NBER WORKING PAPER SERIES PUBLIC AVOIDANCE AND THE EPIDEMIOLOGY OF NOVEL H1N1 INFLUENZA A. Byung-Kwang Yoo Megumi Kasajima Jay Bhattacharya

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1 NBER WORKING PAPER SERIES PUBLIC AVOIDANCE AND THE EPIDEMIOLOGY OF NOVEL H1N1 INFLUENZA A Byung-Kwang Yoo Megumi Kasajima Jay Bhaacharya Working Paper hp:// NATIONAL BUREAU OF ECONOMIC RESEARCH 50 Massachuses Avenue Cambridge, MA February 20 Prof. Yoo s work on his projec is suppored by Naional Insiue of Healh (1K25AI073915). Prof. Bhaacharya s work on his projec is suppored in par by he Naional Insiue on Aging. We hank Peer G. Szilagyi, MD, MPH and Charles E. Phelps, PhD for heir suppor in concepion and Andrea Berry, MS for her daa analysis and ediing suppor. The views expressed herein are hose of he auhors and do no necessarily reflec he views of he Naional Bureau of Economic Research. NBER working papers are circulaed for discussion and commen purposes. They have no been peerreviewed or been subjec o he review by he NBER Board of Direcors ha accompanies official NBER publicaions. 20 by Byung-Kwang Yoo, Megumi Kasajima, and Jay Bhaacharya. All righs reserved. Shor secions of ex, no o exceed wo paragraphs, may be quoed wihou explici permission provided ha full credi, including noice, is given o he source.

2 Public Avoidance and he Epidemiology of novel H1N1 Influenza A Byung-Kwang Yoo, Megumi Kasajima, and Jay Bhaacharya NBER Working Paper No February 20 JEL No. I1,I ABSTRACT In June 20, he World Healh Organizaion declared ha novel influenza A (nh1n1) had reached pandemic saus worldwide. The response o he spread of his virus by he public and by he public healh communiy was immediae and widespread. Among he responses included volunary avoidance of public spaces, closure of schools, he ubiquious placemen of hand saniizer, and he use of face masks in public places. Exising forecasing models of he epidemic spread of nh1n1, used by public healh officials o aid in making many decisions including vaccinaion policy, ignore avoidance responses in he formal modeling. In his paper, we build a forecasing model of he nh1n1 epidemic ha explicily accouns for avoidance behavior. We use daa from he U.S. summer and he Ausralian winer nh1n1 epidemic of 20 o esimae he parameers of our model and forecas he course of he epidemic in he U.S. in 20. We find ha accouning for avoidance responses resuls in a beer fiing forecasing model. We also find ha in models wih avoidance, he marginal reurn in erms of saved lives and reduced infecion raes of an early vaccinaion campaign are higher. Byung-Kwang Yoo School of Medicine and Denisry 601 Elmwood Ave, Box 644 Rocheser, New York yoobk3@gmail.com Megumi Kasajima School of Medicine and Denisry 601 Elmwood Ave, Box 644 Rocheser, New York kasajimamegumi@gmail.com Jay Bhaacharya 117 Encina Commons Cener for Primary Care and Oucomes Research Sanford Universiy Sanford, CA and NBER jay@sanford.edu

3 1. Inroducion In June 20, he World Healh Organizaion (WHO) declared a worldwide novel influenza A (nh1n1) pandemic aler (World Healh Organizaion (WHO) 20). As of December 20, officials a he Ceners for Disease Conrol esimaed nearly,000 deahs due o nh1n1 infecion beween April and early December 20 around he world (Ceners for Disease Conrol and Prevenion (CDC) 20; World Healh Organizaion (WHO) 20). One unique feaure of he novel influenza pandemic has been he widespread aenion paid o i by he public. In Mexico, he U.S. and oher counries, early repors abou he novel influenza led o closure of schools, cancellaion of public sporing evens, and counless individual behavioral decisions regarding he exen o go ou in public, e.g., during a school-closure period (Ceners for Disease Conrol and Prevenion (CDC) 20). The decision o forego conac wih oher people is called an avoidance response. One implicaion of hese sors of public responses is ha he illness aack rae and he reproducion rae (RR) of he virus (he number of secondary infeced cases per primary infeced case) are lower han hem oherwise would be in he absence of an avoidance response. 1 Despie he imporance of a public avoidance response on he illness aack rae and he RR of he virus, exising forecasing models of he novel influenza pandemic do no accoun for i (Boelle e al. 20; Fraser e al. 20; Yang e al. 20). Economiss have found avoidance response o be imporan in oher infecious disease conexs, including seasonal influenza vaccinaion (Li e al. 2004; Yoo and Frick 2005; Yoo e al. 20) and measles vaccinaion (Philipson 1996). Researchers have found ha higher disease prevalence moivaes people o underake aciviies ha subsequenly reduce he exen of an 1 The RR plays a key role in models forecasing he exen of an epidemic. For example, if RR<1 he oubreak will evenually die ou. 3

4 epidemic. The logic runs in he opposie direcion as well a decreasing disease prevalence may lead o a reducion in prevenive behaviors ha makes i difficul o eradicae a prevenable infecious disease even if an effecive vaccine is available (Philipson 2000). Our aim here is o develop a beer forecasing model for he nh1n1 pandemic pah from April 20 o Sepember 20 by incorporaing his concep of avoidance response, in comparison wih models ha do no include his concep. A secondary aim is o forecas he benefi of vaccinaion programs (available from Ocober 20) in changing he U.S. nh1n1 pandemic pah, as well as is final size, using he mos recenly available informaion abou he pandemic, e.g., he pas winer pandemic in Ausralia, and he newly developed nh1n1 vaccines. 2. A Model of Avoidance The main ool we use in our analysis is a hree-comparmen differenial equaion model, known in epidemiology as a suscepible-infeced-recovered (SIR) model (Rvachev and Longini 1985). In his model, people ransiion beween hree muually exclusive healh saes suscepible o nh1n1 influenza, infeced, and recovered (and hence immune). Le N be he oal populaion in a given sae as of July 1, 2008 (US Census Bureau) we conduc a separae esimaion for each sae in he U.S. N is he sum of four erms: S (he number of suscepible people), I (he number of infeced people), R (he number of recovered, and hence immune, people), and oal deahs. 2 The model hese comparmens follow he following equaions of moion over ime: (1) ds β = S I d N 2 For simpliciy, we assume is consan for all. This is a reasonable assumpion because he populaion size of each sae is orders of magniude larger han he number of people infeced wih nh1n1. 4

5 (2) di β = S I d N ( γ + α) I (3) dr = d γ I The hree parameers α, β, and γ denoe he case faaliy rae, he aack rae and he recovery rae, respecively. The firs erm of di d represens newly infeced people moving from comparmen S o I a ime ; γ I represens hose who recover from nh1n1 infecion and hence mover from comparmen I o R a ime ; and finally, α I represens hose who die from infecion a ime. The sandard SIR-model assumes ha he illness aack rae, which is he rae a which suscepible become infeced, depends upon wo facors. The firs is he rae of ransmission from a single conac beween an infeced and suscepible individual. The second is he frequency of such conac among individuals, which varies across people of differen age, family size, and oher facors (Coulombier and Giesecke 20). We modify his sandard model o incorporae avoidance response ha is, he idea ha he frequency of conac among individuals will iself depend on he prevalence of he disease in he populaion. Unlike he sandard SIR-model, in our model he aack rae changes over ime as disease prevalence changes. We assume aack rae o be he produc of hree facors: a consan baseline aack rae ha represens a biological ransmission rae; a baseline conac frequency which differs among subgroups; and avoidance response parameers which are influenced by he prevalence rae of he disease. Because he aack rae in our model changes over ime, so does he reproducive rae of he virus. The appendix secion provides more deails. There, we also 5

6 describe how we esimae he parameers of he model and how we modify he model o accoun for vaccinaion agains nh1n1 infecion. 3. Mehods Our empirical analysis consiss of hree seps. Firs, we specify and esimae a model of he nh1n1 flu epidemic along he lines of he model described in he previous secion. The Appendix provides deails on our primary daa source laboraory confirmed daily repors on nh1n1 cases and on our esimaion procedure. We esimae versions of he model ha accoun for avoidance behavior as well as versions of he model ha do no. We also esimae separae versions of he model using daa from Ausralia. Second, we use our models o forecas he baseline U.S. pandemic pah (wihou vaccinaion) beween April 20 o Sepember 20. Our preferred forecas accouns for avoidance response. In hese forecass, we assume ha severiy of he epidemic mimics he severiy experienced in Ausralia beween May 20 and Sepember 20 during is winer flu season. Finally, we characerize he benefi of vaccinaion programs (available since Ocober 20) in changing he U.S. H1N1 pandemic pah. 3.1 Tesing validiy of avoidance response model Our primary daa sources consis of daily couns of laboraory confirmed repors from he U.S. (a he sae level) beween April 23, 20 o July 17, 20 (Ceners for Disease Conrol and Prevenion (CDC) 20) and from Ausralia beween May 9, 20 o Sepember 18, 20 (also a he sae and province hereafer jurisdicion level) (Ausralian Governmen Deparmen of Healh and Ageing 20). These cases represen only a small fracion of all nh1n1 cases as he vas majoriy of H1N1 cases are no laboraory confirmed. In our models we assume a case 6

7 deecion rae of 5%; ha is, he CDC s repor of over 40,000 laboraory confirmed cases over he observaion period implies ha here were 1 million infeced cases in he U.S. (Ceners for Disease Conrol and Prevenion (CDC) 20). This assumpion is consisen wih CDC guidelines as well as U.S. experience during previous flu epidemics. We esimae versions of his model in which we assume values of up o % for he case deecion rae. Our model also requires informaion on how long each infecion lased, which is no available in he CDC daa. Based on daa from previous flu epidemics, we assume a disribuion of infecion lengh wih a mean of 4.1 days. For each case in he CDC daa, we draw a random infecion lengh from his disribuion. We hen aggregae over individual cases back o he day and sae level o derive a panel of nh1n1cases for each sae in he U.S. over 86 days. We derive, using similar mehods, a similar secondary daase for Ausralia. We assume ha faaliy rae among nh1n1 cases was 1% wih a range of 0.5%-1.2%. We base his assumpion on he observed confirmed-case faaliy rae in he U.S. and Ausralia (Ausralian Governmen Deparmen of Healh and Ageing 20; Ceners for Disease Conrol and Prevenion (CDC) 20) and a recen sudy (Presiden's Council of Advisors on Science and Technology 20). We esimae several differen versions of our SIR model using a generalized leas esimaor. As we have said, we esimae a version of he model ha permis an avoidance response. In addiion, we esimae a version of our model in which we impose ha here be no avoidance response. Our purpose is o compare he predicions of hese wo versions of he model agains he acual pah of he epidemic afer Sepember 20. For boh of hese versions, we conduc obain separae esimaes for wo groups of saes wih higher and lower epidemic levels. The higher epidemic level group includes he en saes California, Connecicu, Florida, Illinois, 7

8 Massachuses, New Jersey, New York, Pennsylvania, Texas, and Wisconsin ha had a leas 1,000 confirmed cases per sae. Togeher hese saes consis of 70% of he naional confirmed cases in oal as of July 3, 20 (Ceners for Disease Conrol and Prevenion (CDC) 20). We also esimae a separae version of he model wih he Ausralian daa. Since he infecion lengh is randomly drawn in he underlying daa, we conduc 200 ieraions of our esimaion procedure. In each ieraion, we draw a new infecion lengh realizaion for he enire daa se. Using he panel daase produced in each ieraion of he microsimulaion model, we generae 200 differen esimaes of he parameers of our SIR model, once for each ieraion. 3.2 Forecasing he baseline U.S. pandemic pah wihou vaccinaion Using our SIR model and he parameers derived from he esimaion procedure, we calculae a prediced pah of he U.S. pandemic beween April 23, 20 and July 17, 20. We compare hese predicions agains he acual pah of he epidemic over ha period. We similarly calculae a prediced pah of he Ausralian epidemic beween May 9, 20 and Sepember 18, 20 and compare agains he acual pah. Since he vaccine agains nh1n1 was no available a all during his ime, he esimaes we produce in his secion ignore any possible benefi from a vaccine in reducing he spread of infecion. We use our model o forecas he pah of he U.S. epidemic afer Sepember 1, 20, which we call he U.S. winer. In hese forecass, we use he illness severiy parameers from he Ausralian version of he SIR model. There are a leas wo reasons why using he Ausralian winer pandemic parameers o forecas he U.S. winer pandemic is jusified. Firs, he reproducion rae of he flu virus, including nh1n1 varies wih he ambien emperaure, and is 8

9 higher in he winer han i is in he summer. Thus, he Ausralian experience during he winer provides a beer guide for he U.S. winer han does he U.S. summer experience. Second, he Ausralian populaion is among all naions in he Souhern Hemisphere, mos similar o he U.S. in erms of is healh saus and social-demographic characerisics a he naional level. In addiion, he informaion released o he general public abou he pandemic in boh counries by heir respecive governmens and by he mass media is similar. The average of he moraliy rae due o pneumonia and influenza in he pas hree years, prior o he nh1n1 pandemic, was similar: 0.020% in he U.S. (Ceners for Disease Conrol and Prevenion (CDC)), and 0.013% in Ausralia (Ausralian Bureau of Saisics 20; Ausralian Bureau of Saisics 20). 3.3 Characerizing he benefis of nh1n1 vaccinaion Our analysis up o now has been predicaed on he assumpion ha here is no effecive vaccine available agains nh1n1 infecion. As an exension o our work, we modify our procedure o ake accoun of he fac ha a vaccine did acually become available in he U.S. in Ocober, 20. The deails of his modificaion o our SIR model o accoun for vaccinaion are described in deail in he Appendix. Our modified SIR model reflecs he mos recen informaion available o us a he ime of our wriing: in Ocober 1-7 here were 1 million doses per day of he vaccine, in Ocober 8-14, 6 million doses per day, in Ocober 15- December 2, 3 million doses per day. In oal, here were 196 million doses available (McNeil 20; McNeil 20). In his version of our model, we assume ha he vaccine upake rae ranges beween 50% and 90%. A 50%, we effecively assume ha everyday 0.5 million doses (ou of 1 million doses available) were delivered and effecive, and ha he remaining 0.5 million doses were lef unused by he end of a simulaion period. For simpliciy and because here are no on-poin daa 9

10 currenly available, we assumed vaccine doses o be disribued equally across he all U.S. subpopulaions. A 50% upake rae is plausible because ofen a large number of doses remain unused even during pas usual influenza seasons wih vaccine supply problems (Orensein and Schaffner 2008). 4. Resuls 4.1. Tesing he validiy of avoidance response models Figure 1 plos he cumulaive pah of confirmed nh1n1 infeced cases in he U.S. beween April 23 and July 17, 20 as represened in he CDC daa and assuming a 5% case deecion rae. Figure 1 also shows he epidemic pahs forecased by our primary model (solid line) accouning for avoidance response beween April 23 and Augus 31, 20. I also plos he 2.5 and 97.5 percenile pahs (based on case raes on he las day) among 200 ieraions of ha model, indicaed by doed lines. Boh models produce esimaes wih a narrow inerval beween he 2.5 and 97.5 percenile pahs. Finally, Figure 1 plos he epidemic pah implied by he version of he model in which here is no avoidance response. Evidenly, no accouning for he avoidance response models produces a prediced epidemic pah ha does a poor job of fiing he acual daa on cumulaive infeced cases over he observed period Forecasing he baseline U.S. pandemic pah wihou vaccinaion Figure 2 indicaes our forecass of he he pah of he nh1n1 pandemic in he U.S. up o Sepember 20 (exending he ime period shown in Figure 1) in he absence of a vaccinaion campaign. We plo hree differen forecass. The firs assumes ha here is no avoidance response, while he second and hird forecass incorporae an avoidance response. The second

11 model is exacly he one we described in secion 4.1 above. The hird model incorporaes a renewed upsurge in nh1n1 infecions in he fall of 20, using he winer parameers derived from he Ausralian daa microsimulaion. The model which assumes no avoidance response predics ha he epidemic should have died ou compleely by Augus 31, 20 wih 61.1% of he populaion infeced a some poin during he pandemic. The second model, which incorporaes avoidance response forecass ha he epidemic will coninue hroughou he simulaion period of 500 days, wih abou 46.2% of he populaion infeced by Sepember 20. In his avoidance response model, he reproducion rae (RR) of he virus flucuaes around 1.1 in he saes wih high incidence rae and around 0.9 in he 40 saes wih low incidence. In hird model we use o forecas he pandemic pah, he wo key facors are he onse iming of he second epidemic upsurge and he severiy of winer parameers derived from he Ausralian daa microsimulaion. In his Ausralian microsimulaion model, we found a median illness aack raes ha ranged beween 0.23 and 0.74 (wih an average rae of 0.68) among eigh jurisdicions. Our baseline forecass assume an aack rae of 0.68 o forecas a U.S. winer epidemic. In our forecass, on he firs onse day of he second epidemic upsurge, we replaced he measured aack rae in each U.S. sae wih he Ausralian number. Prior o he onse of he second upsurge (eiher Sepember 1 or Ocober 1), he mean illness aack raes was 0.29 in he highes incidence saes and 0.22 in he lowes incidence saes. This model (also shown in Figure 2) forecass ha he epidemic will die ou in January 20 wih 40% of he populaion ulimaely infeced. The forecass of he baseline U.S. pandemic pah from April 23, 20 o Sepember 5, 20 are summarized under seven alernaive scenarios in Tables 1 and 2. Table 1 shows he 11

12 proporion of he populaion ulimaely infeced, oal deahs from he epidemic, and he effec of a vaccinaion campaign on hese measures. Table 2 shows he forecased peak pandemic prevalence rae and he peak dae, as well as he effec of a vaccinaion campaign on hese measures. The seven scenarios differ wih regard o assumpions abou he presence and iming of a second epidemic upsurge (indicaed in column 1) and abou wheher here is a vaccinaion campaign. In all seven scenarios we assume here is an avoidance response. In column 2, we indicae our assumpion abou wheher a vaccinaion campaign akes place, as well as our assumpion abou vaccine effeciveness in hose scenarios where here is a campaign. Column 3 shows our assumpion abou he vaccinaion upake rae (eiher 50% or 90%) if here is a campaign. Columns 4 and 5 in Table 1 show forecased oal pandemic impacs measured by he cumulaive infeced populaion over he course of he epidemic and oal deahs, while columns 4-5 in Table 2 indicae he forecased pandemic peak measured by he prevalence rae and he peak dae. Columns 6 and 7 in each able show he forecased effec of vaccinaion on epidemic pahs and impacs. Our models wih avoidance response have he following boom line implicaion for he pah of he epidemic in he U.S. (shown in Table 1). If here is a second upsurge, we forecas ha beween 33.9% and 57.7% of he populaion will ulimaely be infeced. Wihou a second upsurge (scenario 7), we forecas 46.2% will ulimaely be infeced. We forecas ha he peak of he upsurge occurs wihin hree weeks of onse wih a maximum prevalence ranging beween 5.5% and 7.5% if he second upsurge occurs (Table 2). Wihou a second upsurge, we forecas a peak o occur as lae as mid-february wih a much lower maximum prevalence rae of 1% Forecasing he benefis of a vaccinaion campaign in he U.S. 12

13 Since here is an effecive vaccine for nh1n1 infecion which has been developed (Hancock e al. 20) and widely disribued despie early shorages (McNeil 20; McNeil 20), i is imporan o accoun for i in our forecass. Figure 3 presens our esimaes ha ake his vaccinaion campaign ino accoun. Our wors case scenarios assume ha he vaccine is 50% vaccine effecive and ha 50% of he populaion ulimaely upake he vaccine. Our forecass when he vaccine is available are sensiive o he iming of he second surge in nh1n1 infecions. A delayed second upsurge (paricularly he Ocober onse) leads o a lower proporion of he populaion ulimaely infeced because he immune proecion conferred by he vaccine (which ypically akes up o 9 days) has more ime o ake hold. For insance, if here is a second upsurge, we forecas ha 57.2% of he populaion will ulimaely be infeced if he second surge sars in Sepember, 36.3% if he surge sars in Ocober (also in columns 4 in Table 1). Our conservaive scenarios wih he vaccine predic and a 1% confirmed-case faaliy rae imply ha here will be beween 55,0 and 86,900 oal deahs in he U.S. due o nh1n1 infecion. Figures 5 and 6 presen he four scenarios (from he 7 scenarios presened in Tables 1 and 2) ha we believe are mos likely o occur. 3. In wo scenarios we assume a second upsurge saring on Sepember 1, 20, and in he oher wo scenarios we assume a second upsurge saring on Ocober 1, 20. All four scenarios assume 50% vaccinaion effeciveness. These correspond o scenarios 3-7 in Tables 1 and 2. Figure 4 indicaes he forecased benefis from vaccinaion in erms of reducions in proporion of he populaion ulimaely infeced. Increasing he vaccinaion upake rae from 50% o he maximum 90% (of he 196 million doses available) reduces he final size of he epidemic from 57.2% o 56.8% of he populaion in he scenarios wih an Sepember onse of he 3 The reasons for choosing hese scenarios are deailed in he Discussion secion. 13

14 second upsurge, and from 36.3% o 33.9% in hose scenarios wih he Ocober onse second upsurge (also in Columns 4 and 6 in Table 1). Figure 5 shows he benefi of he vaccinaion campaign in erms of reducing he peak levels of he epidemic. We plo he same four scenarios ha we plo in Figure 4. If a second upsurge begins on Ocober 1, a vaccinaion program saring Ocober 1 wih he 90% upake rae and 50% effeciveness will reduce he peak prevalence only slighly from 5.56% o 5.50% and move peak iming by one day earlier (also in Columns 4-7 in Table 2). When a second upsurge begins on Sepember 1, vaccinaion won make any change due o is availabiliy afer Ocober. If here is a severe second surge saring in November 1, his same vaccinaion program will reduce he peak prevalence from 5.35% o 3.5% and delay he peak dae by one day. 5. Discussion In his secion, we discuss our view on which of our forecased pahs are mos likely o occur. While his exercise is necessarily speculaive, we include i because i helps make clear which of he various moving pars of our model are mos imporan in realiy. Figures 5 and 6 show he epidemic pahs from he versions of he model ha we believe o be mos accurae. The forecased pahs in hose figures accoun for demonsraed vaccine efficacy (Hancock e al. 20), repored vaccine availabiliy (McNeil 20; McNeil 20), and he U.S. pandemic siuaion as of Ocober 17, 20 (Ceners for Disease Conrol and Prevenion (CDC) 20). In he U.S., he second pandemic upsurge sared in 12 saes in early Sepember 20 and spread o 46 saes by mid-ocober (Ceners for Disease Conrol and Prevenion (CDC) 20). Therefore, he scenario 7 in Table 1, which forecas no second upsurge, will no occur. We include i parly because here may be oher flu varian epidemics in he fuure where such 14

15 forecass are appropriae, and parly because i is a good reference in comparison wih he nonresponse model in Figure 2 ha died ou prior a second upsurge in fall 20. The number of people infeced by he nh1n1 virus has been increasing since early Sepember 20, exceeding he levels of regular seasonal influenza and he firs H1N1 upsurge in May 20 in he U.S. The number of infeced individuals has ye o reach a peak as of Ocober 17, 2007, based upon he percenage of visis for influenza-like illness (ILI) a he naional level (Ceners for Disease Conrol and Prevenion (CDC) 20). Thus, for he naional level forecass, he scenarios forecasing an epidemic peak iming prior o mid-ocober (such as hose which assume no avoidance behavior) are no appropriae. Based on his reasoning, we idenify hose scenarios in which effecive vaccines are available saring in Ocober and in which a second upsurge occurs as mos appropriae (Scenarios 1-6 in Tables 1 and 2). Among hese scenarios, he forecass imply: (1) beween 33.9% and 57.7% of he populaion ulimaely infeced wih nh1n1 flu; (2) beween 51,600 and 87,700 as a resul of he nh1n1 flu; (3) a peak prevalence beween 5.50% and 7.46% of he populaion;, and (4) a peak level of he epidemic occurring beween Sepember 21 and Ocober 19, 20. The forecased ranges of vaccinaion benefis were as follows: (1) a reducion in he oal populaion ulimaely infeced beween 0.8% and 6.2% of he populaion; (2) a reducion in oal deahs due o he vaccine of beween 1,300 and 9,500 people; (3) a reducion in he peak prevalence of he epidemic of beween 0.00% (ha is, less han 0.00and 0.16% of he populaion; and (4) a change in peak iming of he epidemic of only 1 day. Our forecass from he scenarios ha we idenify as mos appropriae are qualiaively similar o oher recen forecass of he nh1n1 epidemic. Yang and colleagues esimaed he oal infeced cases in he oal U.S. populaion wih hree levels of pandemic ransmissibiliy: (i) 21-15

16 31% (low ransmissibiliy), (ii) 32-39% (moderae) and (iii) 40-49% (high) (Yang e al. 20). The Presiden's Council of Advisors on Science and Technology published a scenario in which 30% o 50% of he populaion is ulimaely infeced and here are beween 30,000 and 90,000 deahs (Presiden's Council of Advisors on Science and Technology 20). These deah esimaes are smaller han earlier esimaes published by he U.S. Deparmen of Healh and Human Services, which prediced 90 million infeced cases (30% of he U.S. populaion) and beween 2,000 and 1,903,000 deahs (he laer case assumes ha he nh1n1 has characerisics similar o he 1918flu virus) (Unied Saes Deparmen of Healh and Human Services (DHHS) 20). The forecased range of deahs (51,600-87,700) in our likely scenarios is likely o be comparable or greaer han all-associaed deahs due o seasonal influenza (36,200 wih a range of 8,7-51,203) (Thompson e al. 2003) and largely overlaps wih he recen governmen repor (30,000-90,000) (Presiden's Council of Advisors on Science and Technology 20) menioned earlier. Deahs due o pandemic nh1n1 are likely o add o, raher subsiue for, seasonal influenza deahs because he wo flu srains affec differen populaions. nh1n1 flu is more likely han seasonal flu o kill younger people, while around 90% of he influenza-relaed deahs in he U.S. occur among he elderly (Thompson e al. 2003). Our esimae of he benefis of vaccinaion are difficul o compare direcly wih pas sudies because hese sudies use differen assumpions abou vaccinaion policy (for example, some sudies assume ha wo vaccine doses for aduls as well as children), prioriies in arge subpopulaions, and in vaccine availabiliy (Flahaul e al. 20; Yang e al. 20). The assumpions we make on hese poins reflec acual vaccine availabiliy and acual vaccinaion policy. Yang e al. (20) esimae only a small benefi from universal vaccinaion wih a 30 16

17 day delay a reducion of in he ulimae proporion of he populaion infeced beween % and 15% if here is a moderae pandemic, and less han 7% if here is a severe pandemic. 6. Conclusion In our view, he wo mos imporan conribuions of his paper are: (1) o highligh he imporance of accouning for avoidance response in SIR models of infecious disease spread, when such a response is possible, and (2) o show ha vaccinaion campaigns are mos effecive if hey ake place before an epidemic has spread. While hese are no new insighs (Philipson 2000; Yoo e al. 20), hey have no been widely undersood in he applied lieraure on disease epidemics and o our knowledge have no been applied in he case of he nh1n1 flu epidemic a all. These wo resuls highligh he difficuly ha public healh officials face in managing an infecious disease like he nh1n1 flu. A he ime when vaccinaion would be mos effecive, demand for he vaccine is lowes because he prevalence of he disease is low. These resuls also emphasize he imporance of avoiding early shorages of vaccines during a flu epidemic. We show ha i is possible o fi SIR models ha ake ino accoun of he populaion s avoidance response o an epidemic using readily available daa. Accouning for his response involves a simple modificaion o a sandard SIR model, bu resuls in a subsanially beer fi o he daa. In he case of nh1n1 flu, accouning for avoidance makes paricular sense since he spread of he flu has led he closure of schools and oher cosly responses aimed a decreasing he spread of infecion. More accurae pandemic pah forecas regarding he peak iming and he peak level of an epidemic is also paricularly useful in aiding public healh officials o allocae limied resources in a seing where vaccine availabiliy is limied. 17

18 We find evidence of he imporance of accouning for an avoidance response in boh he U.S. and in Ausralia. Our finding ha baseline pandemic pah and proporion ulimaely infeced are lower because of a robus avoidance response is consisen wih common sense, as well as he lieraure on economic epidemiology. For insance, Yoo e al. (20) found a robus avoidance response in he conex of he seasonal flu among a naionally-represenaive elderly people in he U.S. (Yoo e al. 20). If he models of oher sudies (Boelle e al. 20; Fraser e al. 20; Presiden's Council of Advisors on Science and Technology 20; Yang e al. 20) also accoun for avoidance response, heir forecass of ulimae epidemic size would likely decrease as hey did in our forecass. One limiaion of our sudy is ha we rely on case repor daa from he CDC which is cerainly measured wih error (Ceners for Disease Conrol and Prevenion (CDC) 20). These daa are known o face biases due o under-reporing and delayed-reporing. Though i is impossible o know how exensive. To address his limiaion, we vary our assumed deecion rae over a considerable range in our sensiiviy analysis. These sensiiviy analyses show ha several of our mos imporan resuls (such as he shape of he epidemic pahs and our esimaes on confirmed cases and deahs) are only modesly influenced by such measuremen errors. A second limiaion is ha our models do no explicily accoun for he effec of aniviral medicaion in reducing he lengh of infecion. In a sense, we do accoun for he use of drugs such as Tamiflu in our forecass because we rely on acual case repors of nh1n1 daa. These daa reflec he effecs of anivirals as hey are acually used in he populaion. Unless he paern of use of aniviral medicaions has changes beween Sepember 20 and Sepember 20, which appears less likely according a recen CDC repor (Ceners for Disease Conrol and Prevenion 18

19 (CDC) 20), our forecass of pandemic pah and vaccinaion benefis are unlikely o be affeced by his limiaion. A hird limiaion is ha we do no calculae separae forecass of he effec of he epidemic on heerogeneous groups in he populaion. This is an imporan omission because, as we have noed, he nh1n1 flu virus affecs people of differen ages differenly. As he nex sep in his research agenda, we are planning o address his lacuna by incorporaing avoidance response ino agen-based models, which explicily accoun for heerogeneous characerisics across subpopulaions (Longini e al. 2004; Ferguson e al. 2006). In par because of avoidance behavior (including he closing of schools and he avoidance by individuals of public places a he peak of he epidemic), we expec ha he nh1n1 influenza pandemic his year o be relaively mild in he U.S. when compared wih pas pandemics bu likely o be comparable o or more severe han he ypical seasonal influenza epidemic. To he exen ha people coninue o avoid public places hroughou he year due o he nh1n1 epidemic, he seasonal flu epidemic his year will also be less severe han i migh have been. However, he fac ha avoidance in he face of an epidemic is an imporan phenomenon makes he early availabiliy of vaccines more imporan no less. We argue hese lessons ough o be incorporaed ino forecass of fuure flu epidemics of all sors. More accurae and more useful forecass will resul and beer enable public healh officials o make good decisions abou he allocaion of limied funds, ani-virals, vaccines, and oher resources such as quaranines and school and public even closures o miigae he impac of fuure pandemics. 19

20 Appendix Our aim in his paper is o develop and esimae a model of he nh1n1 epidemic ha akes accoun of he avoidance response o he spread of he virus. We rely on he experience of he U.S. and Ausralia in he early sages of he epidemic as our primary daa sources. We esimae he parameers of our model using hese daa and hen forecas he implicaions of our model for he fuure of he epidemic. In his appendix, we describe our empirical work in some deail. A.1. Inferring he Number of Suscepible, Infeced, and Recovered from CDC Daa We consruc a microsimulaion model of he nh1n1 epidemic wih he aim of esimaing he aack rae of he nh1n1 influenza on each of he 86 days beween April 23, 20 and July 17, 20 of our U.S. daa. We forecas he course of he epidemic separaely for every sae in he U.S. This secion explains he microsimulaion procedures o esimae he numbers of infecives (I ), recovered (R ), suscepibles (S ), and he sae-specific daily aack rae (β ). A he end of he secion, we go hrough a hypoheical example of our microsimulaion exercise o illusrae how we esimae he number of infecious cases (I ). We sar wih our procedure o esimae he number of infecious cases (I ). Our primary daa source is he Ceners for Disease Conrol (CDC) which repors he cumulaive daily number of sae-specific laboraory confirmed cases of nh1n1 saring on April 23, 20. The CDC di daa correspond o d in our noaion. However, since no every case of nh1n1 is laboraory confirmed, we need an assumpion abou he deecion rae. In our base case, we assume a deecion rae of 5%, which implies ha he CDC measures only one in 20 of he acual cases 20

21 (Ceners for Disease Conrol and Prevenion (CDC) 20). In sensiiviy analyses, we assume a % deecion rae, which cus our forecas in half. The CDC daa does no indicae he dae when an infeced individual exied he infecive comparmen, so we need a credible assumpion o infer he exi dae (i.e., lengh of say in he infecive comparmen, or he infecious period) for each case who conracs nh1n1 disease. Following pas sudies (Elveback e al. 1976; Longini e al. 2005), o each person in he CDC daabase we randomly assign he infecious period (τ) as 3 days (wih he probabiliy of 0.3), 4 days (0.4), 5 days (0.2) or 6 days (0.1), which implies ha he mean lengh of infecion period is 4.1 days. We addiionally assume ha he infecious period disribuions are he same for individuals who recover and individuals who die from nh1n1 infecion. Togeher, hese assumpions imply ha ( α + γ ) 1 = We adop hese periods wih probabiliies, parly because daa on his parameer for nh1n1 are no available and parly because hese values are wihin he range of he CDC s inerim guideline for nh1n1 influenza (Ceners for Disease Conrol and Prevenion (CDC) 20). Le { τ = k k = 3,...,6} represen he se of infeced paiens in he CDC daabase o whom we randomly assign o an infecious period of k days. Under our assumpions, he oal number of infeced individuals oday equals he sum over all he paiens who ransiioned ino he infeced comparmen over he pas six days. Thus, he oal number of infeced people on day is given by: (A1) I = di 2 k k=0 d τ = 3 + di 3 k k=0 d τ = 4 + di 4 k k=0 d τ = 5 + di 5 k k=0 d τ = 6 4 Recall ha α is he case moraliy rae and γ is he case recovery rae. 21

22 For simpliciy, we assume ha newly infeced individuals had a laboraory es and were diagnosed on he firs day of heir infecion. Therefore, if here was a one-week ime-lag beween he beginning of he infecious period and he laboraory es diagnosis among all infeced cases, our esimaed epidemic pahs will reflec an epidemic one week prior. We experimened wih alering our assumpions abou he lengh of his ime-lag; hese experimens led us o conclude ha his assumpion has lile effec on he ime pah and magniude of he forecased epidemic. Nex, we describe our procedure for esimaing he number of recovered ( R ) and suscepible ( S ) individuals. Among hose exiing he infecive comparmen, we assumed ha he deah rae was a consan 1%. We base our assumpion on case repors of nh1n1 infecion (Ausralian Governmen Deparmen of Healh and Ageing 20; Ceners for Disease Conrol and Prevenion (CDC) 20; Presiden's Council of Advisors on Science and Technology 20). We calculae R simply as he cumulaive number of survivors among he infeced as below. (A2) R = I x 0 dx Our calculaion of S follows from he definiion of N as he populaion size in any given sae. N is he sum of four erms: oal deahs due o novel influenza infecion, S, I, and R. Therefore, he number of suscepible people is S = N I R (oal deahs due o novel influenza infecion a ). Finally, we esimae he sae-specific daily infecion rae (β ). Equaion (2) from he main ex, rearranged, implies he following: (A3) β = di N d + ( γ + α) I S I 22

23 Since we already eiher direcly observe (in he case of di ) or calculae all of he quaniies on d he righ hand side of (A3), we have an esimae of β. To characerize he uncerainy in his infecious period, we ran 200 ieraions. In each ieraion, we assigned each individual in he CDC daabase a new draw from he disribuion of infecive periods. This microsimulaion daa were generaed o mach wih he real CDC-daa in erms of he cumulaive infecives on he final microsimulaion day, July 17, 20. For our base case of a 5% deecion rae, we inflaed he number of infeced paiens (I ) (based on he confirmed cases) by 20 imes by summing 20 ieraions of he microsimulaion by randomly choosing from he 200 ieraions already creaed earlier. Similarly, for our sensiiviy analysis of a % deecion rae, we inflaed I by imes. A.2 Example of a microsimulaion ieraion In his secion, we illusrae our microsimulaion procedure by walking hrough a single ieraion in a single hypoheical sae. For simpliciy, we assume he CDC deecs 0% of all nh1n1 cases in is daa (in he acual simulaion, we assume a 5% deecion rae). Table A1 documens his example ieraion. In our example, we suppose ha one sae repors wo confirmed cases of nh1n1 infecion on = 1 bu does no repor any addiional cases up o = 7. On = 8, he sae repors a hird case o he CDC. This is indicaed on he firs on he firs row of Table A1. For each case ha arrives a = 1, we draw a random number represening he number of days ha each individual remains infeced. For he firs case, represened by he grey boxes on he second row of Table A1, we drew 3 days. For he second case, we drew 4 days. The oal number of infeced paiens in he sae on any paricular day, equals he number of gray boxes in 23

24 any given column. Thus, he number of infeced (I ) individuals, shown on he fifh row of Table A1, is no consan. I = I = I = ; I 1; and I = I = I = = From he daa on row 5, we calculae he number of individuals exiing he infecive comparmen a each. These consis of hose who recover or die from nh1n1 infecion. In his hypoheical example, shown on row 6 of Table A1, one person leaves he infeced sae a = 4 and anoher leaves a = 5. Similarly, we can calculae he number of newly infeced individuals wo people ener a = 1 and hen no one else eners afer. This is shown on row 7 di of Table A1. Finally, he change in he number of infeced people, or, is shown on row 8 of d Table A1. A.3. Esimaion of baseline aack rae and avoidance response parameers The procedure oulined in Secion A.1 and illusraed in Secion A.2 generaes, for each sae and a each ime poin, an enriched sae-level daa se from he original CDC daa which includes he key ime varying numbers we need o generae esimaes of he baseline aack rae and he avoidance response parameers. In his secion, we ouline our mehods for generaing hese laer quaniies. Our primary echnology involves esimaing a generalized leas squares (GLS) regression model from he panel of sae daa oulined in Secion A.1 (for each ieraion of he microsimulaion model). A his poin in he discussion, he variaion across saes becomes imporan since i is needed o idenify our parameer esimaes, so we subscrip our variables and parameers wih boh i (represening each sae) and (represening each ime poin). Our panel daa includes he sae-specific daily aack rae (β i ) and he number of infecious people (I i ) for each of 50 saes and he 86 days ha we observe in our daa. We model β i as follows: 24

25 (A4) β i = β 0 exp( c0 m0 w( I i )) where w I ) is a measure of he cumulaive prevalence of nh1n1 disease over he previous ( i seven days: (A5) = 1 w ( I i ) ln I it T = 8 We esimae β 0, c 0, and m 0 wih generalized leas squares (GLS) models by applying (A4) and (A5) o our panel daa se. We perform he esimaion separaely for each of 200 ieraions of he microsimulaion models and also separaely for each of he wo groups classified based on he epidemic aciviy: one group wih en saes wih above median incidence and a second group of 40 saes wih below median incidence. The sandard errors we repor for he GLS model accoun for heeroskedasiciy. A.4. Forecasing and validaion Using our esimaes from secion A.3 and our microsimulaion model equaions (1)-(3), (A4), and (A5) we forecas he baseline pah of he U.S. pandemic (wihou vaccinaion) beween April 23, 20 and July 17, 20. Among he oupus of our forecas include he cumulaive numbers of (boh oal and confirmed) infeced cases, deahs, he reproducion rae (RR ) of he virus, and he prevalence rae in he oal populaion. We calculae he ime-varian reproducive rae (RR ) as he produc of hree erms: he aack rae, he proporion of suscepibles in he oal populaion, and he duraion in he infecive comparmen β N S. ( γ + α) Since we run 200 ses of forecass (one for each ieraion of he microsimulaion model) we can repor represenaive ses of pandemic pah based on he size of he epidemic. In Figures 1 25

26 and 2, we repor pahs ha correspond o he median, and he upper and lower 95% perceniles of he final exen of he epidemic. We also forecas versions of he model in which we assume ha here is no avoidance response wih m 0 = 0. Our purpose in hese alernae forecass is o deermine wheher forecass produced using our primary avoidance response models fi beer wih he available daa on he epidemic (ha is, he confirmed cumulaive infecion raes up o July 17, 20) han do models ha ignore an avoidance response. The resuls from hese comparisons are shown in Figures 1 and 2. In he versions of he model ha we repor in he paper, we fi our models based on daa spanning from May 7 o July 3, dropping he firs and he las wo weeks of he available daa. Versions of model ha do no drop hese four weeks yield implausibly small epidemic impacs. Besides yielding more plausible resuls, here is anoher independen reason o drop hese weeks. According o he CDC, daa from hese four weeks were subjec o more serious underesimaion of confirmed cases. This is because, in he early weeks here were only a limied number of laboraory es orders; in he laer weeks, he surge in es orders were limied by he limied capaciies of laboraory esing afer he firs pandemic upsurge in many saes (Ceners for Disease Conrol and Prevenion (CDC) 20). This was why CDC sopped collecing and releasing he deailed confirmed case numbers afer July 17, 20 (Ceners for Disease Conrol and Prevenion (CDC) 20). Therefore, our paper presens resuls based on he U.S. daa from May 7 o July 3. In addiion o our U.S. forecass, we also perform an enirely parallel forecas using daa from Ausralia. The mehods we use for our Ausralian forecass are exacly analogous o hose we use in he U.S. forecass. However, he Ausralian confirmed case daa are available a he 26

27 jurisdicion-level (here are 8 jurisdicions in Ausralia) only up o July 19. Afer ha dae, here only daa on confirmed cases are available are a he naional level. So for he laer period, we inferred jurisdicion based on our microsimulaion resuls which allocaed he daily newly naional-level confirmed cases among eigh jurisdicions. Our allocaion rule assumes ha he incidence raios of he daily newly confirmed cases among eigh jurisdicions are equal o hose of he daily newly hospialized cases among hese jurisdicions. A.5 Forecasing he benefis of vaccinaion in he U.S. Our analyses shown in Figures 1-3 have been predicaed on he assumpion ha here is no effecive vaccine available agains nh1n1 infecion. As an exension o our work, we modify our procedure o ake accoun of he fac ha a vaccine did acually become available in he U.S. in Ocober, 20. Our modified SIR model reflecs he mos recen informaion: in Ocober 1-7 here were 1 million doses per day of he vaccine, in Ocober 8-14, 6 million doses per day, in Ocober 15- December 2, 3 million doses per day. In oal, here were 196 million doses available (McNeil 20; McNeil 20). In his version of our model, we assume ha he vaccine upake rae ranges beween 50% and 90%. A 50%, we effecively assume ha everyday 0.5 million doses (ou of 1 million doses available) were delivered and effecive, and ha he remaining 0.5 million doses were lef unused by he end of a simulaion period. For simpliciy and because here are no on poin daa currenly available, we assumed vaccine doses o be disribued equally across he all U.S. subpopulaions. A 50% upake rae is plausible because ofen a large number of doses remain unused even during pas usual influenza seasons wih vaccine supply problems (Orensein and Schaffner 2008). 27

28 Le p be he upake rae of he vaccine. We randomly selec p percen of he individuals from he suscepible (S) and he recovered (R) comparmens of he SIR model o receive he vaccine. We selec people from R because in realiy only a small proporion of he recovered populaion has a laboraory confirmed diagnosis of nh1n1. We assume, herefore, ha all subjecs in R wans o be vaccinaed, which approximaes he acual U.S. siuaion. (This assumpion reduces he effeciveness of he vaccine because providing he vaccine o people in R does no conribue miigaing he pandemic. These individuals have presumably already gained naural immuniy o nh1n1 infecion which we assume o be 0% proecive agains H1N1 infecion.) Following he mos recen vaccinaion guideline (Ceners for Disease Conrol and Prevenion (CDC) 20), aduls receive only one dose and children aged under receive wo doses separaed by 28 days (second dose conained half he amoun of he firs dose). We accoun for his recommendaion as well in our model. We assume vaccinaion is 30%-70% effecive in reducing infecion, severe illness, and deah due o novel influenza. We incorporaed his assumpion ino our model as follows. Suppose vaccine effeciveness is 50%. In ha case, only 50% of he vaccinaed individuals ransi direcly from he suscepible (S) comparmen direcly ino R wihou passing hrough he infeced (I) comparmen. The remaining 50% of hese vaccinaed individuals (wih poor immune-response) remain in S despie vaccinaion. We assume ha, hese vaccinaed wih a poor immune-response were no vaccinaed more han once, since individuals do no ypically know heir immune-response o a vaccine ha requires a laboraory es. The vaccine becomes proecive roughly 9 days afer i is adminisered. In he case of children under, i becomes effecive only afer he second dose (Ceners for Disease Conrol and Prevenion (CDC) 20). We modeled his fac as follows: all of he vaccinaed remain in 28

29 he suscepible comparmen for 9 days afer he vaccinaion dae, excep for children under who remain in S for 37 days afer he firs vaccinaion. Formally, le µ indicae vaccine upake rae (ranging beween 50% and 90%), le indicae he proporion of populaion aged or older, le θ indicae vaccine effeciveness (ranging beween 30% and 70%), and le V indicae he oal number of vaccine doses available on day. When we incorporae he assumpions abou vaccinaion ino our modified SIR model, equaions (1)-(3) become: (A6) ds d β S I = N µρθv S S µ (1 ρ θv 9 9 ) 9 + R 9 37 S S R 37 (A7) di d β S = N I ( γ + α) I (A8) dr d = γ I + µρθv S S + µ (1 ρ θv 9 9 ) 9 + R 9 37 S S R 37 29

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