This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal non-commercial research and

Transcription

1 Ths artcle appeared n a journal publshed by Elsever. The attached copy s furnshed to the author for nternal non-commercal research and educaton use, ncludng for nstructon at the authors nsttuton and sharng wth colleagues. Other uses, ncludng reproducton and dstrbuton, or sellng or lcensng copes, or postng to personal, nsttutonal or thrd party webstes are prohbted. In most cases authors are permtted to post ther verson of the artcle (e.g. n Word or Tex form) to ther personal webste or nsttutonal repostory. Authors requrng further nformaton regardng Elsever s archvng and manuscrpt polces are encouraged to vst:

2 Vaccne (2008) 26, avalable at journal homepage: Dynamcs and control of measles n Portugal: Accessng the mpact of antcpatng the age for the frst dose of MMR from 15 to 12 months of age Ana Crstna Paulo a,, Manuel C. Gomes b,c, M.Gabrela M. Gomes a,d a Insttuto Gulbenkan de Cênca, Apartado 14, Oeras, Portugal b Faculdade de Cêncas, Unversdade de Lsboa, Campo Grande, Lsboa, Portugal c Center for Bodversty, Functonal and Integratve Genomcs BoFIG, Faculdade de Cêncas, Unversdade de Lsboa, Campo Grande, Lsboa, Portugal d Centro de Matemátca e Aplcações Fundamentas, Unversdade de Lsboa. Av. Prof Gama Pnto, 2, Lsboa, Portugal Receved 3 October 2007; receved n revsed form 18 February 2008; accepted 22 February 2008 Avalable onlne 19 March 2008 KEYWORDS Measles; Portugal; Mathematcal modelng; Vaccnaton Summary The all-tme low ncdence of measles n Portugal n the recent years, rases questons regardng whether the dsease has been elmnated, the role of recent control measures, and the epdemologcal consequences of the rse n the proporton of newborns to vaccnated mothers, as opposed to those born to mothers who acqured mmunty by natural nfecton. We estmate the vaccnaton coverage aganst measles n Portugal on a cohort-by-cohort bass, and ncorporate ths nformaton nto an age-structured seasonally-drven mathematcal model amed at reproducng measles dynamcs n the past decades. The model reproduces documented trends n dsease notfcatons and the serologcal profle of the Portuguese populaton, as estmated by a recent Natonal Serologcal Survey. We provde evdence that the effectve reproducton number (R e ) of measles has been drven below 1 n Portugal, and that sustaned measles elmnaton s crucally dependent upon the mantenance of a hgh (>95%) coverage wth the MMR I vaccne n the future. If the vaccnaton coverage decreases to levels around 90% the antcpaton of the frst dose of the MMR I from 15 to 12 months of age, wll ensure that R e remans below Elsever Ltd. All rghts reserved. Introducton Correspondng author. Tel.: ; fax: E-mal address: acpaulo@gc.gulbenkan.pt (A.C. Paulo). Over the past 5 years, the ncdence of measles n Portugal has declned to an all-tme low. Between 2002 and 2005, a total of 24 suspected cases of measles were notfed to the Portuguese authortes [1], correspondng to an annual X/$ see front matter 2008 Elsever Ltd. All rghts reserved. do: /j.vaccne

3 Dynamcs and control of measles n Portugal 2419 ncdence of <0.6 cases per mllon ndvduals. Ths follows a strategy put nto place aganst measles that ncluded a two-year catch-up vaccnaton campagn ( ), the antcpaton of the age of the second dose of the measlesmumps-rubella vaccne (MMR II) from to 5 6 years old (snce January 2000), and the mantenance of a hgh level of mmunzaton coverage by routne vaccnaton, as documented by the Natonal Serologc Survey [2] conducted n Portugal thus appears to be on track to fulfll the 2010 measles elmnaton target set by WHO [3]. Nevertheless the hgh transmssblty of measles poses a sgnfcant challenge to any attempt to elmnate t. Recently, measles re-emerged n the European Regon of the WHO, ncludng countres that had already acheved good levels of measles control [4 8]. Most cases occurred n nonmmunzed ndvduals that ether faled vaccnaton or were too young to be vaccnated, usually chldren younger than 15 months of age [4 6]. The buldng of a susceptble pool of these nfants s of partcular concern, as a dsproportonate number of measles-assocated deaths occur n chldren under the age of routne mmunzaton [9,10]. The resurgence of measles n the Unted States of Amerca, between 1989 and 1991, provdes an outstandng example. Durng ths epdemc, the epdemology shfted dramatcally from school-aged to preschool chldren [11]. Infants below 15 months of age were not yet elgble for vaccnaton and, despte comprsng only 2% of the general populaton, accounted for 24% of the 55,622 cases reported. Sxty percent of measles related deaths occurred among preschool chldren [11,12]. Other examples of outbreaks among the very young have been recently reported n Europe. In a cluster of 580 cases n south London, between December 2001 and May 2002, 40% were aged under 12 months [4]. At La Roja, Span, where vaccne coverage was estmated to be 96.3% at 15 months of age, 13 out of the 18 confrmed cases of measles that took place n , were n chldren aged under 15 months [5]. Prevous studes have ndcated that nfants whose mothers acqured mmunty to measles by vaccnaton, have ncreased susceptblty to clncal measles, as compared to nfants born to mothers who have been exposed to the wld vrus [12]. Ths s n agreement wth evdence for a faster seroprevalence decay of passvely acqured maternal antbodes n unvaccnated nfants born to vaccnated mothers, as compared to those whose mothers had measles [13 16]. As the proporton of mothers who have been vaccnated ncreases over the years n the current vaccnaton era, so does the proporton of chldren who should respond to the measles vaccne at younger ages [14]. As a consequence, n January 1994 the routne age for MMR I vaccnaton n the USA was lowered from 15 months to between 12 and 15 months [17]. Recently, concern has also been rased n Europe regardng ths ssue [3,5] and, accordngly, the Portuguese authortes are contemplatng to antcpate the age of MMR I from 15 to 12 months old by the tme the proporton of newborns from vaccnated mothers exceeds 50%. We nvestgate the current epdemologcal stuaton of measles n Portugal, focusng on whether recent vaccnaton strateges created condtons for measles elmnaton. We estmate vaccnaton coverage along cohorts and nput ths nformaton nto an age-structured PSEIR (protected-susceptble-exposed-nfected-recovered) mathematcal model, where the protected category keeps track of newborns from vaccnated, unvaccnated nonsusceptble, and unvaccnated susceptble mothers. The model s amed at revealng the most mportant aspects of measles dynamcs n Portugal n the recent past, but we also nvestgate how future scenaros of measles control are effectve at ensurng sustaned measles elmnaton. In partcular, we show that, for a narrow regon of vaccnaton coverage around 90%, the antcpaton of the recommended age for the frst dose of the vaccne, from 15 to 12 months, s crucal to mantan the effectve reproducton number below 1 and thus, preventng measles outbreaks. For hgher levels of vaccnaton coverage however, t contrbutes to hamper the buldng of a pool of susceptble chldren younger than vaccnaton age, decreasng the lkelhood that mported cases result n small clusters among that age group. We also show that the success n sustanng measles elmnaton s crucally dependent on the mantenance of a very hgh vaccnaton coverage wth the MMR I. Data and methods Past-vaccnaton strateges and vaccne data Vaccnaton aganst measles n Portugal started n 1973, wth a major catch-up campagn amed at chldren under 10 years old. The campagn lasted untl 1977 wth 650,000 vaccnes beng delvered throughout. Routne vaccnaton started n 1974, wth a sngle-dose at 15 months of age. In 1987, the monovalent measles vaccne was replaced by the MMR I and, n late 1990, the second dose (MMR II) was ntroduced n the routne calendar for chldren between 11 and 13 years old. In 1998, the forecast of an upcomng measles outbreak from tme seres analyss [18] prompted health authortes to conduct a two step catch-up campagn for unvaccnated chldren. Ths second campagn targeted ages months n 1998 and ages 6 18 years old n In 2000, further analyss [19] led authortes to antcpate the recommended age of the MMR II to 5 6 years old. The number of vaccnes delvered every year, has been publshed by the Portuguese Natonal Insttute of Statstcs [20] wth varyng age groups over tme. Prevous attempts to estmate vaccnaton coverage n Portugal [21,22], were based upon the rato between vaccnes gven durng the second year of lfe and estmates of the standng populaton at the same age. By not followng cohorts, these estmates mss the combned mpact of campagns wth routne vaccnaton and dsregarded vaccnaton wth the MMR II. In order to estmate vaccnaton coverage along cohorts, we have separated vaccnes by age, followng a procedure smlar to the one by Fne and Clarkson [23]: 1. Vaccnes gven to age group 0 4 years old: In years , , and , there s nformaton avalable on the number of vaccnes by age. These records show that before 1988, less than 80% of the vaccnes were gven between 12 and

4 2420 A.C. Paulo et al. Table 1 Proportonal dstrbuton per year of the 650,000 vaccnes gven durng the vaccnaton campagn Scenaro Vaccne dstrbuton /7 2/7 1/7 1/7 1/7 2 5/15 4/15 3/15 2/15 1/15 3 4/8 1/8 1/8 1/8 1/8 24 months of age. After 1989, the percentage gven at months rose above 80%, ndcatng a tendency to vaccnate closer to the recommended age of 15 months. Whenever necessary, we have thus dsaggregated vaccnes by age, n years before 1989, followng the percentages 2.6%, 65.8%, 18.4%, 7.9% and 5.3% for ages 0, 1, 2, 3, and 4 years old, respectvely. In 1989 and later years, we have used the percentages 2.6%, 89.5%, 2.6%, 2.6% and 2.6% for the same ages. 2. Vaccnes gven to age group 5 10 years: We have assumed that the majorty of chldren were vaccnated between 5 and 7 years, as they are requred to present the vaccnaton booklet at regstraton for the frst school grade. Vaccnes were thus dstrbuted by age, attrbutng a weght of 2/8 to ages 5, 6, and 7 and 1/8 to ages 8 and Vaccnes gven to age group years old were unformly dstrbuted by ages. It s assumed that these ages receved MMR II, whereas ages 1 10 receved MMR I. There s no nformaton avalable regardng the break up of the 650,000 vaccnes gven n the campagn by year and age, so we have consdered three plausble scenaros of vaccne dstrbuton throughout ths perod whch are descrbed n Table 1. Vaccnaton coverage Vaccnaton coverage wth the MMR I s the cumulatve proporton of vaccnated ndvduals along each cohort, estmated as follows, VC = 10 =0 [v v d n ] (1) 10 N 0 d =0 For each cohort, the number of vaccnes, v, gven to chldren n yearly age groups = 0, 1, 2,...10, was added up to gve the total number of vaccnees at age. As the cohort ages, ts ntal number of ndvduals, N 0, dmnshes because of deaths, d. We denote the number of chldren alve at age j by n j = N 0 j d =0. A proporton of deaths v d n, s subtracted from those who were vaccnated, assumng that the lkelhood of dyng s ndependent of the vaccnaton status. To estmate the vaccnaton coverage wth the MMR II, Eq. (1) was adapted to ages between 11 and 16 years old. Epdemologcal model Basc structure The transmsson dynamcs of measles was modelled by a determnstc PSEIR (protected by maternal antbodes, susceptble, exposed, nfectous, recovered) age-structured model [24,25], where the protected compartment has been splt nto two, one for newborns to vaccnated mothers and another for newborns to mothers who became mmune by contact wth the wld vrus; newborns to susceptble mothers enter drectly nto the susceptble compartment. Indvduals are classfed nto cohorts, where each cohort conssts of chldren born at the begnnng of the school year (startng 1st of October). The age of all chldren s ncremented by one year at the end of the school year (30th September). The mean number of brths per year, lfe expectancy and the fertlty functon used n the model (Table 2), were estmated from Portuguese data [26,27]. Epdemologcal parameters (Table 2), were drawn from the lterature [28]. Markowtz et al. [14] demostrated that 98% of chldren born from vaccnated mothers had a serologcal response to measles vaccne at 12 months of age, compared wth 83 90% of chldren born from naturally mmune mothers. Assumng an exponental decay of antbodes, these percentages can be accounted by, respectvelly, a maternal mean antbody duraton of, approxmately 3 and 6 months. The model keeps track of daly changes between epdemologcal compartments wthn each cohort, due to dsease transmsson, dsease recovery, and vaccnaton. The latter was nput based on our estmates of vaccnaton coverage along cohorts, followng the methodology descrbed above, and attemptng the three campagn scenaros n Table 1. Mathematcally, the model s represented by a set of ordnary dfferental equatons (Appendx A), one for each compartment. Transmsson rates The model ncorporated age-dependent force of nfecton and seasonalty drven by the school calendar. The contact patterns of four age groups (0 4, 5 10, 11 20, >20) are descrbed by the Who Acqures Infecton From Whom (WAIFW) matrx [28] presented n the Appendx A. These age groups roughly correspond to the man school grades n Portugal: preschool (0 4 years old), prmary school (5 10 years old), secondary school (11 20 years old), and adults. The structure of the matrx embodes the opnon that the man route of transmsson for measles s whthn the school playground or classroom. There s a unque coeffcent, b(2), descrbng the presumed hgh transmsson among susceptble and nfectous ndvduals of age group 5 10 and other coeffcents, b(1) and b(3), for contacts among ndvduals less than 20 years old whle the older age group s descrbed as lkely to acqure nfecton from a wder range of age groups. Ths structure was used n Schenzle [24] and n Anderson and May [28] to model measles notfcaton data n England and Wales before the ntroducton of mass vaccnaton. Followng prevous authors [24,25,28], we have assumed that the contact rate wthn the 5 10 age group depended upon the school calendar. Transmsson attaned a maxmum n school days and a mnmum n weekends and holdays. We have also assumed that the contact rate n the

5 Dynamcs and control of measles n Portugal 2421 Table 2 Values of demographc and epdemologcal parameters used n the model Parameter Symbol Value References Number of newborns 126,666 per year [26,27] Lfe expectancy 75 years [26,27] Mean duraton of latency 1/ 8 days [28,29] Mean duraton of nfectousness 1/ 5 days [28,29] Mean duraton of passve mmunty due to measles nfecton 1/m 6 months [14,30] Mean duraton of passve mmunty due to vaccne-nduced mmunty 1/p 3 months [14,30] 5 10 years old group was always equal or greater than that n the 0 4 years old group. In Portugal, notfcaton reports of measles started n 1987, 14 years after the begnnng of mass vaccnaton, renderng the drect estmaton of the force of nfecton from notfcatons unfeasble. To crcumvent ths problem, we have ntally approxmated the transmsson rates by numercal values derved from estmates of the basc reproducton numbers used to characterze the transmsson dynamcs of measles n England and Wales (case 1 n Table 3) [24]. The age-specfc basc reproducton number, R 0,, s defned as the average number of secondary nfectons (n all age classes) generated by one prmary case n the th age class, when the populaton s wholly susceptble [28]. Wth ths defnton, N 0 R 0, = ˇj(a j a j 1 ) (2) j=1 where N 0 s the number of newborns, s recovery rate from the nfectous state, and the a j are bounds on dscrete age classes. The transmsson coeffcents ˇj are the elements of the WAIFW matrx, and represent the probablty per unt tme of an effectve contact of ndvduals n age group wth ndvduals n age group j. Eq. (2) can be smplfed by lmtng the number of dstnct elements n the WAIFW matrx, namely, by settng t symmetrc, such that ˇj = ˇj and assumng equal contact rates among selected age groups [24,28]. Assumng that the pattern of R 0 varaton wth age has not been too dfferent across European countres [31], we have adopted the R 0,k values 4.5, 9.0, 3.5, and 3.0, respectvely, for preschool chldren, prmary school chldren, adoles- Table 3 Values for R 0,k and the correspondng b k values Case R 0,k b k (10 6 ) 1 a 4.5, 7, 3.5, , 1.05, 0.10, , 5, 3.5, , 0.41, 0.10, , 12, 3.5, , 2.63, 0.10, , 10, 3.5, , 1.99, 0.10, , 8, 3.5, , 1.36, 0.10, , 9, 3.5, , 1.44, 0.10, b 5, 9, 3.5, , 1.60, 0.10, , 9, 3.5, , 1.28, 0.10, , 9, 5, , 1.32, 0.22, , 9, 4, , 1.64, 0.14, 0.06 a Base lne values gven n Schenzle [24]. b Parameter values selected for Portugal. cents, and adults, whch have been used n Schenzle [24] for England and Wales. We have then calculated four correspondng numercal values for the transmsson parameters, ˇk, that satsfy that baselne R 0,k vector. Furthermore, we have consdered nne addtonal plausble R 0,k sets (Table 3) that are slght modfcatons of the baselne vector, gatherng a total of ten possble R 0,k sets that were used to access the senstvty of model results. The model was run for each R 0,k set untl reachng equlbrum. Those sets yeldng sustaned 2 3-year epdemc cycles, typcal of measles n absence of mass vaccnaton [32], were then selected. The vaccnaton campagn was allowed to start both n epdemc and non-epdemc years. Model valdaton The model was valdated by several crtera. Frst, transmsson parameters were selected to yeld sustaned ncdence oscllatons wth an nter-epdemc perod of 2 3 years. Second, measles ncdence smulated by the model was compared wth case-notfcatons avalable n Portugal for the perod ; attenton was partcularly drected to () the model s ablty to reproduce three epdemc peaks known to have occurred n , , and , and () the ablty to reproduce the fve-fold ncrease observed n case-notfcatons, between pre-epdemc and epdemc peaks. Thrd, the dstrbuton of seropostves by age predcted by the model n 2001, was compared wth the results of the Natonal Serologc Survey conducted n Portugal for Fourth, seasonalty coeffcents (mean devaton between monthly ncdence and overall mean) predcted by the model were compared wth case-notfcaton seasonalty. Fnally, we have compared the ncdence by age n epdemc years predcted by the model wth notfcatons by age n the and epdemcs. The selecton of epdemc years for comparson s meant to avod the nose assocated wth under-reportng and false postves, both known to be more pervasve n nter-epdemc perods [33]. Effectve reproducton number The effectve reproducton number, R e, s defned as the actual mean number of secondary cases produced by a typcal nfectous ndvdual n the populaton. If measles s n endemc equlbrum, one expects R e 1, as each case produces on average one other case, whereas f the nfecton s drven to elmnaton, one expects R e to be consstently below 1. Mathematcally, R e s the largest egenvalue of the followng matrx [34,35]: Dag(S)G (3)

6 2422 A.C. Paulo et al. where Dag(S) s a matrx wth the proporton of susceptble per age group n the man dagonal and G = [g j ]sthe so-called next generaton matrx. The elements g j can be decomposed as g j = ˇj (4) where s the nstantaneous rate of recovery from nfectousness, 1/ s the average duraton of the nfectous perod (wth type I mortalty), and ˇj s the transmsson coeffcent. In the smulatons, R e was computed on a daly bass, by buldng the (4 4) matrx n Eq. (3) and extractng ts largest egenvalue. Control scenaros We have examned the lkely contrbuton of the catch-up campagn to the elmnaton of ndgenous measles n Portugal, and smulated realstc scenaros of measles control, n order to determne whch are lkely to sustan measles elmnaton. In partcular, we have explored the ongong vaccnaton coverage wth the MMR I, ether at 90% or 95%, assumng that ndvduals effectvely mmunzed by vaccnaton stay lfelong mmune. Vaccnaton coverage wth the MMR II was smulated at 10% and 70% of those that remaned susceptble. We have also examned how mportant t s to antcpate the recommended age of the MMR I from 15 to 12 months of age. Vaccne effcacy s assumed to be of 95%. Results Vaccnaton coverage The number of vaccnes aganst measles gven n Portugal ncreased over the years, snce vaccnaton begun n 1973 (Fg. 1), wth peak uptakes observed shortly after 1985, 1989, and 1994, probably a reacton to the epdemc outbreaks that took place n those years. The number of MMR II doses decreased snce ts ntroducton (Fg. 1). Nevertheless, as the effort to accurately target the recommended year olders mproved, estmates of MMR II coverage at 12 years old ncreased from about 20% n the 1979 cohort to above 40% n subsequent cohorts (Fg. 2). It has not been possble to determne what percentage of those that receved the MMR II were already mmune by ether vaccnaton or nfecton. In the years followng the ntroducton of mass vaccnaton, the number of vaccnes was much smaller than the number of newborns, but ths rato changed around 1989 (Fg. 1). Accordngly, at 2 years of age the vaccnaton coverage of the 1975 cohort was around 20%, but coverage gradually ncreased n subsequent cohorts, reachng 80% n the 1989 cohort and remanng above ths value thereafter. Chldren n cohorts born before 1987 were vaccnated at ages older than recommended and consequently, at 7 years of age, the cumulatve coverage of these cohorts almost doubled the cumulatve coverage at 2 years of age (Fg. 2). Vaccnaton coverage wth the MMR II, as accessed at 12 years of age, remaned at low levels, varyng between 20% and 60% between 1991 and 2000 (cohorts ). An unknown proporton of ndvduals were already mmune by Fgure 1 Number of vaccnes aganst measles gven between 1974 and 2000 (dashed lnes) and number of newborns per year over the same tme perod (full lne). We assume that frst dose vaccnes are gven to chldren less then 11 years old and second dose vaccnes are gven to chldren between 11 and 16 years old. the tme they took the MMR II, so the addtonal coverage of susceptbles brought about by the MMR II should be yet lower. Incdence and model valdaton The smulaton results were very senstve to the set of basc reproducton numbers adopted. Only the set number 7 (Table 3), when combned wth scenaro 1 of the vaccnaton campagn (Table 1), produced ncdence patterns resemblng measles epdemology between 1987 and 1998 (Fg. 3). There s a good match between smulated ncdence and notfca- Fgure 2 Vaccnaton coverage of the cohorts wth the MMR I at 2 and 7 years old (bars), and wth the MMR II at 12 years old (dark lne).

7 Dynamcs and control of measles n Portugal 2423 Fgure 3 Incdence of measles per month for the perod between 1967 and 1998, resultng from the model (full lne), and from notfcatons multpled by a factor of 7 (dashed lne). The arrow ponts the begnnng of mass vaccnaton. tons when the latter are amplfed by a factor of seven. Ths can be consdered an estmate of the degree of subnotfcaton of measles and t s concdent wth a prevous estmate of the sub-notfcaton of chckenpox n Portugal [36]. The smulated rato between ncdence n pre-epdemc and epdemc peaks, both n and n , was 1:6.8. Ths s not too dfferent from the 1:5.5 rato calculated drectly from measles notfcatons. The model was also able to reproduce the dstrbuton of measles cases by age group, as observed n a comparson wth notfcatons of the (11,791 notfcatons) and (3230 notfcatons) epdemcs (Fg. 4 A), and n a comparson wth the dstrbuton of seropostves estmated by the Natonal Serologcal Survey (NSS) conducted n (Fg. 4B). The NSS was based on a sample of 851 ndvduals older than 2 years old, attendng a network of health-care clncs present throughout the 18 dstrcts of manland Portugal. Impact of vaccnaton strateges Fg. 5 presents the changng epdemology of measles by age (0 15 years old), between 1967 and 2000, as predcted by the model. Before mass vaccnaton, the susceptble pool was concentrated n 0 5 year olders, wth the majorty of people beng already mmune by 7 8 years old. Oscllatons n the pool of susceptbles, due to the accumulaton of susceptble newborns and ther consumpton by epdemcs, s represented n the lower part of Fg. 5 by the wdenng and narrowng of the whtsh spots. The grey spkes extendng to the top rght n the fgure, represent cohorts wth hgher proportons of susceptbles wthn the 0 15 age range. Wth the ntroducton of mass vaccnaton n 1974, the whtsh areas decrease gradually and susceptblty concentrated ncreasngly n newborns too young to be vaccnated. In the smulatons, the effectve reproducton number exhbt damped oscllatons around 1 untl 1998 (Fg. 6). We Fgure 4 (A) Dstrbuton of measles cases by age class from notfcatons and from the model n the epdemcs of and (B) Dstrbuton of seropostves by age class n the NSS and n the model n The NSS, conducted n , was based on a sample of 851 ndvduals older than 2 years old, attendng a network of health-care clncs present throughout the 18 dstrcts of manland Portugal. fnd that n absence of the catch-up campagn, R e would not have decreased enough to avod a return to 1 and measles would have remaned endemc n Portugal. The model shows how the campagn pulled R e to values around 0.4 n and how ts evoluton n the future depends on the vaccnaton coverage acheved (Fg. 6). Once R e became systematcally lower than 1, an MMR I coverage < 90% s too low to guarantee R e < 1, gven an MMR II coverage of only 10% of those who are susceptble at 6 years old (ether due to MMR I falure or because they were never vaccnated or nfected). In spte of the progress so far made to control measles, a very hgh vaccnaton coverage (>95%) wth the MMR I s stll the most effectve way to mantan herd mmunty n Portugal to a level where R e stays below 1. The smulatons also ndcate that these results are lttle nfluenced by whether the recommended age for the

8 2424 A.C. Paulo et al. Fgure 5 Evoluton between 1967 and 2000 of the proporton of mmune ndvduals snce brth to 15 years old (smulated by the model). MMR I remans at 15 months or s antcpated to 12 months of age (Fg. 7) unless vaccnaton coverage s near 90%. The rato between newborns to vaccnated mothers versus newborns to naturally mmune mothers has been rsng steeply snce the late 1980s (Fg. 8). We estmate that by 2011 t should ht 50%, an estmate that s lttle senstve Fgure 7 Relaton between the effectve reproducton number and dfferent levels of vaccnaton coverage when the age for MMR I s 18 months (full lne), 15 months (dashed lne) or 12 months old (dotted lne). Smulatons corresponds to the case where 60% of newborns are born to vaccnated mothers. to assumptons concernng vaccnaton coverage wth the MMR I so long as t remans wthn realstc lmts (more than 90 98%). Gven the shorter duraton of passve mmunty n newborns to vaccnated mothers, more nfants less than 15 months old wll experence a larger perod durng whch the tter of maternal antbodes falls below a protectve level. At 10 months of age, for example, the prevalence of susceptble chldren s expected to ncrease from 87% to 93% and 96%, respectvely n the cohorts of 1998, 2010, and If vaccnaton coverage decreases to levels around 90%, antcpaton of the age from 15 to 12 months of age should decrease R e below 1 and avod outbreaks. For hgher levels of vaccnaton coverage, f ndgenous measles remans absent, Fgure 6 Smulated evoluton of the effectve reproducton rate R e for measles n Portugal. Values of R e from 1967 to 2000, based on estmates of real vaccnaton coverages n the model. The smulaton shows that n absence of the catchup campagn, R e would have not remaned well below 1. After 2000, R e s smulated under dfferent vaccnaton scenaros. Full lne curves follow the catch-up campagn and represent dfferent coverages wth MMR I and II, respectvely, (a) 9% and 10%, (b) 95% and 10%, (c) 95% and 70%. Dashed lnes llustrate the same three scenaros, from top to bottom, f the catch-up campagn had not taken place. Fgure 8 Evoluton between 1967 and 2036 of the proporton of newborns born to vaccnated mothers. Proportons were calculated based on model smulatons where dfferent vaccnaton coverages are consdered.

9 Dynamcs and control of measles n Portugal 2425 the system wll reach a state where every newborn chld wll be born ether to a vaccnated or to a susceptble mother. In such a lmt stuaton, the antcpaton of the age of MMR I from 15 to 12 months of age should decrease the number of susceptble nfants per day n about 25% (assumng Type I mortalty and average duraton of passve mmunty of 3 months). We have found that ths s not an mportant determnant for sustaned measles elmnaton n Portugal, but t would reduce the lkelhood of nfants beng nvolved n localzed outbreaks trggered by mported cases of measles. Conclusons The vaccnaton coverage n Portugal ncreased consstently snce 1974, as the number of vaccnes gven over tme ncreased and the yearly number of newborns decreased (Fg. 1). Vaccnaton coverage per cohort, evaluated at 2 years of age, was estmated to rse from about 20% n 1974 to current levels at about 95% (Fg. 2). The peak vaccne uptakes observed shortly after 1985, 1989, and 1994 (Fg. 1), probably n reacton to the epdemc outbreaks that took place those years, are also a lkely consequence of the new vaccnaton schemes ntroduced n 1987 (monovalent vaccne was substtuted by the MMR) and 1990 (the two-dose scheme began). The age-structured seasonally-forced model presented here, has the capablty to reconstruct the epdemologcal patterns of measles ncdence n Portugal durng the most recent decades, gven the approprate set of basc reproducton numbers and plausble assumptons about how vaccnaton was dstrbuted over ages and tme. The model reproduces the pre-vaccnaton 3-year nter-epdemc perod, whch had prevously been reported from tme seres analyss of deaths by measles [32], as well as the major outbreaks that took place n , , and As expected, the absolute number of cases over tme, predcted by the model, s much larger than the number of measles notfcatons reported to authortes n Portugal. Indeed, the model suggests that notfcatons underestmate the number of cases by a factor of seven. Ths fgure s concdent wth the concluson by Flemng et al. [36] that chckenpox ncdence s seven tmes hgher than the number of notfcatons reported by the Portuguese sentnel survellance network. The dstrbuton of seropostves by age (>2 years old) produced by the model s n good agreement wth results of the NSS based on blood samples collected n 2002 (Fg. 4B). Both show that the most promnent pool of susceptbles s n the cohorts (20 24 years of age n 2002), wth an estmate of 10% and 14% susceptbles, respectvely, n the model and n the NSS. Cohorts from 1974, the year that correspond to the ntroducton of vaccnaton, untl 1983 were shown to have low vaccnaton coverages (Fg. 1) whch alled to smaller outbreaks (Fg. 3) cause ths ncrease n susceptblty. Nonetheless, durng the years from 1974 to 1977, there was supplementary vaccnaton due to the catch-up campagn held between 1973 to 1977, makng ths cohorts less susceptble then the 1978 to 1982 ones. The model ndcates that the catch-up campagn, put nto place by health authortes to avod an outbreak projected for , created condtons to brng the effectve reproducton number of measles to values contnuously below 1. The smulatons thus support the clam that the reduced notfcaton of suspected cases of measles n Portugal snce 2002, and the absence of laboratory confrmed cases, s a consequence of the nterrupton of ndgenous measles transmsson n Portugal snce the late 1990s. Outbreaks lnked to mported cases are lkely to contnue to occur as long as measles remans endemc n parts of the world. Importatons to well mmunzed countres wll affect susceptble nfants and prevously vaccnated ndvduals whose mmunty may not be complete. The capacty to keep mported cases from trggerng endemc dsease resurgence, s very much dependent on our ablty to mantan a very hgh level of vaccnaton coverage (>95%) wth the MMR I. Ths concluson remans vald, rrespectve of whether the vaccne s gven at 12 or 15 months, and s lttle senstve to changes n realstc levels of vaccnaton coverage wth the MMR II. It s also n agreement wth prevous theoretcal results on how crucal t s to keep hgh levels of frst-dose coverage n two-dose vaccnaton schemes aganst chldhood dseases [19]. The antcpaton of the age of the MMR I has a sgnfcant mpact on global transmsson levels for a narrow band of vaccnaton coverage around 90%. Below ths level of vaccnaton R e wll be above 1 rrespectve of whether the age for MMR I s antcpated or not. Also f the level of vaccnaton coverage s above ths band the reproducton number s always below 1. Ths result dffers from other authors [37] who consdered the contact rate n the frst age group (0 4 years old) the lowest one. In our case ths s the second hghest contact rate, whch s n accordance wth the hgh rates of attendance of very young nfants (from 4 months old) to daycare centers n Portugal. In concluson, Portugal s expected to reman free of endemc measles transmsson f the present socal and demographc condtons are mantaned and levels of vaccnaton coverage wth the MMR I reman above 95%, together wth tmelness n the applcaton of the recommended schedule. The greatest threat to measles elmnaton n countres lke Portugal s reduced complance wth vaccnaton n face of a false sense of securty created by absence of publczed outbreaks over the years. The longer the communty goes wthout crculatng measles vrus, the more strct publc health offcals must be n handlng mported cases and fghtng the tendency to lower defences aganst what mght become perceved as a dsease of the past to the eyes of health workers and the general publc. Acknowledgements We thank Frank Hlker and Natala Mantlla-Beners for ther valuable comments. AC Paulo was funded by FCT/POCTI- III Quadro Comuntáro de Apoo, grant SFRH/BPD/7160/2001 and MGM Gomes by the European Comsson, grant MEXT-CT Appendx A. Model descrpton We have used an age-structured model wth sx epdemologc compartments: maternally protected newborns, splt

10 2426 A.C. Paulo et al. nto newborns to vaccnated mothers (M) and newborns to naturally mmune mothers (P), susceptbles (S), exposed (E), nfectous (I), and recovered (R) ndvduals. Newborns enter cohorts defned by the academc year (1st October to 30th September), movng altogether to the next year of age at the begnnng of a new academc year. A total of 75 cohorts were ntated wth n 0 = 126, 666 newborns. Those born to susceptble mothers enter drectly nto the susceptble compartment, whereas newborns wth passve mmunty enter the approprate maternally protected compartment. The model keeps track of daly changes of ndvduals between epdemologcal compartments throughout the year, usng a 4th order Runge Kutta approxmaton. The smplfed model equatons used throughout the whole school year are formalzed as For = 0, 1 dp dt = pp dm dt = mm ds 0 dt = (a, t)s 0 + pp 0 + mm 0 ds 1 dt = (a, t)s 1 + pp 1 + mm 1 ϕ 1 S 1 for = 2,...,74 ds dt = (a, t)s ϕ S else, for = 0,...,74 de dt = (a, t)s E di dt = E I dr dt = I dv dt = ϕ S Intal condtons are defned every year as: P 0 = n o ( f S + f V ) M 0 = f V S 0 = f S Also, E 0 (0) = I 0 (0) = R 0 (0) = V 0 (0) = 0 and P (0) = M (0) = S (0) = E (0) = I (0) = R (0) = V (0) = 0 After runnng the dfferental equatons for 365 days, the ntal values are update as: P 1 (0) = P 0 (365) M 1 (0) = M 0 (365) For = 2,...,74 P (t) = M (t) = 0 and for = 1,...,74 S (0) = S 1 (365) E (0) = E 1 (365) I (0) = I 1 (365) R (0) = R 1 (365) V (0) = V 1 (365) Here m and p are the rates of loss of protecton by maternal antbodes n newborns to, respectvely, vaccnated and naturally mmunzed mothers. Indvduals leave the susceptble compartment ether by vaccnaton at rate ϕ, that depends on age a and tme t, or by nfecton at a rate defned by the force of nfecton (a, t). Once nfected, ndvduals become latent and then nfectous at rate, recoverng from nfectousness at rate. Indvduals who become mmune, ether by vaccnaton or natural nfecton, are assumed to stay mmune lfelong. Numercal values for the parameters are lsted n Table 2. The force of nfecton s defned by the functon, (a, t) = 4 b(a)i(a, t) a=1 (A.1) where b(a) s the age-related transmsson rate (number of contacts per unt tme). I(a, t) s the number of nfectous ndvduals n age group a at tme t. Age groups are defned as 0 4, 5 10, and more then 20 years. The force of nfecton depends on the WAIFW (Who Acqures the Infecton From Whom) matrx, a way of representng assumptons about how ndvduals mx among ages [24,28]. We have used a WAIFW matrx that conveys the common opnon that the man route of transmsson takes place n prmary schools (5 10 years old chldren). The structure of the WAIFW matrx was defned as n Schenzle [24] and Anderson and May [28], b(1) b(1) b(3) b(4) b(1) b(2) b(3) b(4) WAIFW = b(3) b(3) b(3) b(4) b(4) b(4) b(4) b(4) There s a unque coeffcent (b(2)) descrbng the transmsson among susceptble and nfectous n age group 2 and there are two other coeffcents, b(1) and b(3), for the contacts among ndvduals aged less then 21 years; whereas adults are descrbed as beng lkely to acqure nfecton from a wder range of age groups. We further use a symmetry relaton, ndcatng that ndvduals n age group j make contact wth ndvduals n age group at the same rate as ndvduals n the latter group make contact wth those n the former. Transmsson n the 5 10 age group, b(2), takes a mnmum value (equal to b(1)) every Sunday, durng Chrstmas holdays (23rd of December to January the 7th), Easter holdays

11 Dynamcs and control of measles n Portugal 2427 (11th to 25th of Aprl) and durng the summer holdays (14th of July to the 7th of October). The set of values used for the WAIFW matrx elements are n Table 3. The adopted structure fts the pattern found by Del Valle et al. [38] when studyng contact patterns that determne the transmsson of ar born dseases. To compute the number of newborns through tme as a functon of women s age, we have used the fertlty functon f estmated for Portugal n 1994 [26], defned as the average number of chldren per women at age. We assumed that all ndvduals de as they reach the age of 75 years (type I mortalty). References [1] Drecção Geral de Saúde. Doenças de Declaração Obrgatóra, Lsboa: Drecção Geral da Saúde, Mnstéro da Saúde; [2] Andrade HR, Gíra M. Vírus do sarampo. In: Avalação Naconal de Vacnação. 2 Inquérto Serologco Naconal, Portugal Contnental Mnstéro da Saúde. Lsboa 2004: [3] Spka JS. Measles elmnaton 2010 target: the need to meet the specfc rsk group. Euro Survell 2006;11(10), [4] Atknson P, Cullnan C, Jones J, Fraser G, Magure H. Large outbreak of measles n London: reversal of health nequaltes. Arch Ds Chld 2005;90(4): [5] Perucha M, Ramalle-Gómara E, Lezaun ME, Blanco A, Qñones C, Blasco M, et al. A measles outbreak n chldren under 15 months of age n La Roja, Span, Euro Survell 2006;11: [6] Sedler A, Tsher A, Mankertz A, Santbanez S. Two outbreaks of measles n Germany. Euro Survell 2006;11(4): [7] Stefanoff P, Czarkowsk MP. Unexpected rse n measles ncdence n Poland n 2006 may be related to Ukranan outbreak. Euro Survell 2006;11(6). E [8] Georgakopolou T, Gryll C, Kalamara E, Katerelos P, Spala G, Panagotopoulos T. Current measles outbreak n Greece. Euro Survell 2006;11(2). E [9] Burstrom B, Aaby P, Mute DM. Chld mortalty mpact of a measles outbreak n a partally vaccnated rural Afrcan communty. Scand J Infect Ds 1993;25: [10] Rodgers DV, Gndler JS, Atknson WL, Markowtz LE. Hgh attack rates and case fatalty durng a measles outbreak n groups wth relgous exempton to vaccnaton. Pedatr Infect Ds J 1993;12: [11] Wood DL, Brunell PA. Measles Control n the Unted States:problems of the past and challenges for the future. Cln Mcrobol Rev 1995;8(2): [12] Papana M, Baughman AL, Lee S, Cheek JE, Atknson W, Redd S, et al. Increased susceptblty to measles n nfants n the Unted States. Pedatrcs 1999;104(5):59. [13] Maldonado YA, Lawrence EC, DeHovtz R, Hartzell H, Albrecht P. Early loss of passve measles antbody n nfants of mothers wth vaccne-nduced mmunty. Pedatrcs 1995;96(3): [14] Markowtz LE, Albrecht P, Rhodes P, Demonteverde R, Swnt E, Maes EF, et al., Kaser Permanent Measles Vaccne Tral Team. Changng levels of measles antbody tters n women and chldren n the Unted States: mpact on response to vaccnaton. Pedatrcs 1996;97(1):53 8. [15] De Serres G, Joly JR, Fauvel M, Meyer F, Masse B, Boulanne N. Passve mmunty aganst measles durng the frst 8 months of lfe of nfants born to vaccnated mothers or to mothers who sustaned measles. Vaccne 1997;15(6 7): [16] Szenborn L, Tscher A, Pejcz J, Rudkowsk Z, Wojk M. Passve acqured mmunty aganst measles n nfants born to naturally nfected and vaccnated mothers. Med Sc Mont 2003;9(12). CR [17] CDCP. Centers for Dsease Control and Preventon. General recommendatons on mmunzaton. MMWR CDC Survell Summ 1994; 43. No RR-1:8 12. [18] Gomes MC, Gomes J. Projecções para a ncdênca do sarampo em Portugal até ao ano Saúde de em Números 1998;13(1):1 3. [19] Paulo AC, Gomes MC, Casnhas AC, Horta A, Domngos T. Vaccnaton aganst chld dseases wth mult-doses of vaccne: a general analytcal soluton of lnear compartment models. IMA J Math Appl Med Bol 2000;17:1 12. [20] Insttuto Naconal Estatístca. Estatístcas da Saúde. Lsboa: Insttuto Naconal de Estatístca; [21] Letão A. Sarampo em Portugal Alguns aspectos do surto epdémco. Boletm Epdemológco do Insttuto Naconal de Saúde Rcardo Jorge 1989; 4:1 13. [22] Lma G. O sarampo que anda temos. Saúde em Números 1996;11(2):9 14. [23] Fne P, Clarkson J. Measles n England and Wales II: the mpact of measles vaccnaton programme on the dstrbuton of mmunty n the populaton. Int J Epdemol 1982;11(1): [24] Schenzle D. An age-structured model of pre- and postvaccnaton measles transmsson. J Math Bol 1984;1: [25] Babad HR, Nokes DJ, Gay DJ, Mller E, Morgan-Capner P, Anderson RM. Predctng the mpact of measles vaccnaton n England and Wales: model valdaton and analyss of polcy optons. Epdemol Infect 1995;114: [26] Insttuto Naconal Estatístca. Estatístcas Demográfcas. Lsboa: Insttuto Naconal de Estatístca; [27] Insttuto Naconal Estatístca. Estatístcas Demográfcas. Lsboa: Insttuto Naconal de Estatístca; [28] Anderson RM, May RM. Infectous Dseases of Humans. Oxford: Oxford Unversty Press; [29] Isselbacher KJ, Braunwald E, Wlson JD, Martn JB, Fauc AS, Kasper DL, edtors. Harrnson s Prncples of Internal Medcne. MacGraw-Hll, Inc.; [30] Leurdan E, Van Damme P. Passve transmsson and persstence of naturally acqured or vaccne-nduced maternal antbody aganst measles n newborns. Vaccne 2007;25: [31] Edmunds WJ, Gay NJ, Kretzschmar M, Pebody RG, Wachmann H. The pre-vaccnaton epdemology of measles, mumps and rubella n Europe: mplcatons for modellng studes. Epdemol Infect 2000;125(3): [32] Gomes MC, Gomes JJ, Paulo AC. Dphthera, pertusss, and measles n Portugal before and after mass vaccnaton: a tme seres analyss. Eur J Epdemol 1999;15(9): [33] Brown D, Ramsay MEB, Rchards AF, Mller E. Salvary dagnoss of measles: a study of notfed cases n the Unted Kngdom, BMJ 1994;308(6935): [34] Dekmann O, Heesterbeek JAP, Metz JAJ. On the defnton and the computaton of the basc reproducton rato R 0 n models for nfectous dseases n heterogeneous populatons. J Math Bol 1990;28: [35] Wallnga J, Lévy-Bruhl D, Gay NJ, Wachmann CH. Estmaton of measles reproducton ratos and prospects for elmnaton of measles by vaccnaton n some Western European countres. Epdemol Infect 2001;127(2): [36] Flemng DM, Schellevs FG, Falcão I, Alonso TV, Padlla FL. The ncdence of chckenpox n the communty. Eur J Epdemol 2001;17(11): [37] Mossong J, Muller CP. Modellng measles re-emergence as a result of wanng of mmunty n vaccnated populatons. Vaccne 2003;21(31): [38] Del Valle SY, Hyman JM, Hethcote HW, Eubank SG. Mxng patterns between age groups n socal networks. Socal Networks 2007;29(4):