Vaccine 24 (2006) 3530–3537

Stockpile levels for pediatric vaccines: How much is enough?

Sheldon H. Jacobson a,∗, Edward C. Sewell b,1, Ruben A. Proano a, Janet A. Jokela c,2

a Department of Mechanical and Industrial Engineering, 1206 West Green Street (MC-244), University of Illinois,Urbana, IL 61801, United States

b Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, IL 62026-1653, United Statesc College of Medicine, University of Illinois, Urbana, IL 61801, United States

Received 17 November 2005; received in revised form 1 February 2006; accepted 3 February 2006Available online 20 February 2006

Abstract

In recent years, several factors have led to pediatric vaccine manufacturers experiencing vaccine production interruptions that resulted invaccine supply shortages. One unfortunate consequence of such events is that not all children in the United States could be vaccinated ontime, as set forth by the Recommended Childhood Immunization Schedule, and hence, created the potential for epidemic outbreaks of severalchildhood diseases. The Centers for Disease Control and Prevention (CDC) have responded to such events by releasing vaccine supplies fromttptyi©

K

1

(smsciIc

((

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he national pediatric vaccine stockpiles, which were designed to mitigate the impact of vaccine production interruptions. This paper analyzeshe CDC-proposed vaccine stockpile levels using a stochastic inventory model. The results from this analysis examine the adequacy of theroposed pediatric vaccine stockpile levels, as well as provide insights into what the appropriate pediatric vaccine stockpile levels should beo achieve prespecified vaccination coverage rates. Given that the average pediatric vaccine production interruption has lasted more than 1ear, the model is used to compute appropriate pediatric vaccine stockpile levels sufficient to absorb the effect of such vaccine productionnterruptions. The level of funding needed to create such pediatric vaccine stockpile levels is also reported.

2006 Elsevier Ltd. All rights reserved.

eywords: Pediatric vaccines; Vaccine stockpiles; Pediatric vaccine coverage rates; Pediatric immunization

. Introduction and background

The Advisory Committee on Immunization PracticeACIP) establishes pediatric immunization regulations andtandards for the United States by managing the Recom-ended Childhood Immunization Schedule, a comprehen-

ive sequence and timing of pediatric vaccines to protecthildren from several pediatric diseases that once posed majornfectious disease health risks throughout the nation [1].mmunization is considered by many within the public healthommunity to be one of the great medical advances of the

∗ Corresponding author. Tel.: +1 217 244 7275; fax: +1 217 244 6534.E-mail addresses: shj@uiuc.edu (S.H. Jacobson), esewell@siue.edu

E.C. Sewell), rproano@uiuc.edu (R.A. Proano), jokela@uiuc.eduJ.A. Jokela).

1 Tel.: +1 618 650 3262; fax: +1 618 650 3771.2 Tel.: +1 217 337 2398.

twentieth century. For example, the risk of polio and measleshas been almost entirely eradicated through nationwide pedi-atric immunization programs [2].

Biotechnology advances, educational programs spear-headed by government agencies, the responsible attitude ofparents and guardians, and strategic solutions directed toimprove vaccine delivery systems have led to significantimprovements in pediatric immunization practices. One indi-cator of such improvements is that vaccination coverage ratesare now at all-time highs, which in turn has resulted in recordlow disease rates [4]. Maintaining such rates requires a safeand reliable pediatric vaccine supply. However, in recentyears, different vaccine manufacturers have experienced pro-duction interruptions that have led to several pediatric vaccinesupply shortages [4] (see Table 1 for a sample of such vaccineproduction interruptions).

Based on surveys and interviews of immunization pro-gram managers and providers of the Vaccine for Children

264-410X/$ – see front matter © 2006 Elsevier Ltd. All rights reserved.oi:10.1016/j.vaccine.2006.02.004

S.H. Jacobson et al. / Vaccine 24 (2006) 3530–3537 3531

Table 1Duration of recent pediatric vaccine supply shortages

Vaccine Start of shortage End of shortagea Duration (month)

Combined tetanus-diphtheria toxoids (Td) November, 2000 June, 2002 19Diphtheria-tetanus-acellular pertussis (DTaP) March, 2001 July, 2002 16Pneumococcal conjugate (PNU7) September, 2001 March, 2003 20Measles-mumps-rubella (MMR) October, 2001 July, 2002 9Varicella (VAR) October, 2001 August, 2002 10Pneumococcal conjugate (PNU7)b February, 2004 September, 2004 7

a Month and year of publication in Morbidity and Mortality Weekly Report announcing resolution of the shortage.b NIP, vaccine shortages archives.

Program at the end of 2001, Stokley et al. [3] evaluate theimpact of vaccine supply shortages on the immunizationprograms and providers. They observe that a minority ofproviders implemented the temporary immunization recom-mendations, as suggested by the ACIP, which were designedto minimize the negative impacts of the shortages. They alsonote that after the ACIP calls for the resumption of the rec-ommended vaccine schedule, a certain proportion of childrenmay actually never receive their missed immunization doses.

The National Vaccine Advisory Committee [6] and Santoliet al. [4] describe several contributing factors that have causedvulnerability in the pediatric vaccine supply chain. First, theyobserve the low valuation of vaccines reflected in the lowprice that the public and legislators are willing to pay forvaccines. Moreover, the high cost and complexity associatedwith the development, approval, production, and distribu-tion of pediatric vaccines provides barriers that a shrinkingnumber of vaccine manufacturers are willing to tackle. Theyalso note that confidentiality requirements in communica-tion between key stakeholders in the vaccine industry andthe federal government make it difficult to promptly rec-ognize and manage potential shortages. Lastly, Santoli etal. [4] observe that over the past two decades, the numberof pediatric vaccine manufacturers in the United States hasbeen decreasing [6], while the number of vaccines in theRecommended Childhood Immunization Schedule has beeniivoiplalthtvcilns

production problems and/or precipitously cease production.For example, in the Spring of 2001, Wyeth Pharmaceuticalsceased production of diphtheria-tetanus-acellular pertussis(DTaP), leaving the United States with just two manufactur-ers for this vaccine. Temporary production interruptions in thesupply of the measles-mumps-rubella (MMR) and varicella(VAR) vaccines were due to the reconstruction of a vaccinemanufacturer’s vaccine filling suite [4]. A shortage of thepneumococcal conjugate (PNU7) vaccine occurred when itwas initially introduced because of production problems dur-ing the startup period [6].

Based on a request by the United States Department ofHealth and Human Services (HHS) to investigate the rootcauses of pediatric vaccine supply shortages, the NationalVaccine Advisory Committee (NVAC) formed the workinggroup, “Strengthening the Vaccine Supply of Routinely Rec-ommended Vaccines” [6]. In 2002, this working group held aworkshop with industry representatives, regulatory authori-ties, public health officials, purchasers, providers, consumers,legislators and academic investigators to consider relevantissues surrounding the pediatric vaccine supply shortageproblem. This discussion identified several possible solu-tions, including providing financial incentives to motivatevaccine manufacturers, enacting changes in the vaccine reg-ulatory process, and expanding the rotating pediatric vaccinestockpiles [7]. Sloan et al. [8] discuss the rational implemen-tecsotutvtr

epacvv

ncreasing. This reduction of manufacturers can be blamed,n part, to the pressure on the industry to provide low-priceaccines. For example, the federal government purchasesver one-half of all pediatric vaccines that are administeredn the United States (in 2001, approximately 57% of allediatric vaccines were purchased with federal, state andocal funds, through the Vaccine for Children program) [4],nd negotiated government contract prices are significantlyower than private sector prices [5]. It has been suggestedhat the resulting low profit margins on pediatric vaccinesave made it financially unattractive for vaccine manufac-urers to either enter the pediatric vaccine market or increaseaccine production capacity ([10]). The small number of vac-ine manufacturers is critical, not only since it may lead tonsufficient vaccine production capacity, but also because itimits the ability of the health care immunization commu-ity to quickly respond to unanticipated changes in markethare when one or more vaccine manufacturers experience

ation of a pediatric vaccine subsidy system that could serve toncourage more pharmaceutical companies to enter the vac-ine market, and hence, create a more reliable vaccine supplyystem for the future. Kurian et al. [9] outlines the positionf the American College of Preventive Medicine with respecto the Institute of Medicine [10] and the NVAC reports. Theyse the arguments posed from both sets of recommendationso align its own position about needed financial changes in theaccine supply chain system. Hinman [11,12] further clarifieshe position of the NVAC towards the Institute of Medicineecommendations in the vaccine financial system.

The General Accounting Office and the Centers for Dis-ase Control and Prevention (CDC) deemed that a nationalediatric vaccine stockpile program would provide the mostdvantageous short-term solution against possible future vac-ine supply shortages [7]. Note that the first national pediatricaccine stockpiles were created in 1983 to address short-termaccine supply interruptions. According to the CDC, vaccine

3532 S.H. Jacobson et al. / Vaccine 24 (2006) 3530–3537

stockpiles have helped to mitigate vaccine supply shortagesduring no less than eight different time periods over the pasttwo decades [6].

The goal of the national vaccine stockpiles is to maintain a6-month demand level of rotating inventory for all routinelyrecommended vaccines. At present, pediatric vaccine stock-piles exist for inactivated polio (IPV), MMR, Haemophilusinfluenzae type B (HiB), Hepatitis B (HBV), Hepatitis A(HAV), VAR, DTaP, PNU7, and a pentavalent combinationvaccine (DTaP-HBV-IPV). Note that since the influenza vac-cine requires annual antigenic determinant updates and mod-ifications, stockpiles for this vaccine cannot be created as forthe nine vaccines listed here, and hence, are not consideredin this analysis. Table 2 depicts the CDC-proposed vaccinestockpile levels [13], which are proportional to the numberof doses required per child, as defined by the RecommendedChildhood Immunization Schedule. To raise the existing vac-cine stockpile levels to these levels, a United States federalbudget allocation of over $170 M for fiscal year 2003 wasallocated to provide partial funding to support the necessaryexpansion of the national vaccine stockpile program [13].

The proposed pediatric vaccine stockpile levels reportedin Table 2 constitute a 6-month rotating supply. Such vaccinestockpiles would be used to absorb the impact and alleviatethe stress of pediatric vaccine production interruptions. Thechoice of 6 months is unclear, given that recent vaccine pro-daatssditpdcpp

stci

TP

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levels, as well as provide insights into appropriate pediatricvaccine stockpile levels as a function of vaccination coveragerates, the time duration of vaccine production interruptions,and the rate at which vaccine production returns to full capac-ity. The model provides an approximation for the probabilitythat a pediatric vaccine supply shortage will occur, given aspecified stockpile of vaccines available when a productioninterruption occurs. It also uses this probability to quantifyappropriate pediatric vaccine stockpile levels for differentvaccination coverage rates and vaccine production interrup-tion scenarios. The paper is organized as follows. Section2 briefly describes the unreliable vaccine production model,including the assumptions used in constructing and applyingthe model. Section 3 reports the results of the analysis. Sec-tion 4 discusses the implications and limitations of the resultsobtained. Given that the average pediatric vaccine produc-tion interruption has lasted more than 1 year, the model isused to compute appropriate pediatric vaccine stockpile lev-els sufficient to absorb the effect of such vaccine productioninterruptions. The amount of funds that would be needed tocreate such pediatric vaccine stockpiles is also reported.

2. Methods: model overview and assumptions

A stochastic inventory model, termed the unreliable vac-cvitwcfdtaepccrttttssou

vnnboi

uction interruptions reported in Table 1 lasted between 7nd 20 months, with a mean of just over 1 year. Given thispparent conflict, several questions can be posed concerninghe proposed stockpile levels. In particular, are these vaccinetockpile levels sufficient to vaccinate 95% (or some otherpecified vaccination coverage rate) of all children over aefined vaccine production interruption time period? Whats the relationship between the vaccine stockpile level andhe vaccination coverage rates, the duration of the vaccineroduction interruption, and the rate at which vaccine pro-uction returns to full capacity? Answers to such questionsan provide insights into appropriate pediatric vaccine stock-ile levels that can absorb the effect of future pediatric vaccineroduction interruptions.

This paper analyzes the CDC-proposed pediatric vaccinetockpile levels using a stochastic inventory model (termedhe unreliable vaccine production model; see [14] for techni-al details of this model). The results from this analysis exam-ne the adequacy of the proposed pediatric vaccine stockpile

able 2roposed vaccine stockpile levels

accine Number of doses

nactivated polio 8,000,000easles, mumps, rubella 4,000,000aemophilus influenzae type B 8,000,000epatitis B 6,000,000epatitis A 4,000,000aricella 2,000,000iphtheria-tetanus-acellular pertussis 10,000,000neumococcal conjugate 8,000,000

ine supply model, is used to capture the relationship betweenaccine supply and vaccine demand when vaccine productions temporarily interrupted. This model is used to approximatehe probability that all children who require immunizationith a particular vaccine (i.e., the vaccination coverage rate)

an receive all their required doses on schedule, given theollowing input data: a vaccine stockpile level, a probabilityistribution for the length of the vaccine production down-ime, a function for the vaccine production ramp-up process,nd a probability distribution for the number of children bornach day. The model considers three phases for the vaccineroduction process: a steady-state phase during which vac-ine production equals the expected vaccine demand; a vac-ine production interruption phase; and a vaccine productionamp-up phase. The model analysis focuses on the second andhird phases, which captures the vaccine supply/demand rela-ionship when a vaccine manufacturing facility (and hence,he vaccine supply process) fails due to a temporary produc-ion interruption, and then ramps-up again to a full vaccinetockpile. For further information on this model, see Jacob-on et al. [14], which includes a detailed technical derivationf the model, as well as a description of all the assumptionssed in the analysis.

To provide an overview of the model, consider a mono-alent vaccine that requires C doses to provide full immu-ization, as defined by the Recommended Childhood Immu-ization Schedule [1]. Suppose that the number of childrenorn on day t (and hence, the number of children that requirer demand immunization each day) are independently anddentically distributed random variables {Xt} with mean

S.H. Jacobson et al. / Vaccine 24 (2006) 3530–3537 3533

λ = 11,000 and standard deviation σd = 1100 (both measuredin children per day). Without loss of generality, assume thatthis vaccine is produced by a single source provider (whichis the case for three of the eight vaccines listed in Table 2; forvaccines produced by two or more manufacturers, the ensu-ing analysis can be applied to the vaccine deficit created ifone or more of these manufacturers experiences a productioninterruption). Suppose that the vaccine production is inter-rupted and remains down during a time period of length T,a positive random variable (measured in days) that is greaterthan 30 with probability one.

Assume that the initial vaccine stockpile level, I, is knownprior to the vaccine production interruption. Suppose that t = 0is labeled as the time at which the vaccine manufacturer pro-duction operation becomes available and begins a productionramp-up phase, from a production rate of zero to a maximumproduction capacity rate of 1.1Cλ, until the vaccine stock-pile is replenished to I doses, where u(t) denotes the vaccineproduction ramp-up rate function at time t. Let tM denote thediscrete point of time at which the vaccine manufacturer’sproduction capacity returns to its maximum production rate(i.e., u(tM) = 1.1Cλ), and hence, the vaccine stockpile can bereplenished back to I doses (since vaccine production willexceed vaccine demand). Assume that vaccine demand istracked once per day (daily) and that the vaccine produc-tion rate monotonically increases from time t = 0 until timet

otpidnatvabrlttapf

aacpfzsct

(which corresponds to a pessimistic scenario, since the pro-duction rate increases slowly and only accelerates near theend of the time period [0,tM]) is given by

u(t) = 1.1Cλ

(t

tM

)2

, (1)

while the concave vaccine production ramp-up rate function(which corresponds to an optimistic scenario, since the pro-duction rate increases rapidly and then levels off near the endof the time period [0,tM]) is given by

u(t) = 1.1Cλ

(t

tM

)1/2

. (2)

Define S(t) to be the vaccine supply level at time t. Fig. 1depicts the expected vaccine supply level as a function of theinitial stockpile level I. Lastly, to determine the probabilitythat at least α100% of all children that require vaccination canindeed be immunized, during the time period defined fromwhen the vaccine production is interrupted until time t = tM,define the discrete random variable tm to be the time when theexpected vaccine supply reaches its minimum level. There-fore, after the T days during which the vaccine productioninterruption occurred, the vaccine production facility thenbecomes available again and begins a production ramp-upperiod, from a production rate of zero to its maximum pro-dan

(ddcrptoop

= tM.Given the dearth of available data, due to the propriety

f vaccine production information, there is no way to knowhe exact form of u(t). For example, setting the maximumroduction capacity rate to be 10% above the demand rates arbitrary. If this value is set too close to zero, it may beifficult to satisfy the backlog of children requiring immu-ization and to replenish the vaccine stockpile in a reasonablemount of time (which seems unlikely). If this value is setoo high (e.g., 50% above the demand rate), then providingaccines for the backlog of children requiring immunizationnd replenishing the vaccine stockpile replenishment couldoth be done sufficiently fast that there would be a minimalamp-up time period (which also seems unlikely). In fact, thisatter situation would be equivalent to reducing the length ofhe vaccine production interruption. Therefore, changes inhe maximum production capacity rate have the same effects shortening or lengthening the effective time of a vaccineroduction interruption. The implication of such an effect isurther discussed in Section 4.

To better understand the form of u(t), two extreme casesre considered, which provide an envelope between the bestnd worst case scenarios. In particular, a concave and aonvex functional form for u(t) over time period [0,tM] areroposed as two possible vaccine production ramp-up rateunctions, as the supply rate monotonically increases fromero to its maximum production capacity. Note that by con-idering these two extreme scenarios, a mean or base casean be extracted from this analysis by interpolating betweenhem. The convex vaccine production ramp-up rate function

uction capacity rate (which is assumed to be 110% of theverage production rate needed to meet the immunizationeeds of all children).

The parameter α denotes the vaccination coverage ratehence a specified value of α implies that α100% of all chil-ren are immunized on schedule). Under these assumptions,efine P(α, I, T) as the probability of achieving a vaccinationoverage rate of α100% during a vaccine production inter-uption, as a function of the vaccine stockpile level I and therobability distribution for the length of the vaccine produc-ion interruption period T. Therefore, for each vaccine, thebjective is to determine the probability that at least α100%f all children that require vaccination during the vaccineroduction interruption can be immunized on schedule.

Fig. 1. Expected vaccine supply function.

3534 S.H. Jacobson et al. / Vaccine 24 (2006) 3530–3537

Table 3P(α, I, T) for the CDC-recommended pediatric vaccine stockpile levels

Vaccine: I η Scenario tM = 60 tM = 120 tM = 180

IPV: 8,000,000

120Optimistic 0.99 0.92 0.73MMR: 4,000,000

HiB: 8,000,000Pessimistic 0.87 0.23 0.00HBV: 6,000,000

HAV: 4,000,000

180Optimistic 0.31 0.14 0.05VAR: 2,000,000

DTaP: 10,000,000Pessimistic 0.11 0.01 0.00PNU7: 8,000,000

3. Results

This section reports results with the unreliable vac-cine supply model described in [14] to evaluate the pro-posed vaccine stockpile levels (see Table 2) and to deter-

mine appropriate pediatric vaccine stockpile levels in theevent of production interruptions that last longer than 6months.

Table 3 reports approximations for P(α, I, T) for the eightvaccines listed in Table 2, for the CDC-proposed values of I,for α = 1.0, tM = 60, 120, 180, and T distributed as a trun-cated normal (labeled NT(η, σt)), with η = 120, 180 (andσT = η/6), for both concave (optimistic scenario) and con-vex (pessimistic scenario) vaccine production ramp-up ratefunctions, with {Xt} assumed to follow a normal distribution.From the definitions and notation described here, completerecovery of the vaccine production facility is assumed to takeon average slightly more than η + tM days. Therefore, forη = 180 and tM = 60, the resulting vaccine production inter-ruption lasts for approximately 8 months (which includes a2-month production ramp-up period). For less than a 100%vaccination coverage rate, Tables 4 and 5 report initial vaccine

Table 4Pediatric vaccine stockpile levels (in millions of doses, pessimistic scenario)

Vaccine η α = 0.90 α = 0.95

tM, 60 tM, 120 tM, 180 tM, 60 tM, 120 tM, 180

IPV120 8.1 9.6 11.1 8.6 10.2 11.7180 11.4 12.9 14.4 12.0 13.6 15.2

MMR120 4.1 4.8 5.6 4.3 5.1 5.9180 5.7 6.5 7.2 6.0 6.8 7.6

HiB120 8.1 9.6180 11.4 12.9

HBV120 6.1 7.2180 8.6 9.7

HAV120 4.1 4.8180 5.7 6.5

VAR120 2.0 2.4180 2.9 3.2

DTaP120 10.1 12.0180 14.3 16.2

PNU7120 8.1 9.6180 11.4 12.9

TP

V

I8.6 7.7 8.3 9.0

M

H

H

H

V

D

P

able 5ediatric vaccine stockpile levels (in millions of doses, optimistic scenario)

accine η α = 0.90

tM, 60 tM, 120

PV120 7.3 7.9

180 10.6 11.2

MR120 3.6 4.0180 5.3 5.6

iB120 7.3 7.9180 10.6 11.2

BV120 5.4 5.9180 7.9 8.4

AV120 3.6 4.0180 5.3 5.6

AR120 1.8 2.0180 2.6 2.8

TaP120 9.1 9.9180 13.2 14.0

NU7120 7.3 7.9180 10.6 11.2

11.1 8.6 10.2 11.714.4 12.0 13.6 15.2

8.4 6.4 7.6 8.810.8 9.0 10.2 11.4

5.6 4.3 5.1 5.97.2 6.0 6.8 7.62.8 2.1 2.5 2.93.6 3.0 3.4 3.8

13.9 10.7 12.7 14.718.0 15.1 17.0 19.011.1 8.6 10.2 11.714.4 12.0 13.6 15.2

α = 0.95

tM, 180 tM, 60 tM, 120 tM, 180

11.9 11.1 11.8 12.54.3 3.8 4.2 4.55.9 5.6 5.9 6.38.6 7.7 8.3 9.0

11.9 11.1 11.8 12.56.4 5.7 6.3 6.88.9 8.4 8.9 9.44.3 3.8 4.2 4.55.9 5.6 5.9 6.32.1 1.9 2.1 2.33.0 2.8 3.0 3.1

10.7 9.6 10.4 11.314.8 13.9 14.8 15.78.6 7.7 8.3 9.0

11.9 11.1 11.8 12.5

S.H. Jacobson et al. / Vaccine 24 (2006) 3530–3537 3535

stockpile levels that provide α100% vaccination coveragerates for each pediatric vaccine, α = 0.90, 0.95 such that P(α,I, T) = .99; these levels are provided for the same set of val-ues for η and tM used for Table 3, for both the optimistic andpessimistic scenarios. To provide a frame of reference forthese values, they should be compared to the recommendedvaccine stockpile levels reported in Table 2. Alternatively, tocompute the amount of time it would take for the vaccinestockpile levels reported in Tables 4 and 5 to be depleted(assuming no vaccine production over this time period), thevalues in Tables 4 and 5, for a given vaccine, would need tobe divided by the product of λ = 11,000 children per day andC doses of the vaccine required for each child. For example,for the value 11.1 million doses for vaccine IPV in the firstrow of Table 4, this corresponds to a supply of just over 252days (since C = 4). Note that all these results were obtainedusing Mathematica 5.1.

4. Discussion and recommendations

The results in Table 3 suggest that the CDC-proposedpediatric vaccine stockpile levels for IPV, MMR, HiB, HBV,HAV, VAR, DTaP, and PNU7 are adequate to absorb theimpact of a 6-month vaccine production interruption forthese vaccines. In particular, the proposed vaccine stock-p9fvmsrda[

Pesgf(panpfim(ipdip

to mitigate the impact of vaccine production interruptionsthat last for 8 or more months, which could pose sig-nificant risks to children not being fully immunized onschedule.

If a vaccine production interruption lasts longer than 6months, then vaccine stockpile levels will need to be higherto absorb the impact of the resulting vaccine supply shortage.The values in Tables 4 and 5 report initial vaccine stock-pile levels that provide α100% vaccination coverage ratesfor each pediatric vaccine, α = 0.90, 0.95 such that P(α, I,T) = 0.99, for different sets of values for η and tM, for boththe pessimistic and optimistic scenarios. Note that the goalof the CDC is to achieve 95% vaccination coverage rates[17]. For example, for IPV, with α = 0.95, η = 120, tM = 60,in the optimistic scenario, a stockpile of 7.7 million doseswill be adequate to absorb the impact of a vaccine produc-tion interruption of approximately 6 months, with a 4-monthdown period and a 2-month production ramp-up period. Onthe other hand, for the same parameter values in the pes-simistic scenario, the stockpile level would need to be 8.6million doses. For η = 120 and tM = 120, a stockpile of 8.3million doses will be adequate to absorb the impact of a vac-cine production interruption of approximately 8 months, witha 4-month down period and a 4-month (optimistic scenario)production ramp-up period, while for the same parameter val-ues in the pessimistic scenario, the stockpile level would needtstm(tslvitosapdtcolllss

avoew

ile levels for these diseases are moderately likely (i.e.,9% for the optimistic scenario, down to a 87% chanceor the pessimistic scenario) to be able to provide all theaccines needed to fully immunize the nation during a 6-onth production interruption. Given that these vaccine

tockpile levels have been set for such a production inter-uption time period, these results are reasonable. What theyo provide is some empirical validation for the unreli-ble vaccine supply model introduced in Jacobson et al.14].

The results in Table 3 also provide approximations for(α, I, T) for the proposed vaccine stockpile levels, in thevent of longer production interruption periods, as mea-ured by larger values for η and tM. These results sug-est that in the event of a vaccine production interruptionor any of the vaccines that lasts for 8 or more monthswhich has been the case for all but one of the recentroduction interruptions; see Table 1), there is a reason-bly high risk (i.e., between 8% in the optimistic sce-ario up to 89% in the pessimistic scenario) that the pro-osed vaccine stockpile levels will not be adequate toully vaccinate all children that require immunization dur-ng such a production interruption. In the event of a 12-

onth production interruption, there is a very high riski.e., between 95% in the optimistic scenario up to 100%n the pessimistic scenario) that the proposed vaccine stock-ile levels will not be adequate to fully vaccinate all chil-ren that require immunization during such a productionnterruption. In practical terms, this means that the pro-osed pediatric vaccine stockpiles levels are inadequate

o be 10.2 million doses. Lastly, for η = 180 and tM = 120, atockpile of 11.8 million doses will be adequate to absorbhe impact of a vaccine production interruption of approxi-

ately 10 months, with a 6-month down period and a 4-monthoptimistic scenario) production ramp-up period, while forhe same parameter values in the pessimistic scenario, thetockpile level would need to be 13.6 million doses. Simi-ar conclusions and insights can be drawn for all the otheraccines. In general, as the length of a vaccine productionnterruption increases, as measured by the production downime, η, the length of the ramp-up period, tM, and the formf the production ramp-up rate function (i.e., optimistic ver-us pessimistic scenario), the vaccine stockpile required tobsorb the impact of such a production interruption timeeriod must also increase. Moreover, if the maximum pro-uction capacity rate is assumed to be 1.5Cλ (i.e., 50% abovehe demand rate, rather than 10%), then the pediatric vac-ine stockpile levels reported in Table 4 would be on therder of 2–7% lower, while the pediatric vaccine stockpileevels reported in Table 5 would be on the order of 2–12%ower. All these results suggest that the proposed stockpileevels will only serve to absorb the impact of a 6-month orhorter vaccine production interruption under the optimisticcenario.

It would be useful to determine the cost of purchasingdequate vaccine stockpiles (see Tables 4 and 5) for the eightaccines listed in Table 2. Table 6 reports the purchase costf these eight vaccines (based on various June 15, 2005 fed-rally negotiated contract prices), for η = 120 and tM = 120,hich models an 8-month vaccine production interruption

3536 S.H. Jacobson et al. / Vaccine 24 (2006) 3530–3537

Table 6Cost of vaccine stockpiles (eight month production interruption)

Vaccine Cost per dose α = 0.90 α = 0.95 Baseline cost

IPV $10.42 $82 M $87 M $83 MMMR $16.67 $66 M $70 M $67 MHiB $7.86 $62 M $66 M $63 MHBV $9.00 $53 M $56 M $54 MHAV $12.15 $48 M $51 M $49 MVAR $52.25 $104 M $109 M $104 MDTaP $12.75 $126 M $133 M $127 MPNU7 $54.12 $428 M $452 M $433 M

Total cost $970 M $1023 M $980 M

with a 4-month down period and a 4-month (optimistic sce-nario) ramp-up period with maximum production capacityrate of 1.1Cλ, for 90% and 95% vaccination coverage rates(i.e., values for α). In addition, the cost of the CDC-proposedvaccine stockpile levels are also reported (labelled as base-line cost). Similarly, Table 7 reports the purchase cost of theseeight vaccines for η = 180 and tM = 180, which models a 12-month vaccine production interruption with a 6-month downperiod and a 6-month (optimistic scenario) ramp-up periodwith maximum production capacity rate of 1.1Cλ, for 90%and 95% vaccination coverage rates. The results in Table 6indicate that to stock sufficient vaccines to achieve a 95% vac-cination coverage rate for each of the vaccines would require$1023 M (which is $43 M more than what would be needed topurchase up to the proposed vaccine stockpile levels). More-over, to achieve a 90% vaccination coverage rates for each ofthe vaccines would require $970 M (which is $10 M less thanwhat would be needed to purchase up to the proposed vac-cine stockpile levels). If the maximum production capacityrate is assumed to be 1.5Cλ (i.e., 50% above the demand rate,rather than 10%), then these costs would decrease to $942and $890 M, respectively. Similarly, the results in Table 7indicate that to stock sufficient vaccines to achieve a 95%vaccination coverage rate for each of the vaccines wouldrequire $1534 M (which is $554 M more than what would beneeded to purchase up to the proposed vaccine stockpile lev-eemp

TC

V

IMHHHVDP

T

production capacity rate is assumed to be 1.5Cλ, then thesecosts would decrease to $1415 and $1337 M, respectively.This analysis suggests that modest additional investments inpediatric vaccine stockpile levels could provide significantprotection against longer pediatric vaccine production inter-ruptions, which in turn would improve the chance that thevaccine stockpiles would absorb any production interruptionsthat could place our nation’s children (and health care system)at unnecessary risk.

The results reported here were obtained using a mathemat-ical model that made several assumptions, which impact theconclusions drawn from the analysis. First, it is very difficultto know how long a vaccine production interruption will last.Given the moderate number of actual pediatric vaccine pro-duction interruptions that have occurred since 2000, there isa dearth of available data to adequately understand the prob-ability distribution of such events, which also includes theactual production down time, the length of the productionramp-up period, the maximum production capacity rate, andthe form of the production ramp-up rate function. In addi-tion, the analysis does not consider the number of vaccinedoses that are never administered due to wastage and expi-ration (recent studies and analysis suggest that this numberis fairly small; see [15,16]). This would occur, for example,if the vaccine stockpiles are not appropriately rotated. Toincorporate such losses into the analysis, the vaccine stock-pwvc

tairtioctsioect

aabnndmdo

ls). Moreover, to achieve a 90% vaccination coverage rate forach of the vaccines would require $1454 M (which is $473 More than what would be needed to purchase up to the pro-

osed vaccine stockpile levels). Once again, if the maximum

able 7ost of vaccine stockpiles (12-month production interruption)

accine Cost per dose α = 0.90 α = 0.95 Baseline cost

PV $10.42 $124 M $130 M $83 MMR $16.67 $99 M $104 M $67 MiB $7.86 $93 M $98 M $63 MBV $9.00 $80 M $85 M $54 MAV $12.15 $72 M $76 M $49 MAR $52.25 $155 M $164 M $104 MTaP $12.75 $189 M $200 M $127 MNU7 $54.12 $642 M $677 M $433 M

otal cost $1454 M $1534 M $980 M

ile levels could be rescaled based on the anticipated vaccineastage rates (e.g., using 95% vaccination coverage rateaccine stockpile levels to achieve 90% actual vaccinationoverage rates).

This analysis also focuses only on the one-time outlayo create pediatric vaccine stockpiles. It does not take intoccount the costs associated with holding, rotating, maintain-ng, or transporting vaccines in the stockpile. For example,otating large quantities of vaccines requires diligent inven-ory management. In addition, centralized versus localizednventory and distribution systems could have a large impactn overall stockpile management costs. Once a pediatric vac-ine stockpile is created, such on-going costs would needo be considered to determine the costs of maintaining thetockpile. As data becomes available to support changesn the assumptions of the unreliable vaccine supply model,r if other assumptions are deemed more appropriate byither public health administrators, CDC personnel, or vac-ine manufacturers, they can and will be incorporated intohe analysis.

This analysis only considers monovalent vaccines. Therere a growing number of combination vaccines that are nowvailable (e.g., HBV-HiB, DTaP-HBV-IPV) that could alsoe stockpiled. Although it would appear that this would sig-ificantly reduce the total number of vaccines that wouldeed to be stockpiled, it would also create a complex depen-ency between the different vaccines covered in the Recom-ended Childhood Immunization Schedule. Such a depen-

ency would likely result in the need for a larger stockpilef combination vaccines, which may closely rival the sum

S.H. Jacobson et al. / Vaccine 24 (2006) 3530–3537 3537

of the monovalent components. Work is in progress to studythis highly complex situation.

In conclusion, the results reported suggest that the CDC-proposed pediatric vaccine stockpile levels for IPV, MMR,HiB, HBV, HAV, VAR, DTaP, and PNU7 are adequate toabsorb the effect of a vaccine production interruption lastingno more than 6 months. If a vaccine production interrup-tion exceeds 6 months, then modifications to the vaccinationguidelines must be instituted to preserve and optimally useexisting vaccine stockpiles, and hence, to ensure that all chil-dren receive at least some doses of the required vaccines.However, modest increases in the vaccine stockpile levelsmay have a significant impact to ensure that vaccinationcoverage rates remain high during vaccine production inter-ruptions [17].

Acknowledgments

The authors wish to thank Bruce G. Weniger, MD, MPH,assistant chief for Vaccine Development within the VaccineSafety and Development Branch of the National Immu-nization Program, Centers for Disease Control and Preven-tion, for suggesting the problem addressed in this paper,and for his longstanding encouragement of applying opera-tions research methodologies to address important and timelypThhbebt0oaNsR

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ublic health problems related to pediatric immunization.he authors also wish to thank Mr. Ivan Shyryayev foris initial contributions to this research effort. The paperas been significantly improved by the comments providedy two anonymous referees, to which the authors wish toxpress their thanks and appreciation. This research haseen supported in part by the National Science Founda-ion (DMI-0222554, DMI-0222597, DMI-0457176, DMI-456945). Any opinions, findings, and conclusions or rec-mmendations expressed in this material are those of theuthor(s) and do not necessarily reflect the views of theational Science Foundation. The first author has also been

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