Why are public health authorities not concerned about Ebola in the US? Part I. Fat tailed distributions

Risking It All: Wh y are public health authorities not concerned ab out Eb ola in the US? P art I. F at tailed distributions Y aneer Bar-Y am New England Complex Systems Institute 210 Br o adway, Suite 101, Cambridge MA 02139, USA (Dated: No v. 5, 2014) Abstract US public health authorities claim imp osing quarantines on healthcare work ers returning from W est Africa is incorrect according to science. Their p ositions rely upon a set of studies and exp erience about outbreaks and transmission mec hanisms in Africa as well as assumptions ab out what those studies imply ab out outbreaks in the US. According to this view the probabilit y of a single infection is lo w and that of a ma jor outbreak is non-existen t. In a series of brief rep orts w e will provide insigh t into wh y properties of netw orks of con tagion that are not considered in traditional statistics suggest that risks are higher than those assumptions suggest. W e b egin with the difference b et w een thin and fat tailed distributions applied to the num ber of infected individuals that can arise from a single one. T raditional epidemiological models consider the contagion process as describ ed by R 0 , the a verage num b er of new infected individuals arising from a single case. Ho wev er, in a complex interdependent society it is p ossible for the actual num b er due to a single individual to dramatically differ from the a verage n umber, with severe consequences for the abilit y to con tain an outbreak when it is just b eginning. Our analysis raises doubts ab out the scientific v alidit y of p olicy recommendations of public health authorities. W e also p oin t out that existing CDC public health p olicies and actions are inconsistent with their claims. 1 The Eb ola epidemic b ecame a global public health crisis due to its p ersisten t exp onen tial gro wth ov er half a year despite efforts to contain it in W est Africa. The arriv al of the first Eb ola case b y commercial fligh t to the US, Thomas Duncan, and subsequent infections in Dallas of t wo n urses treating him, led to multiple stages of reev aluation of public health p olicies [ 1 – 6 ]. These c hanges in policy resulted from unanticipated even ts and constituted additional precautions in hospital settings and in monitoring of trav elers from W est Africa to protect the public. A second case, an infected physician returning to New Y ork from pro viding care in Guinea, triggered a set of new policies. Some of these are not b y public health authorities but by elected officials in New Y ork, New Jersey , Illinois and elsewhere [ 7 – 9 ], and include 21 da y quarantines or home observ ation of returning health care w orkers. The resp onse of public health authorities has been to affirm [ 10 , 11 ] that these p olicy c hoices are counter to science and exp erience from Eb ola outbreak resp onse in Africa [ 17 – 23 ]. A cen tral asp ect of the understanding of the risk of outbreaks for Eb ola is the mec hanism of transmission. Generally , it is understo o d that those who hav e b een in direct physical con tact with individuals with Eb ola resulting in exp osure to their b o dy fluids, or indirectly with their b o dy fluids on surfaces, ha v e a probability , not a certaint y , of b eing infected. Healthcare work ers adopt precautions against infection including p ersonal protective equip- men t (PPEs) that are essen tially hazardous materials suits. Nev ertheless, a large n umber of infections and deaths of healthcare w orkers hav e o ccurred [ 24 ]. Differen t kinds of direct and indirect con tact ha ve different lev els of risk. Evidence suggests that there is a coinci- dence b etw een a transition from a non-symptomatic, non-transmissible (laten t) p erio d and a p erio d in which observ able symptoms start, transmission is possible, and blo o d tests are p ositiv e. P olicies are designed, therefore, to assure that individuals are not in contact with others, and PPEs are b eing used, after symptoms start. Hence the imp ortance of isolation once symptoms start, and monitoring prior to symptoms to ensure that a transition to the symptomatic state do es not result in cases of infection. Public health authority positions, including a New England Journal of Medicine (NEJM) editorial [ 11 ], state there is no need for quarantine b ecause isolation is only needed when symptoms are presen t. According to this view it is sufficien t to monitor and isolate when symptoms arise. The NEJM editorial sp ecifically frames its statement as relev an t to health- care work ers and does not explain why they did not adopt this stance for others who hav e b een exp osed. Quaran tines w ere imp osed on four members of the family who were b eing 2 visited b y Thomas Duncan, the first US Eb ola case in Dallas, when he dev elop ed symptoms. None of them had symptoms at the time of the quaran tine or subsequen tly dev elop ed them [ 12 – 16 ]. Since the prop erties of transmission apply equally to Duncan’s p ersonal contacts as to healthcare work ers, is it unclear, why NEJM did not write an editorial ab out the imp osi- tion of quarantines on them nor refer to it in the editorial that was written. An explanation of the discrepancy is of imp ortance as it lea ves the public and officials uncertain ab out how to interpret the inconsistency , and sp ecifically the claim that quaran tine do es not reflect a v alid p olicy option. P erhaps just as significan t, public discussions [ 15 ] imply that the CDC has b een advocating v oluntary acceptance of home isolation that may not differ from enforced home quarantine, reflecting a legal rather than medical or scientific distinction. These issues suggest that the p osition that is b eing taken b y public health authorities is not so well defined as a scien tific one as they indicate. CDC p olicy for monitoring and restrictions on individuals [ 5 ] provides for a n um b er of lev els of risk of an individual b eing infected with Eb ola based on exp osure and suggests dif- feren t levels of self-monitoring or health official monitoring as well as restrictions on trav el and contact b et ween individuals for each lev el. F or example, public places and distances of less than three feet from others are to b e av oided for individuals at high risk even without symptoms . The specification indicates enforced restrictions on tra v el, i.e. “These individuals are sub ject to con trolled mov emen t which will b e enforced b y federal public health trav el restrictions; trav el, if allo w ed, should occur only b y noncommercial con v ey ances...” Authori- ties are g iven wide latitude to enforce higher levels of restriction based up on their judgements ab out exp osure and likelihoo d of compliance with volun tary restrictions. Whether or not differen t lev els of self or publicly imposed isolation and monitoring are considered quaran- tine is a matter of recently adopted terminology . The existence of v arious lev els of risk and asso ciated proto cols manifests tradeoffs of risk versus restrictions, and lev els of trust in the individuals to self monitor and rep ort their conditions as w ell as self-restrict activities. The CDC p olicy iden tifies returning healthcare w ork ers as b eing at a medium level of risk (termed “some risk”). It is imp ortan t to realize that differen t categories of risk should ha ve differen t isolation policies only if there is a so cietal tolerance for the associated risks, i.e. this is not a question of the existence or absence of transmission but of the asso ciated risk lev els. Mathematically , for each risk lev el there is a probability I r of an individual being infected in the latent p eriod b efore it is known. Then there is a probability T p giv en a particular 3 imp osed proto col that an infected individual will transmit the disease, causing another in- fection. The pro duct of these tw o is the probability of an individual in that risk class and follo wing that proto col causing another infection P r,p = I r T p . If a certain level of risk is acceptable, so that we wan t the probabilit y of a new case to b e low er than a v alue P 0 , i.e. P r,p < P 0 , and if the risk of the individual b eing infected is lo wer in one class than another, the proto cols can b e relaxed allo wing T p to b e higher. T o preven t an outbreak from growing the n umber of newly infected individuals only has to b e less than one. Ackno wledging that w e wan t a significantly low er probability , w e can take it to b e muc h less than one, sa y one in 10, or ev en one in 100, out of “an abundance of caution,” and this w ould be enough to con trol an outbreak. W e see from this discussion that the essen tial question is what are the risks that are b eing taken. The question of risks is not directly addressed b y the public health authorities [ 11 ], except to dismiss “cynics” who unreasonably demand 100% certain ty . They do not explain what are the risks they consider reasonable and what they do not. Still, one can infer from their statements that the possibility of individual cases is acceptable and that they are concerned only for a large outbreak, whose risk they consider to b e non-existent. Under these conditions, the taking of risks migh t b e justified, after all a public fear of Eb ola is only justified if it can b e the cause of widespread outbreak and not the deaths of a few individuals, of which there are man y causes in society . This view has b een repeated multiple times, i.e. that the public at large will not be at risk (even if there are a few cases) in the US [ 38 , 39 ]. Indeed, the existence of risk is clearly ackno wledged in the risk lev els asso ciated with the CDC p olicies. Low enough levels of risk of a p erson b eing a carrier of Eb ola can b e addressed b y lo w er lev els of observ ation and isolation. If a case arises, then the consequences m ust not b e very severe, otherwise such a risk stratification do es not make sense. The assessmen t of risks in CDC p olicies are comp osed of a com bination of medical kno wl- edge, b eha vioral assumptions ab out individuals and risk tolerance. The medical kno wledge requires an understanding, among other things, of the coincidence of con tagion, symptoms and blo od tests; the b eha vioral assumptions hav e to do with the levels of trust in suc h matters as whether instructions are sufficien tly clear and p eople will actually follow them; and the risk tolerance has to do with b oth the certain ty of our knowledge and the levels of risk so ciet y is willing to tak e. An imp ortan t asp ect of an y ev aluation of these issues is the sensitivit y of the p olicy conclusions to the level of uncertain ty in our knowledge, i.e. a sensi- 4 tivit y analysis. The statemen ts of public health authorities are equiv alen t to the statement that the policies are robust to the uncertain ties in our kno wledge and statistical v ariation in transmission and contagion even ts. W e will sho w that this statement is correct only if traditional statistical assumptions are v alid. That traditional assumptions are not likely to b e applicable to the current conditions leads to a different understanding that is b etter describ ed by complex systems science [ 25 ]. Th us, public health authorities are advocating p olicies that put many at risk. Moreo v er, their claims that science is b ehind their p ositions may discredit science at a time when it is imp ortan t to demonstrate that science provides clear and effective p olicy recommendations. Giv en a higher lev el of risk, the claims b y public health authorities that they do not w an t to discourage or inappropriately incon v enience healthcare work ers who are devoting their service to containing the outbreak is in v alid. Healthcare work ers dev oted to service of the public in con taining and preven ting the Eb ola outbreak should see a conserv ativ ely designed isolation proto col after returning from treatment of patien ts in W est Africa as part of that service. This is true whether or not the proto col is called a quarantine. In order to explain these issues, w e will provide a set of discussions of particular complex systems concepts and their mathematical basis. In this, the first, we will lo ok at the p ossibilit y that a single individual migh t cause a muc h larger num ber of infected individuals than is exp ected. Ev en one such case may cause a breakdown in our ability to contain the outbreak. As a first step i n this discussion w e consider the role of assumptions ab out the distribution of transmission probabilities relev an t to standard mo dels of con tagion. The abilit y to monitor sufficien tly to preven t large num bers of transmission is at issue. T raditional statistical studies are based up on the assumption that probability distribu- tions are “thin tailed” (often Gaussian distributions) so that the range of actual v alues is narro w, confined to a few standard deviations from the mean. In cases where the mean is prop ortional to the n um b er of elements, an y particular instance is not v ery far aw a y from the a v erage v alue. T raditional mo dels of con tagion assume that ev ery infected individual giv es rise to a n um b er R 0 of subsequen t infected individuals on a verage. But is this the v alue w e can reliably exp ect to happ en in a particular instance? The answer to this question is of critical imp ortance, esp ecially in the first few stages of an outbreak. Complex systems science suggests that distributions are not alwa ys thin tailed, they can b e fat tailed (also called heavy or long tailed). Among fat tailed distributions are p o w er 5 la w (scale free) distributions that are often observed. This means that there are situations in whic h a single sick individual can give rise to 10s, 100s or 1000s of cases in a single generation. The likelihoo d of this happ ening ma y not b e as high as ha ving only a few, but it cannot b e dismissed as it can in a thin tailed distribution. The difference betw een thin and fat tailed distributions has b een well explained in dis- cussions of risk by Nassim T aleb [ 40 ]. As an illustration he considers the difference b et ween w eight and wealth. Randomly taking 1 , 000 p eople, their total weigh t is ab out 1 , 000 times the weigh t of an a verage individual, but their wealth ma y b e dominated by the wealth of a single one. It is imp ossible to find a p erson who w eighs 10 times the av erage w eigh t of an individual (thin tailed distribution). On the other hand a single p erson can ha ve as m uch w ealth as the tw o billion p o orest p eople (fat tailed distribution). In the Eb ola outbreak in W est Africa, the v alue of R 0 is about 2 with v arious studies pro viding sp ecific estimates [ 26 – 28 ]. This means that every infected individual leads to only ab out 2 other infected individuals. A t this v alue it takes 10 sequential infections (generations) to ha ve 1,000 sick individuals. Since each generation takes a couple of weeks, this is ab out 5 months whic h is appro ximately the time from March, when the outbreak started in earnest, till the end of the summer. As man y keep telling us [ 29 – 31 ] this still do es not mak e Eb ola a ma jor cause of death compared to others lik e Malaria. If it keeps going, ho wev er, the result is disastrous with 1 million sic k after 20 generations and 1 billion after 30, in tw o and a half years. Still, this is different from thousands in a single generation, in whic h case it w ould only take 3 generations to get to a billion. A disease that is airb orne, e.g. measles, migh t ha ve an R 0 of 10 or more, in whic h case 9 generations or just ov er 4 mon ths would b e enough to get to a billion sick p eople. The probability distribution that naturally describ es the num b er of contacts that are infected by a single individual in a standard con tagion mo del is a Poisson distribution. This distribution describ es the v ariation in num b er of infection ev ents that happ en randomly in a given p erio d of time, i.e. the infectious p erio d. Similar to the Gaussian distribution, the P oisson distribution is a thin tailed distribution. In this distribution the standard deviation is just the square ro ot of the av erage, i.e. σ = √ R 0 , so that the c hance of ha ving more than t wo or three times the t ypical num b er is v anishingly small for an outbreak in which R 0 is greater than one. This is not the case if there is a long tail distribution. Figure 1 illustrates the difference b et w een thin and fat tailed distributions, sho wing tails 6 1E#12% 1E#11% 1E#10% 1E#09% 1E#08% 0.0000001% 0.000001% 0.00001% 0.0001% 0.001% 0.01% 0.1% 1% 1% 10% 100% 1E#12% 1E#11% 1E#10% 1E#09% 1E#08% 0.0000001% 0.000001% 0.00001% 0.0001% 0.001% 0.01% 0.1% 1% 0% 10% 20% 30% 40% 50% 60% FIG. 1: Comparison of thin tailed Poisson distribution (black) with fat tailed pow er la w distri- bution (red) that has a m uch higher probabilit y of large ev ents. Left panel uses logarithmic axes, righ t has logarithmic v ertical axis only . of the n umber of p ossible instances that o ccur with more than a certain n um b er (cum ulative P oisson and p o wer law distributions). So if we think of this as new Eb ola cases infected b y a single individual, we see that the chance of larger num b ers falls muc h faster for the thin P oisson distribution than for a fat p o wer la w distribution. In the p ow er law case w e ha ve to iden tify a level of risk w e care ab out. W e see that 3 or more cases will happ en 1 in 10 times, 20 or more cases 1 in 100 times, 30 or more cases 1 in 200 times. In the real w orld the num b ers migh t b e higher or low er, but w e do not know them from the information a v ailable from previous outbreaks. In the P oisson distribution, we do not ha ve to worry ab out questions like this. Ha ving more than a few cases just w ould not happ en, as the public health authorities hav e claimed. Empirical evidence for the existence of individuals that cause a muc h larger num b er of other cases than the av erage has b een found in studies of the SARS epidemic [ 32 – 34 ]. Suc h inciden ts w ere rep orted in ev ery region of the epidemic and after con trol measures w ere implemen ted and play ed an imp ortan t role in the outbreak. T raditional studies consider such “sup erspreader” individuals as anomalies rather than as indicating a fat tailed distribution with implications for ev aluation of risks. The primary metho d used by public health authorities for containing an Eb ola outbreak is contact tracing. In this metho d an individual who is infected is asked ab out p eople with whom he or she has been in contact during the con tagious phase. They are then sub ject to a 7 monitoring and isolation protocol for 21 da ys to prev ent further spread. When there w as one individual in Dallas that was sic k, there were more than 100 p otential contacts [ 35 ], man y more if w e count the p eople contacted for b eing on the plane in which an infected nurse flew [ 36 ]. This do es not include every one who rep orted symptoms but did not hav e other reasons to be susp ected and so were rapidly dismissed from consideration [ 37 ]. If ev ery outbreak has only a few individuals who are sick this can work. Ho wev er, if there are 100, we might ha ve to trace 10,000 p eople whic h b ecomes m uch less practical and p erhaps imp ossible. Public health authorities are relying up on the assumption that ev en if a few people get sic k, they will b e able to contain the outbreak and, as they k eep affirming, the public at large will not b e at risk [ 38 , 39 ]. All they hav e to do to achiev e this is to identify enough con tacts so that the resulting effective R 0 is less than one. A few p eople would get sick but there w ould not b e a ma jor outbreak as the num b er would decrease from generation to generation thereafter. Ho wev er, this assumes that a mo del with a sp ecific v alue of R 0 describ es what can b e exp ected to happ en in the US as it do es in Africa, i.e. a thin tailed distribution holds. The difference b et ween situations in whic h thin tailed distributions and fat tailed dis- tributions apply is whether the lo cal even ts are essen tially indep endent, or they are not indep enden t, so they combine to create larger ev ents. In subsistence agrarian so cieties in rural Africa, p eople act mostly in family groups. One p erson is not lik ely to be in close contact with muc h more than about 10 or 20 family mem b ers. If the probabilit y of transmission for a single con tact is lo w, then w e end up with a few transmission even ts p er p erson, whic h is what has b een observ ed. The extent of transmission ev ents by a single individual is b ounded b y the num b er of contacts they ha ve. In urban areas in Africa and in the US, the nature of the contact net work is different. The high density urban areas of W est Africa, including Monro via in Lib eria, hav e p eople pac ked muc h closer together, and they hav e to do a v ariety of things that bring them in con tact with each other to get fo o d eac h da y . Going to the mark et is one such activit y . This can b e exp ected to lead to a higher R 0 and a muc h larger outbreak, one that o verwhelmed the public health efforts to contain it. W e often hear ab out the problem with ha ving to o few hospital beds [ 41 ], but a k ey problem in urban areas of W est Africa is that the main to ol used b y public health authorities to limit outbreaks is contact tracing. Contact tracing in a dense urban en vironment is m uch more difficult than in far rural areas or even less 8 dense urban areas where Eb ola has b een presen t b efore. It becomes essen tially imp ossible when there are many cases. Without con tact tracing, it is hard if not imp ossible to contain an outbreak. While the con tacts in Monrovia are of a higher frequency than those in rural areas, these are still p oor so cieties. This makes p eople mostly connected lo cally to others in their neighborho o d. Still, there are some w ays in which they are connected more generally . Among the ma jor rep orted sources of transmission is taking taxis to a hospital for care [ 42 ]. T axis often carry multiple individuals going in the same direction and, ev en if not, a sic k p erson lea ving b o dily fluids in the taxi can lead to transmission to subsequent passengers as well. As society develops, the actions of p eople b ecome connected in net works that are more in terconnected and highly heterogeneous. Different p eople ha ve very differen t levels of con- nection to others. Th us, the netw ork of connections can b e exp ected to b e muc h more heterogeneous in the US. Individuals play v aried roles in so ciet y and are connected to others to a different degree. V arious wa ys that are used to characterize so cial netw orks show that they generally ha v e fat tail distributions [ 43 ]. W e can infer that most p eople are not in a lot of direct physical contact with others, but some are. In a high densit y city the con tact rate is muc h higher. W e can p oin t to a few examples where transmission by direct con tact migh t tak e place: a masseuse giving multiple massages ev ery day , a p olitician that shakes man y hands, and a n urse in a hospital (not one who is caring for Eb ola patients) who go es from patient to patien t. There are also ev ents where man y people are in direct con tact including conferences in whic h p eople shake hands, and groups who go social dancing. Indirect con tact through b ody fluids (including sweat as well as urine, v omit, blo o d and feces) dep osited on a surface b y one person in a place that other p eople touc h it is a less probable wa y to transmit the disease, according to the exp erience in Africa, but it is still considered p ossible [ 44 ]. There are many suc h indirect contacts for restaurant or cafeteria work ers, and in particular places, suc h as public buses and trains and public toilets, many p eople ma y follow where a single p erson has b een. Unlike the dominan t kinds of con tact in families in p o or so cieties, most of these contacts take place anon ymously betw een p eople who do not kno w eac h other. This w ould make con tact tracing or even kno wing who is at risk muc h more difficult. Let us translate this into a sp ecific scenario. The do ctor who returned from Guinea and w ent out in to public places and on public transp ortation in New Y ork and had symptoms 9 the next day should b e assumed to ha ve a lo w probability of infecting any one through those tra vels. But lo w probabilit y does not mean no probability in this case. If there is one p erson who is infected, that p erson is not a high lik eliho o d carrier. If he or she started to sho w symptoms the possibility of Eb ola w ould b e reasonably dismissed either by them or an y health authority they con tacted. A hospital w ould dismiss their having Eb ola b ecause they were not a trav eler to w est Africa. Hospitals do this ev ery da y for man y cases where symptoms are similar to the early symptoms of Eb ola, whic h are lik e those of the flu or other viral infections. CDC proto col explicitly states that such individuals should only receive routine medical ev aluation and care [ 5 ]. Ev en if the symptoms got worse, an emergency ro om proto col w ould not consider them to hav e Eb ola b ecause of this. So let us say that an infected p erson happ ens to b e a restaurant work er who is afraid of not sho wing up to w ork, or a masseuse that do es not feel they can take off work b ecause of prior app oin tments. T aking an Advil and going to work, p erhaps b y public transp ort, they are in indirect or direct con tact ov er a few da ys with 10s or 100s of p eople. By that time p erhaps the symptoms are so bad that they rep ort to the hospital and someone realizes that Eb ola should b e tested for; at least it would b e b etter if they do. Ev en so, we may hav e 10s of actual Eb ola infections. At that p oin t we cannot consider an yb o dy in the entire city with fev er as not b eing a p ossible Eb ola exp osed case. If the restauran t happ ens to b e a p opular place for trav elers, say at one of the airp orts, w e cannot treat anybo dy anywhere as if they are not a possible carrier. Curren tly w e only ha ve to treat fev er as a p ossible symptom of Eb ola if the p erson trav eled to W est Africa. This is a tin y fraction of all the cases of fever. A t this p oin t the ability to use contact tracing to con trol the outbreak b ecomes doubtful and more sev ere actions must b e tak en including changes in b eha vior of the public. F or healthcare facilities to provide in tensive care to all the infected individuals, and attention to the large num b er of symptomatic but not Eb ola infected individuals, ma y require compro- mising normal op erations. Ho w such an outbreak w ould even tually b e con tained is unclear as the real world exp erience is limited or non-existen t. Surely it would not b e easy to do. What causes the fat tail distribution to arise in this case? Ho w are the infection even ts dep enden t on eac h other? In a standard statistical treatment, we would av erage o ver all professions getting a num b er that is dominated b y lo w con tact w orkers, p erhaps office work- ers sitting at their desk most of the day , who do not hav e muc h ph ysical or indirect contact. In an imaginary w orld this would work if p eople switched professions every hour. Then the 10 probabilit y that a single p erson infected man y others w ould be the same as an y other and w ould equal the a verage. The reason that this is not the case is that a p erson do es not switc h profession from hour to hour. When someone has a profession that inv olves a lot of con tact, if they are sick then there are man y transmission ev ents that are linked to eac h other. Thus the traditional statistical assumptions do not apply . Other, p erhaps b eha vioral, scenarios might b e considered, as in someone who is at an in termediate level of risk and self-monitoring has a few drinks (there are no restrictions on this in the CDC guidelines) and as a result acts in less resp onsible w ays, violates guidelines for trav el or pro ximity to others, and even migh t throw up p erhaps just as he or she is b eginning to show symptoms. Or someone b ecomes sic k from fo o d p oisoning and throws up not b ecause of Eb ola but just as symptoms are dev eloping. These scenarios are only a few of man y but they illustrate the problem of having a highly heterogeneous and interconnected netw ork. The most likely scenario is that no one will b e infected by the infected do ctor’s trav els. The most likely scenario is that ev en if one p erson is infected they will not b e one of the highly connected p eople and will infect only a few others that they are in contact with on a daily basis and kno w p ersonally . This will giv e time to find them and isolate them. In a world of thin tailed distributions it is enough to iden tify the most likely scenario and any other scenario is going to b e ab out the same. But in a world of fat tailed distributions there are other kinds of scenarios that are not the same and they can happ en and often do. The imp ortance of uncertaint y and risks that are associated with it is manifest in this discussion. Unlik e the normal distributions commonly assumed in statistical approaches, fat tailed distributions lead to extreme even ts, i.e. muc h higher risks. This tends to lead to surprise. Indeed we hav e already seen such surprise in public health response in the US to Eb ola, in the hospital resp onse in Dallas and in the infections of n urses and the fligh t one of them to ok when she b egan to ha ve symptoms. In the second installmen t of this series w e will review in greater detail the uncertaint y that arises b ecause existing knowledge arose in rural W est Africa, a differen t con text from that of New Y ork or other cities, or ev en rural areas of the US. One example of a relev ant difference is the weather. Daily temp eratures consisten tly reached highs in the upp er 90s during the outbreak that served as the primary lo cation of transmission analysis [ 17 , 18 ] and air conditioning is not a relev ant factor there. Significan tly lo wer ro om temp erature may change the likelihoo d of indirect transmission 11 through surfaces, an additional and p oten tially significan t source of uncertaint y ab out how outbreaks may spread in the US and other countries. In conclusion, I note that the opinion of public health authorities is not b eing w ell received b y the public [ 45 ] and is b eing resisted by elected officials [ 46 ]. The mathematically based discussion of transmission giv en here supp orts a view that risks are muc h greater. Actions that reasonably an ticipate risks are better than a reactiv e resp onse. Since it can be exp ected that the actual num b er of infected individuals has a fat tail distribution, it is not imp ossible that an outbreak will ov erwhelm the ability of authorities to control it. W e thank John Sterman for helpful comments. [1] J. 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