Modeling Global Policy for Managing Polioviruses:
An Analytical Journey
Kimberly M. Thompson, Radboud J. Duintjer Tebbens
Harvard School of Public Health
677 Huntington Ave., 3" Floor
Boston, MA 02115
(617)432-4285, fax: (617)432-3699
kimt@hsph.harvard.edu, rduintje@hsph.harvard.edu
The success of the Polio Eradication Initiative promises to bring the world the benefits of
sustained Improvements in quality of life (1.e., cases of paralysis and deaths avoided) and saved
costs from cessation of vaccination. Obtaining these benefits requires that policy makers manage
both the transition fiom the current massive use of oral polio vaccine (OPV) to a world without
OPV and the risks of potential future reintroductions of polioviruses. In 2001, we began a case
study on retrospective polio risk management to demonstrate the importance of using a dynamic
disease model to correctly estimate the cost-effectiveness of vaccines. Discussions with the
CDC about the case study led to an opportunity for us to develop a large model to support the
prospective decision making process. This paper tells the story of our journey, emphasizing
Insights about the requirements for analysts to create tools that really help high-level decision
makers.
Key words: polio eradication, decision analysis, risk analysis, dynamic disease model, outbreak,
process, variability, uncertainty
Introduction.
“All decisions are based on models... and all models are wrong” John Sterman (Sterman, 2002)
“All models are wrong but some are useful” George Box (Box, 1979)
In theory, modeling decisions provides the opportunity to analyze options systematically, which
allows explicit consideration of the possible alternatives given the decision makers’ preferences
and constraints. For complex problems, models can help provide a shared vision of the system,
show the different components and how they interact, and synthesize the existing information.
Models can also offer insights about important sources of variability (i-e., real differences
between individuals that matter in the context of the decision) and uncertainty (i.e., imperfect
information) and their implications. Thus, models can theoretically help decision makers choose
more wisely, but how much do models really help in practice?
Behind the story of any model lies a story about the analysts and process that created it, yet these
stories rarely find their way into the literature. Unfortunately, this means that valuable lessons
learned do not help other analysts who would benefit from strategies that might help reduce the
amount of “muddling through.” This paper introduces the complexity of the decisions brought
by eradication of polio and tells the story of the first four years of our experience developing a
decision analytic modeling tool to support global policies for managing the risks of polio after
eradication. By writing such a paper while the modeling process continues to evolve and
expand, we recognize that we run the risk of providing a perspective prior to knowing the final
outcome. We believe that the benefits at this point outweigh the risks, and we hope the reader
will agree. We organize the remainder of this paper by providing the context about polio risk
management a then offer the story of the project structured according to the 5 requirements that
we believe drove its early success.
Context
On April 12, 2005, we celebrated the 50-year anniversary of the publication of the largest and
first clinical trial for a vaccine. In 1955, researchers demonstrated the effectiveness of the Salk
polio vaccine (Francis et al., 1955) and the news media that day exclaimed exciting themes: “The
vaccine works.” “It is safe, effective and potent.” “Polio is conquered.” The promise of a
vaccine that would end the terror caused by polio brought hope and led to long lines of people
wishing to get the vaccine.
Thompson and Duintjer Tebbens (2005) provide a retrospective analysis of the polio vaccination
history for the U.S. and document the incredible story of success, starting from a peak of over
21,000 cases of paralytic polio in 1952 to 0 cases in the U.S. since 1999. During that time, the
U.S. began vaccination in 1955 with the Salk Inactivated Polio Vaccine (IPV), switched in the
early 1960s to the Sabin Oral Polio Vaccine (OPV) due to its relatively lower cost and easier
administration, and finally returned to an enhanced IPV (eIPV) in the late 1990s at a relatively
very high cost to avoid the burden of Vaccine-Associated Paralytic Polio (VAPP) (Miller et al.,
1996). By the late 1990s, use of OPV led to the only cases of paralytic polio (less than 10 cases
per year with an annual birth cohort of approximately 4 million children). The existence of the
eIPV option combined with concern about the perception of risks of vaccination exceeding the
benefits weighed in favor of the shift to eIPV for routine vaccination, and other developed
countries similarly moved toward IPV use. However, the Polio Eradication Initiative (PEI) and
most of the countries in the world continue to rely on OPV, because it provides population or
herd immunity and it remains much cheaper and easier to administer.
In 1988, with an estimated 350,000 global cases of paralytic polio annually, the World Health
Assembly committed to global eradication of polio. In 2003, wild polio viruses only continued
to circulate in 6 countries (Nigeria, India, Pakistan, Niger, Afghanistan, and Egypt), but recent
challenges (political and logistical) led to outbreaks, exportations, and reintroduction of polio in
a number of previously eradicated African countries with outbreaks in 2004-2005. These recent
reintroductions and outbreaks demonstrated the rapid ability of polioviruses to spread in
susceptible populations, and provide important insights about the need to maintain vigilance in
vaccination at least until the successful global eradication of wild polio viruses.
With the success of eradication approaching, many questions emerge and world leaders face a
large range of complicated decisions. For example, while the World Health Assembly leaders
who committed to eradication in 1988 expected that this would mean complete cessation of polio
vaccination (as occurred following the eradication of smallpox), current perceptions by some
countries about the risks of potential bioterrorism and the current use of IPV for routine
vaccination lead to the logical question of whether developed countries will stop using IPV. For
countries now using OPV, the complicated set of options includes switching to IPV (at high cost
and presumably at the expense of investing in other public health measures), continuing to use
OPV, or stopping vaccination. Continuing to use OPV emerges as problematic for 2 reasons: (1)
OPV use leads to a small, but finite and reasonably predictable number of cases of VAPP, and
(2) recent circulating Vaccine-Derived Polio Viruses (ce VDPV) events occurred in countries that
reduced their coverage with OPV resulting in outbreaks (caused by the OPV viruses reverting to
a neurovirulent form and circulating among susceptible individuals). The possibility of cVDPVs
means that low levels of OPV coverage present a significant risk, and that continued use of OPV
should involve efforts to maintain very high coverage, most likely in the form of the
supplemental immunization activities now used in the polio eradication initiative (i.e., National
Immunization Days). The risks for outbreaks after eradication range from the potential for
cVDPVs, potential breaches in containment, intentional reintroduction, and the little known
possibility that one of the very small number of immunocompromised individuals who can
excrete polioviruses that they never cleared after they received OPV (immunocompromised
VDPVs or iVDPVs) might also at some point represent a potential source. The small risks
represent important concerns when we consider the impacts of reintroduction of polioviruses as
the population susceptibility increases.
As national and world health leaders consider the options, they recognize that the opportunity to
stop OPV vaccination necessitates development of a strategy (i.e., response plan) and the tools
(i.e., vaccine stockpile and/or on-going production) for responding to a future outbreak. They
also remain interested in understanding the risks, costs, and benefits of their various options.
With the success of national eradication of polio and the consequent reduction in the burden of
disease, decision makers tend to want to reprioritize resources away from polio risk management
and toward other issues. However, they must recognize that this might not represent the optimal
strategy in the longer term.
Modeling can provide an opportunity to explore the trade-offs, and we currently provide
analytical support to help answer key questions working collaboratively with a large team at the
CDC and WHO. Over the course of this work, we identified several requirements that allowed
us to play a role in the development of national and international policy, and that we believe
transcend the application to polio.
Requirement 1: Vision, hard work, and timing
Our work on this project reflects some good luck, but more importantly it reflects vision and
preparedness. In 1998, the lead author began working with a doctoral student to review the
published, peer-reviewed pediatric cost-effectiveness and cost-benefit analyses in an effort to
assess the state of the literature. That review yielded several key insights, including the
preponderance of analyses for vaccine interventions, little recognition of variability and
uncertainty, little consideration of changes over time, and a lack of dynamic disease modeling in
the context of assessing the benefits of vaccines. The lead author also appreciated the
opportunity that existed to bring together multiple analytical tools into integrated policy
analyses. For example, in the case of cost-effectiveness modeling for vaccine interventions, the
use of system dynamics tools for modeling outbreaks and the importance of factoring in the
benefits of herd or population immunity seemed like an obvious and important combination to
demonstrate quantitatively. In 2000, the second author contacted the lead author looking for a
master’s thesis project and expressed interest in working on this topic. Performing a
retrospective cost-effectiveness analysis emerged as the best strategy for demonstrating the
importance of considering time and using a dynamic disease model, and we selected polio as a
case study because it offered a long history (but not too long) and we did not find any evidence
of other analysts already working on it. We also recognized that the approaching eradication of
polio meant that this would be a good time to reflect on the aggregate benefits of historical
interventions, and while other analysts apparently viewed polio as no longer interesting, we
suspected that it would continue to be of interest for the foreseeable future.
Throughout most of 2001, we reviewed the literature on polio and built a model that allowed us
to perform a first-cut retrospective cost-effectiveness analysis for polio interventions, which we
presented at the December Society for Risk Analysis (SRA) meeting. Figure 1 shows our first
draft model results demonstrating the importance of using a dynamic model to capture the
population immunity benefits of OPV. The lines in the figure demonstrate the expected number
of annual paralytic cases over time in the absence of vaccination, with vaccination using a static
model (one in which only the recipient derives benefits from the vaccine), and with vaccination
using a dynamic model. In the process of reviewing the literature and building our model, we
contacted a number of polio researchers, including leaders at the U.S. Centers for Disease
Control and Prevention (CDC). In addition, the lead author collaborated with another vaccine
economics researcher at Harvard to develop the Harvard-CDC Joint Initiative on Vaccine
Economics (JIVE) project, which created a mechanism for us to develop research collaborations
with the CDC. We traveled from the SRA meeting to the CDC and presented our insights to
leaders of the CDC’s Global Immunization Division and Polio Eradication Branch. We hoped
that our presentation would yield better data and information about some of the big uncertainties
that we brought to the discussion, and we found at the end that the people we met with
immediately appreciated the opportunity that our model offered with respect to modeling
decisions prospectively. The vision that integrated policy modeling is essential to provide the
best possible information about the risks, costs, and benefits of decisions and our efforts to both
dig in to the problem and learn the history made it possible for us to be in the right place at the
right time. Our collaboration with CDC’s polio team really began at that meeting.
Requirement 2: Everyone on the team must recognize that the process matters and manage
expectations
As we started to discuss how we might support the CDC’s efforts, we quickly learned about the
size of the community involved in polio eradication and the complexity of the decisions. We
also recognized that the CDC group included a wide range of scientists, both laboratory experts
and epidemiologists, but that it did not include many economists, modelers, or decision analysts.
At the time, the only economist in the group included a newly hired person working on a paper
that focused on estimating the costs of the five options that the CDC and WHO identified as the
major decisions. We started by developing a proposal for our effort that focused on modeling
these five options and using our dynamic model to estimate the impacts of future outbreaks that
might occur in the context of this set of policies. This generated a lot of questions from everyone
involved. As we learned more, we began to suggest that the model would need to deal with
many complexities not by ignoring them but by characterizing them. We expanded the model to
explicitly consider the risks that could lead to outbreaks and we started to talk about how
different countries might bring very different perspectives to the discussion. We also began to
delve into the uncertainties and to sift through a huge amount of information.
In October 2002, with the project in its infancy, we traveled to WHO to participate in an
informal consultation on economics research on post-certification immunization polices. Figure
2 shows a picture of our model that we presented at that meeting. We felt pleased that we could
fit a simple schematic of the model on a single page, but this proved too complex for some of the
people attending the meeting. That meeting led to three important insights: (1) WHO took the
lead on policy with input from the CDC and other leaders, so influencing the actual policy meant
we ultimately needed to work with and help WHO, (2) the WHO policy makers appeared very
pessimistic about the actual utility of economic models in the context of influencing policy, and
(3) the economists attending the meeting (all with experience working on prior economic
analyses with WHO) expressed frustration about the policy makers asking the wrong questions
or changing the questions at the end of their analyses. We expected to attend that meeting to
give the group an introduction to our efforts. Instead, we realized as we listened to the
discussion that we needed to make the case for why the type of analysis we were doing would be
helpful. One of the most important last-minute additions to our presentation came from
extracting the following quote made by one of the key WHO decision makers who noted that:
“Though the [World Health Assembly] was the appropriate forum for discussing and debating
the merits of an eradication initiative against polio, it has been argued that the delegates may not
have had sufficient information to make a truly informed decision.” The fact that World Health
Assembly committed to the eradication of polio without data on the estimated human or financial
resources and with no clear statement on the strategies that would need to be pursued or
timeframe surprised us, and this helped us make the case that it was not too late to give decision
makers good information.
Listening to the other analysts there, we also recognized that we would need to deal with the
complexities, even if the decision makers did not care about them at the time and would
willingly scope them out. More than one of the analysts talked about being told not to consider
an issue for an analysis and then later finding the results rejected because the analysis did not
consider that issue. We listened carefully to what prior analysts said about their experiences and
we observed the interactions between our CDC collaborators and the WHO. Based on this, we
decided that we needed to make the model as simple as we could and expect to model in the
context of discussions in which some of the participants might prefer to play down the
complexities. However, we also still needed to model the complexities rigorously and expect
that the information might change. This made it essential for us to be flexible and clear about
what others could expect from us and what we needed from them. At this point, we focused on
process and emphasized in our discussions and writing that decision makers that rely on
analytical tools consistently identify the process of developing the model as valuable,
particularly in clarifying the key issues and sorting through the options with the best available
information. We worked to make it clear that instead of focusing on providing a model with
“the” answer, we offered a rigorous process and tools for the entire team that would provide
defensible and helpful insights to help them evaluate the options and make more informed
choices.
Requirement 3: Effective communication (essential!) and beer (helpful)
The enthusiasm about the model within the group of collaborators at CDC helped tremendously
in our efforts to collect and synthesize information. We found one of the most unique aspects of
the CDC polio team came from the impressive collaboration between the lab and field scientists.
Even though the lab lies within one division of the CDC and the field team in another, nearly 10
years ago the leaders of these two groups started a tradition of everyone meeting at Moe’s (a
local dive) on Friday after work to talk over beer and encourage collaborative solutions. We
truly became part of the team when one of the meetings we attended in Atlanta ended with a trip
to Moe’s. From our perspective, the receptivity of our work and recognition of its potential
impact by members of the CDC polio team stemmed initially from a commitment by a high-level
decision maker at the CDC to give us a chance to work on this project following our first
meeting there. However, we believe that the relationships that we developed with our
collaborators as partners in the modeling process became the most important driver for the
expansion and continuation of the project. While analysts cannot always choose to enter a
project with a highly functional team, we appreciated that our efforts on this project did not
include fixing a dysfunctional team as a first step, and that this represented an important
advantage. We also took the approach of working with everyone that we could at all levels, from
the folks at the top to the new people, and we viewed all interactions as opportunities to learn, as
well as to answer any questions that others might raise about modeling.
With respect to working with WHO, we encountered a few bumps in the communication process.
After our first presentation and initial enthusiasm expressed by WHO at the informal
consultation, some of our CDC collaborators attended a follow up meeting where they presented
the model. After that meeting, they returned not with information about some of the key
questions we raised, but with a message of skepticism on the part of the WHO that investment in
our complex model and the process would yield helpful information. Fortunately, our CDC
collaborators remained firm in their commitment to the process and we focused on building the
model working with them. One of our first tasks centered on enumerating the complete list of
the actual decisions and their interactions, which we achieved using the decision tree shown in
Figure 3, and doing so in a way that recognized the different starting points for individual nations
(Sangrujee et al., 2003). We decided that we would need to stratify the world to capture the
highest-level of variability in the decision makers and risks, because we clearly saw the
differences in starting points and that countries might rationally prefer different strategies
depending on their risks and available resources. In particular, we knew that highly developed
countries like the U.S. would probably continue routine inactivated polio vaccine (IPV) use into
the foreseeable future, even with the global eradication of wild polioviruses. At the same time,
competing demands for resources would probably lead developing countries looking at the
opportunity to stop oral polio vaccine (OPV) to prefer to stop polio vaccinations completely as
soon as possible after global eradication. We presented our framework of the decision options
when we gave an update of our model at another consultation meeting at the WHO in September
2003. The presentation proved very useful to the WHO given discussions at the time about the
post-eradication risks and its qualitative framework for characterizing them, and at that point the
WHO took a strong interest in our efforts to characterize the risks. We began to see evidence of
our work in some of the discussions and in the development of the PEI strategic plan.
Requirement 4: Recognition of the responsibility of analysts to organize, demand rigor, and
sustain confidence in the vision
Finally, with the decision options identified, we turned our attention to refining our dynamic
disease model and the other components of the overall model (Duintjer Tebbens et al., 2005a,b,c)
with the simplified diagram of the components shown in Figure 4. The dynamic disease model
represents one of the most significant aspects of our efforts. Remarkably, no similar model
existed, even with all of the historical outbreaks that occurred with polio. Although we started
with a relatively simple SIR (Susceptible-Infected-Removed) model, the model quickly grew in
complexity to account for important aspects of the model. For example, we recognized that the
underlying population immunity structure reflected a mixture of individuals fully susceptible to
disease, and those partially infectible, with important differences between those who had recent
infection with the wild virus or vaccine, those with historic live virus infection, and those
protected by IPV vaccination. Figure 5 shows a simplified schematic for the first age group
(with newborns entering the model, but not showing the similar schematic for the second age
group or the arrows connecting them). We ultimately decided to model 25 separate age groups
with different initial immunity profiles to capture the differences in historical vaccination and to
maintain or ability to include different target population groups in the context of modeling a
wide range of potential outbreak response strategies. We went through several rounds of
iteration on the model as we talked with the experts at the CDC and WHO about the model
inputs. Fortunately, our colleagues also offered to work with us to apply the model to real
outbreaks so that we could learn about how the model predicted some retrospective cases. In the
context of informing future policies, we face the challenge of trying to characterize the impacts
of potential outbreaks prospectively, and given uncertainty about the actual conditions we must
make a significant number of assumptions and model the uncertainty about the many possible
futures. Figure 6 provides an example of a potential outbreak and demonstrates the expected
impacts of different strategies for responding to that outbreak. We emphasize that once specific
information about any real outbreak becomes available the model can and should use that
information to provide a more-informed estimate (e.g., the model uses as a starting point
characteristics of the different types of polioviruses “averaged” for types 1, 2, and 3, but clearly
once we know the type of virus responsible for any given outbreak the model should use inputs
specific for that type).
Early on in the process, we decided that we would develop the various components of the model
and write papers to submit for peer review and publication. We recognized that our model
would need to withstand critical reviews by technical experts in addition to answering the high-
level questions posed by policy makers. This expectation on our part raised the bar with respect
to the rigor and increased the amount of iteration and discussion, but it also led to significant
delays associated with obtaining required clearance on manuscripts with collaborating authors
from CDC and WHO. Fortunately we started the project well in front of the discussions about
post-eradication policy and unfortunately the Polio Eradication Initiative faced significant
challenges in interrupting transmission of wild polioviruses, which also delayed the timing of the
global discussions and negotiation. Our commitment to build the complex model also meant that
we took a longer path than what we expected at the beginning. However, we now find ourselves
with a useful tool at the point in time when it can make a difference.
In September 2004, we presented some of the first key insights from our model at WHO and
found the decision makers at multiple levels very engaged. Our demonstration of the potential
outbreaks and outcomes from one of the key risks in the first few years (i.e., the risks of
circulating vaccine-derived polio viruses) provided strength to the case that eradication of
polioviruses would require eradication of OPV as soon as possible after the confirmed
eradication of wild polioviruses. We also emphasized that policy makers should prepare the
world for the relatively high probability of at least one outbreak occurring after eradication, and
for the concept that we must prepare to respond to such an outbreak and not consider such an
event to signal the failure of global eradication. Our model included key placeholders for a
stockpile and response strategy, and we continue to emphasize the importance of planning and
preparation. After the September 2004 meeting, our CDC and WHO collaborators began to
work with us very intensively to review the model components, investing a significant amount of
time in the final iterations of the model. In the end, our persistence (made possible by strong
collaboration and support from the CDC) prevailed. During 2004, we also began to work with
the vaccine policy leaders of the Pan American Health Organization (PAHO) on a regional
model, which we presented at a Technical Advisory Group meeting in November 2004. At this
point, our efforts continue to expand and utility of the process and the model continue to grow.
However, we continue to also learn more about the multiple feedback loops and stakeholders
with interests in the process.
Requirement 5: Curiosity and good questions
As we look to the future, we see several tests of the model and process that will ultimately
determine its fate. We hope that as long as we continue asking good questions we will provide
valuable contributions to the team. By asking the questions that need asking, as opposed to the
ones with easy answers, our role as analysts has thus far included challenging others on the team
to think about the system more broadly, and to more fully consider the interactions of the various
components and changes over time. Some of the biggest challenges that we anticipate will come
in providing answers to key questions in ways that meet the needs of different audiences and
reflect the best available scientific evidence. While we talk about variability, national leaders
talk about the options as they see them. Our discussions about the future and highly uncertain
risks (e.g., bioterrorism) reveal very different perceptions of the risks and preferences for
managing uncertainties. Successful elimination of paralytic polio will require the elimination of
OPV, yet coordinating the process of cessation will mean obtaining global agreement with the
policy and compliance with its implementation.
Modeling the risks suggests a relatively high probability of at least one case of paralytic polio
occurring after OPV cessation and emphasizes the need for preparations to prevent re-
establishment of circulation, and we emphasize that analysts must consider the dynamic nature of
the choices and use appropriate models. This comes of no surprise to analysts who concentrate
their efforts on system dynamics, but we note that dynamic models remain underutilized in many
policy modeling contexts.
Coming full circle to the retrospective analysis, we make a strong analytical case for economic
analysts to use dynamic models in cost-effectiveness and we highlight the changes that occur in
the cost-effectiveness of vaccines over the course of their lifecycles. We believe that the polio
experience provides a wealth of lessons, most notably the need to appreciate the major changes
that occur over time.
Conclusions
Analysts can contribute significantly to real policy decisions, but only if they commit to a
process for doing so and recognize the dynamic nature of both policy and science. We hope that
providing a review of the requirements for our success (at least success to this point) yield some
useful insights for other modelers and similar processes. We recognize that a model only helps
when people use it, and in this regard we aspire to create and maintain a living model that will
support the decisions of real high-level policy makers as they continue to face the challenges of
managing the global risks of polio over time.
Acknowledgments
The authors used resources from unrestricted grants to the Harvard Kids Risk Project to support
their efforts on this paper. Much of the work described in this paper derives from the authors’
collaboration supported by CDC grant number U50/CCU300860, TS-0675. The authors
gratefully thank their manly collaborators at CDC, WHO, and around the world who continue to
contribute to the team effort required to build a successful model to support real policy.
Figure 1: First results from our retrospective model, presented at the CDC in December 2001,
showing paralytic polio incidence without vaccine (top-blue), with vaccine static (middle-green),
and with vaccine dynamic (bottom-red) transmission model
paralytic polio incidence
25000 f —
20000
15000
10000
5000
year
1960 1970 1980 1990 2000 2010
Figure 2: Initial influence diagram of the polio decision model
Bioterror
Attack
Circulating
‘Wild Polio
Outbreak
Magnitude
Vaccination
Countries’
Population
Immunities
(per country)
Outbreak
Response
Strategy
Cost (per
country)
Response
Model
VAPP
Cases (per
country)
Surveillance
Cost (per
country)
Total
Country-
level Cost
Outbreak
Cases (incl.
VAPP)
Global
Program-
matic Cost
Valuation
Response
Cost
10
Figure 3: Major decision options for all countries — first five years after certification of the world as free of wild polioviruses
Management
Routine Supplemental Outbreak Stockpile: Surveillance: Containment: f Chroni
immunization: immunization: response: Dorstoras
NID with toPv Mavonsl & Passive + Enforce WHO Screening
tOPV NIDs and restart Steekpites environmental recommendations 4 and
routine education
NID with mOPV
and restart
routine
NID with elPV
and restart cisba
routine iobal i
elPV stockpile a
NID with toPV only:
Sus NID with mOPV
only
NID with elPV
National 4
; AFP (Dedicated
None, stockpile + Fr Dedicates)
coordinated Local mass only
cessation immunization with
tOPV
Local mass
immunization
with mOPV
None, not Dedicated Do not enforce N ii
a Local mass Y No lo screening
ecordinated No SNID, immunization stockpile only WHO " or education
cessation or NIDs recommendations
with elPV
11
Figure 4: Simplified diagram of model components
Risks &
Conditions
Decision
options
Paralytic cases
Outbreak &
Response
Financial costs Health Porta
Figure 5: Schematic of dynamic disease model components for the first of 25 age groups
extending on basic SIR though inclusion of 3 different groups with partial immunity (due to
prior recent or historical vaccination or exposure to wild poliovirus)
bN(1-e!™*1PV3-
£°'3*OPV3)
Irate
Fully MO.) Regular Regular |_Y _.) Removeds
susceptibles latents infecteds
irrate(t)+secopvrate(t)
bN(6°"3*OPV3) ;
aia S,e!A(t), ——__ Irate x 1
_ Partially A(t) TAEEPT Infected ¥
infectibles 1 | Pll
8,17 {irrate(t)+secopvrate(t)}
Partially SePM(t) —————_ Irate Infected fi
infectibles 2 Latent PI 2 PID
S,e {irrate(t)+secopvrate(t)}
bN(ciPY3*IPV3 re S,oi° Mt), ————_, Irate e 3
( ) _ Partially col ACO Tan BES Infected Y
infectibles 3 Liters | PI3
A(t= (yRo/N)*D82[RI(t)+ Dosti infected 5 *TPI(t)}]
Figure 6: Example of a prospectively modeled outbreak after cessation in a hypothetical
country
200
sees No response
40 || ~~~ tOPV response
——m0PV response
160
: Second response
140 tround
= :
3
5 120
a
3
@ 100 First response round
8
2
3S
= 80
S
<
60
40 Outbreak detection
20
7 ——— ye
0 28 56 84 112 140 168 196 224 252 280 308 336 364 392 420 448 476
Days after virus introduction
“Source: Duintjer Tebbens et al. (2005a). We assume the outbreak occurs in a low-income
country with Ro=13 and a population of 100 million people 5 years after cessation of all polio
immunizations and 10 years after stopping supplemental immunization activities. Detection
occurs as soon as the cumulative incidence reaches | paralytic case and we assume a delay from
detection to response of 70 days. The response scenarios assume two immunization rounds at a
30-day interval covering 90% of all children younger than 5 years of age in 3 days. The “no
response” curve reaches a peak of over 1,700 cases on day 197, but ultimately the failure to
respond would lead to exportations of cases into other parts of the world and to global
recirculation of polioviruses signaling the failure of eradication.
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