4 Department of Statistic and Economical applied

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1 Scenaros of dffuson and control of an nfluenza andemc n Italy C. Rzzo 1,2, A. Lunell 3, A. Puglese 3, A. Bella 1, P. Manfred 4, Ganaolo Scala Tomba 5, M. Iannell 3, M.L. Cof degl Att 1 on behalf of the EPICO workng grou 1 Natonal Centre for Edemology Survellance and Health Promoton, Isttuto Suerore d Santà, Rome, Italy; 2 Deartment of Pharmaco-Bology, Unversty of Bar, Italy; 3 Deartment of Mathematcs, Unversty of Trento, Italy; 4 Deartment of Statstc and Economcal aled Mathematcs, Unversty of Psa, Italy; 5 Deartment of Mathematcs, Unversty of Tor Vergata, Roma, Italy. Corresondng Author: Caterna Rzzo Natonal Centre for Edemology, Survellance and Health Promoton Isttuto Suerore d Santà Vale Regna Elena, 299 Rome, Italy Tel: , Fax: , e-mal: caterna.rzzo@ss.t Runnng head: Influenza andemc dffuson and control Author s contrbutons CR, and MLCdA desgned the study and contrbuted equally to nterretng the results, draftng and edtng the manuscrt. AL and AP desgned and mlemented the model and ran the smulatons. AB, PM, GST and MI contrbuted to nterretng the results, and to edtng the manuscrt. 1

2 Abstract To redct the sread of a andemc stran of nfluenza vrus n Italy and the mact of control measures, we develoed a SEIR determnstc model wth a stochastc smulaton comonent. We modelled the mact of control measures such as vaccnaton, antvral rohylaxs and socal dstancng measures. In the absence of control measures, the edemc eak would be reached aroxmately 4 months after the mortaton of the frst cases n Italy, and the edemc would last aroxmately 7 months. When combned, the control measures would reduce the cumulatve attack rate to aroxmately 4.2%, at best, though ths would requre an extremely hgh number of treated ndvduals. In accordance wth nternatonal fndngs, our results hghlght the need to resond to a andemc wth a combnaton of control measures. 2

3 INTRODUCTION Followng the emergence n 1997 of a new stran of avan nfluenza, A(H5N1), whch s caable of nfectng humans (1), and the sread of ths stran to Euroe n 2005 (2), concerns were rased over the occurrence of a andemc caused by A(H5N1) or a closely related stran (3;4). Consequently, countres have been urged to strengthen ther rearedness for an nfluenza andemc (5), an mortant asect of whch s redctng the sread of nfecton. Accordng to the redctve models used to date (6-12), nfluenza would sread worldwde over a erod of 2 to 6 months, deendng on the basc reroductve number (R 0 ), and reducng transmsson would ental combnng control measures, secfcally, reducng contacts and erformng both antvral rohylaxs (AVP) and vaccnaton (7-9;11;13). We develoed an SEIR (suscetble exosed, but not yet nfectous - nfectous recovered, and no longer suscetble) determnstc model wth a stochastc smulaton comonent to redct the sread of andemc nfluenza n Italy and to evaluate the mact of vaccnaton, AVP and socal dstancng measures. METHODS The SEIR model We develoed an SEIR model n whch the oulaton s structured accordng to age and regon of resdence. We defned sx age classes: nfants 0-2 years of age, chldren 3-14 years of age, teenagers years of age, young adults years of age, adults years of age and elderly aged 65 and older. In the model, the natonal oulaton (56,995,744 nhabtants) was also dstrbuted n Italy s 20 regons, accordng to natonal demograhc data obtaned from the 2001 Census (14). The contact matrx was defned by consderng, searately, household, school/work-lace and random contacts, and by usng data on household comoston, school attendance, and emloyment status. The transortaton matrx was defned usng data on natonal arlne traffc (15). The model conssts of a system of dfferental equatons, reorted n the Aendx. 3

4 We also ntroduced a stochastc comonent that takes nto account all of the random effects that are mortant durng a andemc s ntal and fnal stages, when the number of nfected ndvduals would be low. Precsely, whenever the determnstc redcton of the number of nfected ndvduals n an age class/regon was below the threshold value of 10, t was relaced by a Posson varable wth the same mean. In each smulaton, the andemc began wth the ntroducton of 5 nfected adults n the Lazo Regon, where Rome s ntercontnental arort s located. Based on ublshed studes (16) and usng the method descrbed by Dekmann et al. (17), we comuted the R 0 =1.8, whch, when alyng the contact matrx, corresonds to a cumulatve nfected attack rate (AR) of 35%. Based on the lterature (6;8;17), n the model we assumed an ncubaton erod of 1 day and an nfectous erod of 3.9 days. The results were obtaned by averagng over 200 smulatons for each scenaro. For all of the results, the 5-95% ercentle values of the AR estmates were wthn 11%. Control measures We consdered both sngle and combned control measures, most of whch are ncluded n the Italan Natonal Plan for rearedness and resonse to an nfluenza andemc (19). We assumed that two doses of vaccne would be admnstered, one month aart. The target oulaton was dvded nto 4 categores: ) ersonnel rovdng essental servces (15% of the year-old workng oulaton) (14); ) elderly ersons (!65 years); ) chldren and adolescents aged 2-18 years; and v) adults aged years. We assumed vaccnaton coverage of 60% of the target oulaton, based on the natonal nfluenza coverage (20). We assumed that a erod of two weeks would be necessary for admnsterng the vaccne to each target category. For vaccne effectveness (VE) we made two dfferent assumtons: ) VE of 70% for all categores; and ) VE of 50% for all categores; for both assumtons, we assumed that the VE would be reached begnnng 15 days after the second dose. We consdered dfferent scenaros of vaccne avalablty; n one scenaro, adequate VE would be reached 4 months after the frst natonal case; n the second scenaro, t would be reached after 5 4

5 months. An adequate VE at 4 months would be feasble only f the frst dose contaned an avan vrus recursor of the andemc stran (3), followed by a dose of andemc vaccne; the actual VE of ths regmen was assumed to be equal to that of two doses of the andemc vaccne. The AVP for unnfected ndvduals was assumed to reduce suscetblty by 30% and nfectousness by 70% (8). We consdered the admnstraton of one course of antvral drugs. We assumed that AVP would be rovded to all household contacts of 80% of the clncal cases (66% of all nfected ndvduals). We consdered admnsterng AVP for the entre edemc erod; however, snce the feasblty of actually dong ths would be lmted, we also consdered other scenaros, that s, admnsterng AVP only for 2, 4, 8, or 16 weeks after the occurrence of the frst Italan case. AVP was assumed to reduce the transmsson rate among household contacts, based on the consderaton that those household contacts already nfected at the tme of begnnng AVP would have a reduced nfectousness, so that t would be as f only a fracton of them were actually nfected; those not yet nfected when begnnng AVP would beneft from both lower suscetblty and lower nfectousness. We consdered the natonwde closng of all schools, ublc offces, and ublc gatherng laces (e.g., restaurants, cnemas, and churches). We smulated school closure for 3 weeks, ublc-offce closure for 4 weeks, and ublc gatherng-lace closure for 8 weeks. We assumed that these measures would be ntroduced smultaneously at dfferent tmes (.e., 2, 4 or 8 weeks after the start of the andemc). In the model, school closure would reduce the contacts among chldren and teenagers (the school comonent of the transmsson rate) by 75%; worklace closure would reduce the job comonent of the transmsson rate by 16%; closure of ublc gatherng laces would reduce the random comonent of the transmsson rate by 50%. Senstvty analyss We evaluated how the results would change deendng on dfferent levels of athogen transmssblty, wth a resultng R 0 of 1.6, 1.8 or 2.0. We also consdered the resultng AR for the 5

6 three R 0 values for the baselne scenaro and for scenaros that dffered n terms of the secfc control measures adoted. RESULTS Baselne dynamcs In the absence of control measures, the edemc eak would be reached aroxmately 4 months after the dentfcaton of the frst case, wth a total of 3 mllon cases durng the eak week. The edemc would be over n 7 months, wth a cumulatve nfected AR of 35% (aroxmately 20 mllon cases). The dynamcs of the edemc were smlar n all age-grous, whereas the cumulatve nfected AR vared markedly by age-grou. The ncdence would be artcularly hgh among year-olds, wth a cumulatve nfected AR of 54% (Fgure 1). Because of the model s stochastc comonent, the ntroducton of few nfectous ndvduals n the oulaton dd not always result n an outbreak; n fact, n around 40% of the smulatons, the number of nfected ndvduals n the early stages of the andemc was nsuffcent for sustanng transmsson, and the edemc exred sontaneously. Sngle control measures The mact of sngle control measures s shown n Table 1. The ntroducton of control measures frequently ncreased the robablty of stochastc extncton of the andemc. Vaccnaton seems to be the most effectve measure, esecally when VE s reached at 4 months. Vaccnatng three of the four target categores (.e., ersonnel rovdng essental servces; elderly ersons; and 2-18 yearolds) would reduce the cumulatve nfected AR from 35% to 25%, wth almost 5 mllon cases avoded by treatng aroxmately 17 mllon ndvduals. Vaccnatng also the fourth target category (.e., year-olds) would not result n an mortant addtonal reducton n the cumulatve nfected AR. If rotectve VE were reached at 5 months (2 doses of andemc vaccne), vaccnatng all four categores, the cumulatve nfected AR would be 32.5%. Assumng a VE of 50% for all categores would not greatly affect the cumulatve nfected AR; n fact, the cumulatve 6

7 nfected AR would be only 2 or 3 ercentage onts hgher than the AR when assumng a 70% VE for all categores (Table 1). Socal dstancng measures and AVP were not effectve n reducng the cumulatve nfected AR. However, rovdng AVP for 16 weeks after the dentfcaton of the frst Italan cases and mlementng socal dstancng measures startng at week 4 or 8 would delay the edemc eak by one or three weeks, resectvely. Combned control measures The combnaton of control measures would be more effectve than sngle measures (Table 2 and Table 3). The hghest reducton (from 35% to 4.2%) would be obtaned by startng socal dstancng measures at week 4, rovdng AVP for the entre edemc, and erformng vaccnaton wth a VE of 70% at 4 months (when combnng measures, we assumed that vaccnaton would be rovded to all categores). Ths would allow for 17 mllon cases to be avoded by vaccnatng around 26 mllon ndvduals and by rovdng AVP to aroxmately 3 mllon ndvduals. The cumulatve nfected AR would be hgher (11%) f VE were reached at 5 months, avodng 13 mllon cases by treatng 25 mllon ndvduals and 7 mllon ndvduals wth vaccne and AVP resectvely (Table 2). Provdng AVP for 16 weeks, nstead of for the entre edemc erod, would ncrease the cumulatve nfected AR to 8.4% or 16.6% f VE were reached at 4 or 5 months, resectvely. However, ths would determne an mortant reducton n the number of treated ndvduals (aroxmately 150,000). Combnng control measures would also ncrease the robablty of stochastc extncton durng the ntal hases of the edemc, due to a low number of nfectous ndvduals. A VE of 50% for all categores consdered would affect the cumulatve nfected AR estmates, but only when consderng adequate VE at 4 months. In fact, the cumulatve nfected AR would be 6 to 8 ercentage onts hgher than the AR assumng a VE of 70%, wth a remarkable dfference n terms of the number of avoded cases (Table 3). The mact of combned control measures (re-andemc vaccne n all categores and AVP and/or socal dstancng measures), comared to the baselne dynamcs of the nfluenza andemc, s shown n Fgure 2. 7

8 Senstvty analyss The results of the senstvty analyss are shown n Fgure 3. For R 0 =1.6, the edemc could be mtgated wth moderate efforts; all strateges would be successful ndeendently of the tmng of vaccnaton, of the duraton of rovdng AVP, and of the tmng of socal dstancng measures. For R 0 =1.8, vaccnatng the target categores wth a re-andemc vaccne, rovdng AVP for 16 weeks, and mlementng socal dstancng measures for 4 weeks would reduce the cumulatve nfected AR from 35% to10%. For R 0 =2, ths combnaton of control measures would result n a less marked decrease n the cumulatve nfected AR, from 42% to aroxmately 20%. CONCLUSIONS Our results, consderng an R 0 value of 1.8, confrmed the need to combne dfferent control measures (7-9). In fact, none of the sngle measures was shown to be effectve n contanng the andemc, wth the cumulatve nfected AR decreasng at most from 35% to 24%. Combnng measures would be more effectve, esecally f usng the re-andemc vaccne (reachng VE at 4 months). In ths case, the cumulatve nfected AR would be 4.2%, but ths would requre an extremely hgh number of AVP doses. Provdng AVP for 16 weeks only would ncrease cumulatve nfected AR to 8.4%, whch s smlar to what observed durng severe seasonal edemcs (21), wth a consderable reducton n the number of doses rovded. Moreover, f the tme to reach adequate VE were 5 months, assumng a dfferent VE (.e., 70% or 50% n all categores) would not substantally affect the cumulatve nfected AR. However, f the tme to reach adequate VE were 4 months, a VE of 70% would result n an AR of 4.2%, comared to 11.0% f assumng a VE of 50% (.e., a 50% dfference n the AR). In any case, usng a less effectve vaccne (.e., wth a VE of 50%) would nonetheless allow the andemc to be contaned, wth an AR below 18% (range %). Combnng dfferent measures markedly ncreased the robablty of stochastc extncton durng the early hases of the andemc. To the best of our knowledge, most of the SEIR models used to 8

9 smulate a andemc do not consder the stochastc factors, whch can strongly nfluence the dynamcs of the andemc n ts early hases. However, we assumed that no other nfectous ndvduals would enter the country after the few ntal cases. If we were to assume that nfectous ndvduals contnued to enter the country, then stochastc extncton would be less mortant. Another mortant fndng s that the decrease n the cumulatve nfected AR would deend on whch target grous were vaccnated. If a andemc were to occur, vaccne sules would be lmted and the target grous would have to be rortzed (.e., ersonnel of essental servces, elderly ersons and ersons wth chronc dsease, chldren and young adults, and healthy adults) (19), requrng the vaccnaton of 26 mllon ersons wth two doses, that would be very dffcult to ut n ractce f a andemc wll occur. However, as reorted n other studes (9), our results showed that, ndeendently of the VE, the vaccnaton of chldren and young adults would consderably reduce the ncdence also n other age grous (.e., resultng n herd mmunty ), robably because of the mortant role of chldren and adolescents n the sread of nfluenza, as also observed n nter-andemc erods (22). In nterretng our results, some lmtatons need to be consdered. Frstly, we assumed that AVP rovded to household contacts would decrease transmsson wthn households but not n other contexts, whch could have resulted n an underestmate of the effect of ths measure. Secondly, the arameters used n our model obvously nfluenced the tme estmated for the andemc to evolve, though our estmate s smlar to those obtaned n other studes based on determnstc SEIR models on a global (13) or local (23) scale or ndvdual-based models (6-9). We examned ths ssue by erformng a senstvty analyss; clearly, the success of control strateges would be strongly nfluenced by the R 0 : for R 0 =1.6, all strateges would be qute successful, whereas for R 0 =2 only the combned strategy wth a re-andemc vaccne would satsfactorly mtgate the andemc. Although the absolute effect of control strateges s strongly nfluenced by the dfferent values of R 0, the relatve worth of strateges are ndeendent from the dfferent R 0 values. 9

10 Another mortant lmtaton s that mathematcal models cannot take nto account the fact that the ast nfluenza andemcs n Euroe and Italy occurred over two consecutve wnters, wth the hghest AR n the second wnter (24-26). Ths two-wave attern s robably an effect of the closng of schools durng the summer. Thus our model robably dects a worst case scenaro, whch could be useful n evaluatng control measures (9). Our smulatons show that arorate and romt measures, when combned, could be effectve n contanng an nfluenza andemc. Tmng s also essental, and measures that at frst glance aear to be less mortant, such as ncreasng socal dstancng, could be extremely useful n delayng the edemc eak and thus rovdng more tme for vaccnes to be roduced. Imlementng such measures, however, would ental organzng a varety of both medcal and non-medcal resources, and some measures, such as the closng of schools, would also have a socal mact. 10

11 Table 1. Effectveness of sngle control measures on the dynamcs of an nfluenza andemc wth an R 0 of 1.8 and an attack rate of 35%, for dfferent values of vaccne effectveness (VE) Control Measures Attack rate* Avoded cases Treated ndvduals Adequate vaccne effectveness at 5 months (VE=70%) Category I and II 33.0% ( ) 974,151 12,076,619 Category I, II, III 32.6% ( ) 1,203,363 17,006,817 Category I, II, III, IV 32.5% ( ) 1,260,666 25,542,092 Adequate vaccne effectveness at 4 months (VE=70%) Category I and II 28.9% ( ) 3,323,574 12,076,619 Category I, II, III 25.3% ( ) 5,386,482 17,279,633 Category I, II, III, IV 24.4% ( ) 5,902,209 25,814,908 Adequate vaccne effectveness at 5 months (VE=50%) Category I and II 33.4% ( ) 744,939 12,076,619 Category I, II, III 33.0% ( ) 974,151 17,008,452 Category I, II, III, IV 33.0% ( ) 974,151 25,543,727 Adequate vaccne effectveness at 4 months (VE=50%) Category I and II 30.4% ( ) 2,464,030 12,076,619 Category I, II, III 27.5% ( ) 4,125,818 17,278,523 Category I, II, III, IV 26.6% ( ) 4,641,545 25,814,799 Antvral 2 weeks 34.7% ( ) weeks 34.7% ( ) weeks 34.7% ( ) 0 12, weeks 33.9% ( ) 458,424 2,993,052 Entre edemc 29.6% ( ) 2,922,454 18,758,578 Socal dstancng measures From week % ( ) 0 not alcable From week % ( ) 0 not alcable From week % ( ) 343,818 not alcable *Value n brackets reresent the 5-95 ercentle values of the Attack Rate estmates 11

12 Table 2. Effectveness of combned control measures on the dynamcs of an nfluenza andemc wth an R 0 of 1.8 and an attack rate of 35%, wth 70% vaccne effectveness (VE) Treated ndvduals Interventons Attack rate* Avoded cases Wth vaccne Wth antvral Adequate vaccne effectveness at 5 months (VE=70%) Socal dstancng measures from week 2 Socal dstancng measures from week 4 Antvral for 2 weeks. 24.6% ( ) 5,787,603 25,821, Antvral for 4 weeks. 23.6% ( ) 6,360,633 25,825, Antvral for 8 weeks. 22.1% ( ) 7,220,178 25,831, Antvral for 16 weeks. 18.3% ( ) 9,397,697 25,837, ,992 Antvral for the entre edemc. 13.0% ( ) 12,434,757 25,837,928 8,224,930 Antvral for 2 weeks. 23.7% (15,1-28.5) 6,303,330 25,824, Antvral for 4 weeks. 22.7% ( ) 6,876,360 25,828, Antvral for 8 weeks. 20.5% ( ) 8,137,026 25,835, Antvral for 16 weeks. 16.6% ( ) 10,371,848 25,837, ,521 Antvral for the entre edemc. 11.3% ( ) 13,408,909 25,837,928 7,177,152 Adequate vaccne effectveness at 4 months (VE=70%) Socal dstancng measures from week 2 Socal dstancng measures from week 4 Antvral for 2 weeks. 12.6% ( ) 12,663,963 25,837, Antvral for 4 weeks. 11.9% ( ) 13,065,084 25,837, Antvral for 8 weeks. 10.9% ( ) 13,638,114 25,837, Antvral for 16 weeks. 9.0% ( ) 14,726,878 25,837, ,028 Antvral for the entre edemc. 5.0% ( ) 17,018,999 25,837,928 3,193,698 Antvral for 2 weeks. 12.0% (7,9-15,9) 13,007,781 25,837, Antvral for 4 weeks. 11.5% ( ) 13,294,296 25,837, Antvral for 8 weeks. 10.1% ( ) 14,096,538 25,837,928 1,690 Antvral for 16 weeks. 8.4% ( ) 15,070,696 25,837, ,056 Antvral for the entre edemc. 4.2% ( ) 17,477,424 25,837,928 2,673,736 *Value n brackets reresent the 5-95 ercentle values of the Attack Rate estmates 12

13 Table 3. Effectveness of combned control measures on the dynamcs of an nfluenza andemc wth an R 0 of 1.8 and an attack rate of 35%, wth 50% vaccne effectveness (VE) Treated ndvduals Interventons Attack rate* Avoded cases Wth vaccne Wth antvral Adequate vaccne effectveness at 5 months (VE=50%) Socal dstancng measures from week 2 Antvral for 2 weeks. 26.4% ( ) 4,756,151 25,821, Antvral for 4 weeks. 26.0% ( ) 4,985,363 25,826, Antvral for 8 weeks. 25.0% ( ) 5,558,394 25,830, Antvral for 16 weeks. 22.1% ( ) 7,220,182 25,837, ,992 Antvral for the entre edemc. 16.5% ( ) 10,429,151 25,837,928 10,494,921 Antvral for 2 weeks. 26.0% ( ) 4,985,363 25,824, Socal dstancng measures from week 4 Antvral for 4 weeks. 25.4% ( ) 5,329,182 25,828, Antvral for 8 weeks. 23.8% ( ) 6,246,030 25,835, Antvral for 16 weeks. 20.9% ( ) 7,907,818 25,837, ,520 Antvral for the entre edemc. 15.4% ( ) 11,059,485 25,837,928 9,763,649 Adequate vaccne effectveness at 4 months (VE=50%) Socal dstancng measures from week 2 Socal dstancng measures from week 4 Antvral for 2 weeks. 18.1% ( ) 9,512,302 25,837, Antvral for 4 weeks. 17.7% ( ) 9,741,515 25,837, Antvral for 8 weeks. 17.3% ( ) 9,970,727 25,837, Antvral for 16 weeks. 16.2% ( ) 10,601,060 25,837, ,341 Antvral for the entre edemc. 11.4% ( ) 13,351,606 25,837,928 7,232,024 Antvral for 2 weeks. 17.9% (15,9-20.3) 9,626,909 25,837, Antvral for 4 weeks. 17.6% ( ) 9,798,818 25,837, Antvral for 8 weeks. 16.9% ( ) 10,199,939 25,837,928 1,664 Antvral for 16 weeks. 16.0% ( ) 10,715,666 25,837, ,130 Antvral for the entre edemc. 11.0% ( ) 13,580,818 25,837,928 6,983,830 *Value n brackets reresent the 5-95 ercentle values of the Attack Rate estmates 13

14 Fgure 1. Weekly attack rate, by age grou, wth no control measures Fgure 2. Imact of dfferent combnatons of control measures consderng the use of a reandemc vaccne rovded to all categores (I to IV) Fgure 3. Total attack rates for dfferent values of R 0, wth no control measures or selected control measures 14

15 Acknowledgment We are grateful to Mark Kaneff for revsng the manuscrt. Foundng Ths work has been artally funded by the EPICO Project, of the Provnca Autonoma d Trento, Italy. Cometng nterests: No cometng nterests to declare 15

16 References (1) L KS, et al. Geness of a hghly athogenc and otentally andemc H5N1 nfluenza vrus n eastern Asa. Nature 2004 July 8;430: (2) Outbreak news. Avan nfluenza, Turkey--udate. Wkly Edemol Rec 2006;81: (3) Monto AS. Vaccnes and antvral drugs n andemc rearedness. Emerg Infect Ds 2006 January;12: (4) Stehenson I, et al. Develoment and evaluaton of nfluenza andemc vaccnes. Lancet Infect Ds 2006;6: (5) Influenza Team ECDPaC. Pandemc rearedness n the Euroean Unon mult-sectoral lannng needed. Euro Survell 2007;12:E (6) Ferguson NM, et al. Strateges for contanng an emergng nfluenza andemc n Southeast Asa. Nature 2005;437: (7) Ferguson NM, et al. Strateges for mtgatng an nfluenza andemc. Nature 2006;442: (8) Longn IM, et al. Contanng andemc nfluenza at the source. Scence 2005;309: (9) Germann TC, et al. Mtgaton strateges for andemc nfluenza n the Unted States. Proc Natl Acad Sc U S A 2006;103: (10) Carrat F, et al. A 'small-world-lke' model for comarng nterventons amed at reventng and controllng nfluenza andemcs. BMC Med 2006;4:26. (11) Colzza V, et al. Modelng the Worldwde Sread of Pandemc Influenza: Baselne Case and Contanment Interventons. PLoS Med 2007;4:e13. (12) Cooer BS, et al. Delayng the nternatonal sread of andemc nfluenza. PLoS Med 2006;3:e212. (13) Flahault A, et al. Strateges for contanng a global nfluenza andemc. Vaccne (44-46): (14) Isttuto Nazonale d statstca. 14 Censmento Generale della Poolazone e delle Abtazon. ISTAT 2001(Avalable from: htt://dawnc.stat.t/dawnc/js/md/dawncmd.js). Accessed 1 May

17 (15) Isttuto Nazonale d statstca. Statstche del trasorto aereo - Anno ISTAT 2006 (Avalable from: htt:// Accessed 1 May (16) Glezen WP. Emergng nfectons: andemc nfluenza. Edemol Rev 1996;18: (17) Dekmann O, Heesterbeek JAP Mathematcal Edemology of Infectous Dseases, Wley, 2000 (18) Flahault A, et al. Modellng the 1985 nfluenza edemc n France. Stat Med 1988;7: (19) Mnstero della Salute. Pano Nazonale d rearazone e rsosta ad una andema nfluenzale 2006 (Avalable from: htt:// Accessed 1 May (20) Mnstero della Salute. Influenza Vaccnaton Coverage (Avalable from: htt://www mnsterosalute t/romozone/malatte/malatte js) (21) Bella A., et al. FLU-ISS: Sstema d sorveglanza sentnella dell'nfluenza basata su medc d medcna generale e edatr d lbera scelta. Raorto sulla stagone nfluenzale ISS; Reort No.: 22. (22) Brownsten JS, Klenman KP, Mandl KD. Identfyng edatrc age grous for nfluenza vaccnaton usng a real-tme regonal survellance system. Am J Edemol 2005;162: (23) Roberts MG, et al. A model for the sread and control of andemc nfluenza n an solated geograhcal regon. J. Royal Socety Interface 2007;4: (24) Vboud C, et al. Influenza edemcs n the Unted States, France, and Australa, Emerg Infect Ds 2004;10: (25) Vboud C, et al. Multnatonal mact of the 1968 Hong Kong nfluenza andemc: evdence for a smolderng andemc. J Infect Ds 2005;192: (26) Rzzo C, et al. Trends for Influenza-related Deaths durng Pandemc and Edemc Seasons, Italy, Emerg Infect Ds 2007;13:

18 18 Aendx The equatons of the model are!!!! "!!!! # $ = % = % = = % & & q j q j q j q j q j q j q j q j I R I E I E N I S E N I S S ' ' ( ( ) ) & & & & & &,,,,,, where 1/" and 1/# reresent, resectvely, the mean length of the latent and the nfectous erods and q j,,! s the transmsson rate between an ndvdual of class n regon and an ndvdual of class j n regon q.

19

20 No nterventons antvrals for 4 weeks antvrals for 8 weeks socal dstancng measures from week 2 socal dstancng measures from week 4 antvrals for 8 weeks and socal dstancng measures from week Weeks snce andemc ntroducton Cases er 1000 ndvduals

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