one stage model settings and th
first and reinfection waning patterns for the Kid Risk waning model give the indicat
Outcomes of vaccination programs (numerical solutions)
No elimination of
poliomyelitis
Unstable
eradication
Silent circulation ends
with new polio case
Stable eradication
Figure 4. Five different WPV prevalence time series patterns generated using the one step
waning model. The plots show the effects of progressively increasing the final level of
vaccination and the progression through the following four endpoints: (a) no case elimination,
Length of silent circulation
as vaccination rate varies
ure 5. The course of silent circulation. The range of vaccination levels that will generate
onged silent circulation is indicated by the levels where the three year level crosses the
Length of silent circulation
as vaccination rate and time to ramp-up vary
Length of sile
5
nt circulation
0
−5
(yr)
20
0.5
Va 1.0
cci
nat 1.5
ion
rat
e
10
5
2.0
(/yr
)
0
yr)
e(
15
0.5
mp
Ra
2.5
1
2
3
5
u
im
pt
Vaccination outcome & length of silent circulation plot
●
Vaccination ramp up time (years)
20
15
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Classification
no case elimination
●
10
5
0
0.0
0.5
●
1.0
1.5
case comeback
unstable eradication
stable eradication
Silent duration (years)
● 3
2.0
Vaccination rate (yr−1)
2.5
reinfections ReRe rises
ReFirst falls so rapidly. The effective reproduction number from
Silent duration (years)
Classification
immunity ramp-up
is no longer interrupted
Vaccination
effectsby reinfections that send individuals in the P compa
● 3
no case elimination
comeback
back to the R compartment. But that rise iscase
too
slow to influence the momentum tow
unstable eradication
eradication.
stable eradication
●
1.2
Low integrated negative force on prevalence
1
1.2
Last polio case
1
Last polio case
0.8
resurgent polio case
0.6
0.8
0.6
0.4
0.4
0.2
EffRep#Re ● EfRep#Frst
0.2
EffRep#Tot
0
4
19
24
29
9
14
Years since vaccination began
Vaccination Ramp Up Time
1
10
20
-1
34
EffRep#Re
0
-1
4
EfRep#Frst
EffRep#Tot
9
14
19
24
Years since vaccination began
29
34
R0=15
1.2
Last polio case
1
0.8
0.6
0.4
0.2
EffRep#Re
EfRep#Frst
EffRep#Tot
0
-1
Final Vaccination rate
4
9
14
19
24
Years since vaccination began
29
34
Other effects
Chance of prolonged silent circulation increases with
I
Higher R0
I
Higher total amount of waning (in pre-vaccination equilibrium)
I
Higher waning depth
I
Lower transmissibility of OPV with respect to WPV
Summary & policy implications
I
With our simple model, we illustrated the possibility of
prolonged silent circulation caused by reinfections due to
long-term waning.
I
High transmission conditions, moderate long-term waning,
and long ramp-up time to final vaccination level interact to
lengthen silent circulation after the last poliomyelitis case.
I
Available data should be examined to help assess whether
waning of immunity is generating enough transmission from
reinfections to generate the phenomena we have illustrated.
I
If our inference about prolonged silent circulation is robust,
further issues that deserve pursuit will be :
a) evaluating strategies to detect low level silent circulation,
b) infering whether vaccinating adults have benefits that
outweight its costs.
Selected references
1. Grassly, N.C., The final stages of the global eradication of
poliomyelitis. Philos Trans R Soc Lond B Biol Sci, 2013.
368(1623): p. 20120140.
2. Manor, Y., et al., Intensified environmental surveillance
supporting the response to wild poliovirus type 1 silent
circulation in Israel, 2013. Euro Surveill, 2014. 19(7): p.
20708.
3. Shulman, L.M., et al., Molecular epidemiology of silent
introduction and sustained transmission of wild poliovirus type
1, Israel, 2013. Euro Surveill, 2014. 19(7): p. 20709.
4. Shulman, L.M., et al., Genetic Analysis and Characterization
of Wild Poliovirus Type 1 During Sustained Transmission in a
Population With ¿95% Vaccine Coverage, Israel 2013. Clin
Infect Dis, 2014.
Thank you.
Questions?
Model diagram
what level of WPV incidence or prevalence of first and/or reinfections led deterministically to
eradication of circulation, and 3) when a new polio case occurred when transmission rebounded
after a period without polio cases. The differences in the results which we present are minimal
so we used the following criteria: 1) fewer numbers of first infections than the infection to
paralysis ratio in the past year, 2) a prevalence of 1 infection, and 3) a cumulative number of
first infections since the last polio case that is greater than the infection to paralysis ratio.
Model parameters
Parameters
n
Ntot
m
c
pt
τramp
Vfinal
γW,First
κ
η
ν
ipr
ε
V(t)
γW,Re
γO,First
γO,Re
Description
Values used
Number of childhood age groups
40
Total population size
106
Per capital mortality rate and birth rate
0.02/yr
Contact rate
150-500/yr
Transmission probability per contact
0.5
Time to ramp up vaccination level
1 to 20 yr
Final vaccination rate per year
0.2 to 2.5/yr
Rate of recovery from a first wild type infection
13/yr
Relative susceptibility, duration, and contagiousness of
0.2 to .82
reinfections with respect to first infections
Relative duration, and contagiousness of OPV infections with 0.25 & 0.375
respect to WPV infections
Immunity waning rate (value calculated to give a specific average
Age of infection in the absence of vaccination at a given κ)
0.01 to 0.5
Infection to paralysis ratio
100 & 200
Prevalence below which eradication occurs
1
Derived Parameters
Vaccine rate t years after eradication efforts are
Ramp function from 0 to
begun
Vfinal over t = 0 to τramp
Rate of recovery from a reinfection by a wild type virus
γW,First /κdur
Rate of recovery from a first infection by OPV
γW,First /ηdur
Rate of recovery from a reinfection by OPV
γO,First /κdur
Table 1: model parameters
5
Model-specific definitions
I
Last poliomyelitis is observed when the cumulative number of
first infections by wild poliovirus goes below the
infection-to-paralysis ratio.
I
After the last poliomyelitis, elimination of polio cases is
declared.
I
Poliovirus eradication happens when wild poliovirus prevalence
goes below 1.
I
Resurgent poliomyelitis is observed when the cumulative
number of first infections by wild poliovirus exceeds the
infection-to-paralysis ratio since the last poliomyelitis before
case elimination.
Effects leading to prolonged silent circulation
Eventually the vaccination levels and ramp up time get
ratcheted up to where very prolonged silent circulation
takes big leaps to escape (or to where vaccinating adults is
the best option to eliminate silent circulation)
Seasonality hooks the ratchet
Vaccination Ramp Up Time
1
20
R0=15
(2) At their new jacked up
vaccination level, they go longer
without a polio case. But then a
recurrent case occurs.
(1) High transmission country takes
6 years to finally eliminate all
poliomyelitis cases for one year.
But then they have a rebound and
have to jack up vaccination to a
higher level.
Figure 8. Points (1) and (2) illustrate one iteration of a ratcheting up process that eventually
puts high transmission settings into the zone of prolonged silent circulation.
Width of vaccination levels leading to prolonged silent circulation and practical stability
A second important point from Figures 6 & 7 is that longer vaccination ramp up time also widens
In other words, this is the long term system stability concept rather than the practical sta
concept we just discussed. Vaccination ramp-up time affects the transient dynamics wh
subsequently change with further waning
0 of immunity, but not the equilibrium state wher
population level of immunity has waned as much as it can in the face of the birth and de
dynamics of the population system.
Basic reproduction number (R ) effects
Basic reproduction number effects
R0 = 10
R0 = 15
Vaccination Ramp Up Time
1
20
R0 = 5
Final vaccination level at the end of the ramp up
Figure 9: Duration and final outcome of silent circulation across parameter sweeps of fin
vaccination levels and vaccination ramp-up times at three levels of R0. All three panels
identical parameters except for the contact rate which increases from 130 to 260 to 390
establish the three R0 levels. Average age of infection without vaccination = 2.5, relative
transmissibility of OPV/WPV = 0.25, infection to paralysis ratio = 200.
Ramp-up time effects (2)
120000
120000
100000
100000
Last polio case
80000
resurgent polio case
60000
Last polio case
80000
60000
40000
40000
20000
20000
0
0
-1
3
Vaccination Ramp Up Time
1
10
20
<5 waned
7 11 15 19 23 27 31
Years Since Vaccination Began
>5waned
<5Susc
-1
35
<5 waned
>5Susc
R0=15
3
120000
7 11 15 19 23 27 31
Years Since Vaccination Began
>5waned
<5Susc
35
>5Susc
Last polio case
100000
80000
60000
40000
20000
0
-1
3
<5 waned
7 11 15 19 23 27 31
Years Since Vaccination Began
>5waned
<5Susc
35
>5Susc
Final Vaccination rate
Figure 11: The population size changes of fully and partially susceptible population le
five years of age or older that underlie the changes in effective reproduction numbers
Waning rate and depth effects at a given total waning level
Vaccination Ramp Up Time
1
20
has more risk than faster shallower waning. The differences pretty much parallel those
for the effects of R0. The change in the slope of the space that achieves poliomyelitis c
elimination is less steep and more conducive to ratcheting at deeper faster waning regi
Total transmission potential of waned state compared to fully susceptible
12.5%
25%
37.5%
50%
Waning rate adjusted to give an average age of first infection = 2.5
0.0334 / year
0.0196 / year
0.0145 / year
0.0117 / year
Final vaccination level at the end of the ramp up
Figure 12: The effect on silent circulation durations of lowering the waning depth from
level in Figures 10 and 11 but raising the waning rate so as to keep the total waning co
defined by an average age of first infection equal to 2.5 years.
1.2
1
1.2
Last polio case
1
Last polio case
resurgent polio case
Figure 12: The effect on silent circulation durations of lowering the waning depth from the 50
Waninglevelrate
and10depth
in Figures
and 11 buteffects
raising the waning rate so as to keep the total waning constant
defined by an average age of first infection equal to 2.5 years.
1.2
1.2
Last polio case
0.8
0.6
0.6
0.4
0.4
0.2
EffRep#Re
EfRep#Frst
0.2
EffRep#Tot
Vaccination Ramp Up Time
1
7 10
15 20
4
9
14
19
24
Years Since Vaccination Began
EffRep#Re
29
-1
Waning Depth = 0.125
R0=15,
OPV/WPV
trans=0.25,
Average age of
first infection =
2.5 years,
Infection to
poliomyelitis ratio
= 200
Final Vaccination rate
resurgent polio case
EfRep#Frst
EffRep#Tot
0
0
-1
Last polio case
1
0.8
4
9
14
19
24
Years Since Vaccination Began
Vaccination Ramp Up Time
1
7 10
15 20
1
29
Waning Depth = 0.5
Final Vaccination rate
Figure 13: Effective reproduction number dynamics under the influence of faster shallower
waning or slower deeper waning at a total waning level that gives an average age of first
moving people out of the partially immune state faster rather than moving them into that state
more slowly.
OPV transmission potential effects
There is considerable uncertainty in the relative transmissibility of different OPV strains []. But it
is thought that OPV3 is less transmissible than OPV1 which is less than OPV2. Thus this
characteristic would suggest increased risk for silent circulation of OPV3.
Vaccination Ramp Up Time
1
20 1
25%
37.5%
OPV / WPV transmissibility
20
Total transmission potential of waned state compared to fully susceptible
12.5%
25%
37.5%
50%
Final vaccination level at the end of the ramp up
Figure 14: The effect of OPV transmissibility on the duration of silent circulation. The parameter
settings are the same as Figure 12 except for the change in OPV transmissibility.
OPV transmission potential effects
1.2
Last polio case
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
EffRep#Re
EfRep#Frst
0.2
EffRep#Tot
Vaccination Ramp Up Time
1
7 10
15 20
4
9
14
19
24
Years Since Vaccination Began
29
OPV/WPV trans=0.375
R0=15, Waning
Depth=50%,
Average age of
first infection =
2.5 years,
Infection to
poliomyelitis
ratio = 200
Final Vaccination rate
EffRep#Re
resurgent polio case
EfRep#Frst
EffRep#Tot
0
0
-1
Last polio case
-1
4
Vaccination Ramp Up Time
1
7 10
15 20
1.2
9
14
19
24
Years Since Vaccination Began
29
OPV/WPV trans=0.25
Final Vaccination rate
Figure 15: The effect of OPV transmissibility on effective reproduction number dynami
gives an average age of first infection of 2.5 years. At a higher level of total waning that has a
lower average age of first infection, we increase the waning rates for any chosen waning depth.
We can see from Figure 2 how much the increased waning rates increase the level of waning
achieved after 50 years of continuous waning. Those levels are consistent with or less than the
expert elicited long term waning effects from the insightful reviews of literature and expert
opinion that the Kid Risk group has published [11, 12].
Total amount of waning effects
1
R0 = 10
AvgAge = 2.25
Vaccination Ramp Up Time
20 1
R0 = 15
AvgAge = 2.5
20
Total transmission potential of waned state compared to fully susceptible
12.5%
25%
37.5%
50%
Final vaccination level at the end of the ramp up
Figure 17: Comparison of vaccination ramp up time and final vaccination level parameter
sweeps at different levels of waning depth and waning rates, R0 values, and total waning levels.
The waning rates for the waning depths were both set for their corresponding average ages of
infection at R0 = 15. Infection to paralysis ratio = 200, Relative OPV/WPV transmissibility = 25%
22
transmissions back to their most recent common ancestor for every pair of indivi
sample, that distribution will change in a manner that can be predicted mathema
can be used to help estimate the degree of waning. We think this could be one
powerful and least biased estimates of whether the real world falls into the wanin
ranges in our model where there is a real risk of prolonged silent circulation.
1.4
1.2
1
wd.5
wd.125
wd.375
KidRsk
wd.25
0.8
0.6
0.4
0.2
0
-1
0.1
1.2
2.3
3.4
4.5
5.6
6.7
7.8
8.9
10
11.1
12.2
13.3
14.4
Reinfection/First Transmissions
Reinfection transmission ratio
Years Since Vaccination Began
Figure 18: Ratios of transmissions from reinfections over first infections at differe
waning for the one step model and at Kid Risk waning parameters. Model param
R0 of 15, relative OPV transmissibility of 0.25, infection to paralysis ratio of 200,
first infection = 2.5 and a ramp time of 15 years. Vaccination levels were set suc
polio case appeared right at the end of the ramp up time of 15 years and were w