> OQLMN bjbj,, 2NNWs7dHH$$$$$$$$$8$%T$tZ,k-"---Q/Q/Q/,t.t.t.t.t.t.t+wy.t]$Q/M/Q/Q/U/.te4$.9$$--te4e4e4Y/]$8-$-,te4Q/,te4e4RK$$Mui}K$A3$LHN%t0tLze4z<Me4Mb$,NQ/Q/Q/H":
Supporting Information Text S1 for
Social Network Sensors for Early Detection of Contagious Outbreaks
Nicholas A. Christakis1,2*, James H. Fowler3,4
1Faculty of Arts & Sciences, Harvard University, Boston, Massachusetts, USA
2Health Care Policy Department, Harvard Medical School, Boston, Massachusetts, USA
3School of Medicine, University of California, San Diego, La Jolla, California, USA4Division of Social Sciences, University of California, San Diego, La Jolla, California, USA
" To whom correspondence should be addressed, email: christakis@hcp.med.harvard.edu, phone: (617) 432-5890.
Subjects
We enrolled a total of 744 undergraduate students from Harvard College, discerned their friendship ties, and tracked whether they had the flu beginning on September 1, 2009, from the start of the new academic year, to December 31, 2009.
Beginning on October 23, 2009, we approached 1,300 randomly selected Harvard College students (out of 6,650); we waited until a few weeks of the new school year had passed in order to be able to obtain current friendship information. Of these 1,300 students, 396 (30%) agreed to participate. All of these students were in turn asked to nominate up to three friends, and a total of 1,018 friends were nominated (average of 2.6 friends per nominator). This yielded 950 unique individuals to whom we sent the same invitation as the initial group. Of these, 425 (45%) agreed to participate. However, 77 of these 950 subjects were themselves members of the original, randomly selected group and hence were already participants. Thus, the sample size after the enrolment of the random group and the friend group was 744.
Nominated friends were sent the same survey as their nominators; hence, the original 425 friends also nominated 1,180 of their own friends (average of 2.8 friends per nominator), yielding 1004 further, unique individuals. Although we did not send surveys to these friends of friends, 303 (30%) were themselves already enrolled either in the friends group or in the initial randomly selected group.
Thus, in the end, we have empanelled two groups of students of essential analytic interest here: a random sample (N=319) and a friends sample (N=425) composed of individuals who were named as a friend at least once by a member of the random group. In addition, we ultimately had information about a total of 1,789 uniquely identified students (who either participated in the study or who were nominated as friends or friends of friends) with which to draw social networks of the Harvard College student body (27% of all 6,650 undergraduates). Our sample of 744 was thus embedded in this larger network of 1,789 people.
After giving informed consent, all subjects completed a brief background questionnaire soliciting demographic information, flu and vaccination status since September 1, 2009, and certain self-reported measures of popularity. We also obtained basic administrative data from the Harvard College registrar, such as sex, class of enrolment, and information about participation in varsity sports.
We also tracked cases of formally diagnosed influenza among the students in our sample as recorded by University Health Services (UHS) beginning on September 1, 2009 through December 31, 2009. Presenting to the health service indicates a more severe level of symptomatology, of course, and so we do not expect the same overall prevalence using this diagnostic standard as with self-reported flu discussed below. However, UHS data offer the advantage of allowing us to obtain information about flu symptoms as assessed by medical staff. A total of 627 of the 744 students (84%) who agreed to participate in the survey portion of our study also gave written permission for us to obtain their health records. Finally, 7 students reported being diagnosed with flu by medical staff at facilities other than UHS (in response to survey questions asked of all students), so we include these in the data as well.
Notably, we do not expect cases of flu to meaningfully alter the social networks and friendship patterns of Harvard undergraduates, let alone over a two-month period. And, we assume that the friendship network of Harvard students in our sample did not change meaningfully over the period September to December. That is, we treat the network as static over this time interval.
Beginning on October 23, 2009, we also collected self-reported flu symptom information from participants via email twice weekly (on Mondays and Thursdays), continuing until December 31, 2009. The enrolled students were queried about whether they had had a fever or flu symptoms since our last email contact, and there was very little missing data (47% of the subjects completed all of the biweekly surveys, and 90% missed no more than two of the surveys).
Self-report of symptoms rather than serological testing is the current standard for flu diagnosis. Students were deemed to have a case of flu (whether seasonal or the H1N1 variety) if they report having a fever of greater than 100 F (37.8 C) and at least two of the following symptoms: sore throat; cough; stuffy or runny nose; body aches; headache; chills; or fatigue. We checked the sensitivity of our findings by using definitions of flu that required more symptoms, and our results did not change. As part of the foregoing biweekly follow-up, and to supplement the UHS vaccination records, we also ascertained whether the students reported having been vaccinated (with seasonal flu vaccine or H1N1 vaccine or both) at places other than (and including) UHS.
Hence, we had two measures of flu incidence. The medical-staff standard was a formal diagnosis by a health professional and typically reflected more severe symptoms. The self-reported standard captured cases that did not come to formal medical attention. As expected, the cumulative incidence of the latter was approximately four times the former (32% versus 8%) by the time of cessation of follow-up on December 31, 2009.
Network Measures
We use friendship nominations to measure the in-degree (the number of times an individual is named as a friend by other individuals) and out-degree (the number of individuals each person names as a friend) of each subject. The in-degree is virtually unrestricted (the theoretical maximum is N 1, the total number of other people in the network) but the out-degree is restricted to a maximum of 3 due to the name generator used.
We measure betweenness centrality, which identifies the extent to which an individual lies on potential paths for passing contagions from one individual to another through the network. If we let EMBED Equation.DSMT4 represent the number of shortest paths from subject i to subject k, and EMBED Equation.DSMT4 represent the number of shortest paths from subject i to subject k that pass through subject j, then the betweenness centrality measure x for subject j is EMBED Equation.3 . To ease interpretability we divided all scores by max(xj) so that all measures would lie between and including 0 and 1.
To measure k-coreness, we start by removing all individuals with one or fewer friends. After one iteration, some individuals may be left with only one friend, so we continue pruning the system iteratively until there is no individual left who has one or fewer friends. The removed nodes are all assigned a value of k=1. Next, we iteratively remove all individuals who have two or fewer friends, giving them a value of k=2. We continue this process, increasing the threshold each time, until all nodes are assigned a value (the maximum in our network is k=3).
Finally, we also measure transitivity as the empirical probability that two of a subjects friends are also friends with each other, forming a triangle. This measure is just the total number of triangles of ties divided by the total possible number of triangles for each individual. This measure is undefined for individuals with less than 2 friends (23 cases out of 744), and so we treat this measure as missing in those cases.
Note that for the purpose of measuring transitivity, coreness, and betweenness centrality, we assume all directed ties are undirected, so that a tie in either direction becomes a mutual tie. For example, we consider the case where A names B, B names C, and C names A to be transitive. Likewise, if A names B, A names C, and B names C, we consider the relationships to be transitive for all three individuals.
We used Pajek to draw pictures of the networks and used the Kamada-Kawai algorithm, which generates a matrix of shortest network path distances from each node to all other nodes in the network and repositions nodes so as to reduce the sum of the difference between the plotted distances and the network distances. A movie of the spread of flu with a frame for each of the 122 days of the study is available online at HYPERLINK "http://jhfowler.ucsd.edu/flunet_v3.mov" http://jhfowler.ucsd.edu/flunet_v3.mov.
While it is the case that, in situations of chronic illness, people that are sick may have fewer friends or different network architectures as a result of their illness, we do not anticipate a problem with this phenomenon in this setting. That is, we do not think that undergraduate friendships will be modified by virtue of having the flu, especially over the short time intervals being studied here.
Personality Measures
To measure self-perceived popularity, we adapted a set of 8 questions previously used to assess the popularity of co-workers. Specifically, we asked subjects to rate on a 5 point scale their agreement (ranging from strongly disagree to strongly agree) with the following statements: I am popular, I am quite accepted, I am well-known, I am generally admired, I am liked, I am socially visible, I am viewed fondly, and I am not popular (reverse scored). We generated index scores via a one-dimension factor analysis of all 8 items (Cronbachs alpha=0.66).
Analysis
In Table S1 we report summary statistics for the random group and the friend group and the results of a Mann Whitney U test, which is a nonparametric test of differences in the two distributions. Notice that the friend group exhibits significantly higher in-degree and betweenness centrality, and significantly lower transitivity than the random group, as theorized. In addition, we find that the friend group has significantly more females and fewer sophomores than the random group.
In Table S2 we present Spearman correlations with p values to evaluate whether or not any study variables influence overall risk of getting the flu by December 31, 2009. Notice that the self-reported and medical staff measures are highly correlated at ( = 0.40. However, no other variable is significantly associated with both measures. The two strongest associations with self-reported flu are in-degree and being a sophomore, but at 0.08 neither of these associations is strong and neither is confirmed in the data based on diagnoses by medical staff.
In Tables S3-S14, we report results from an estimation procedure designed to measure the shift in the time course of a contagious outbreak associated with a given independent variable. We fit the observed probability of flu to a cumulative logistic function
EMBED Equation.3
where Pit is the probability subject i has the flu on or before day t; t +( + bXit is a function that determines the location of peak risk to subject i on day t that includes a constant (, a vector of coefficients b, and a matrix of independent variables Xit; ( is a constant scale factor that provides an estimate of the standard deviation in days of the time course of the epidemic; and 0 d" ( d" 1 is a constant indicating the maximum cumulative risk. For medical diagnoses by staff, we assume Pit is 1 when subjects have had the flu on any day up to and including t and 0 otherwise. For self-reported flu symptoms in some cases we only have information about the interval from t0 to t1 in which symptoms occurred, so we assume it increases uniformly in the interval, i.e. Pit = ( t t0 ) / ( t1 t0 ).
To fit this equation we conducted a nonlinear least squares estimation procedure that utilizes the Gauss-Newton algorithm. To estimate standard errors and 95% confidence intervals, we used a bootstrapping procedure in which we repeatedly re-sampled subject observations with replacement and re-estimated the fit. This procedure produced somewhat wider confidence intervals than those derived from asymptotic approximations, so we report only the more conservative bootstrapped estimates of the standard errors in the Tables S3-S14.
In the left panel of Figure 2 we calculated the nonparametric maximum likelihood estimate (NPMLE) of cumulative flu incidence for both the friend group and the random group and in the right panel we show the predicted daily incidence based on Model 1 in Table S3. Daily incidence for the random group is the derivative of the cumulative logistic function:
EMBED Equation.3
and for the friends group is:
EMBED Equation.3
In Figure 4, we calculate early detection days for in-degree by multiplying the coefficient and confidence intervals in Table S7 by the difference in in-degree between the above-average-in-degree group and the below-average-in-degree group. Similarly, we calculate early detection days for betweenness by multiplying the coefficient and confidence intervals in Table S9 by the difference in betweenness between the above-average-betweenness group and the below-average-betweenness group. We calculate early detection days for k-coreness by multiplying the coefficient and confidence intervals in Table S11 by the difference in coreness between the above-average-coreness group and the below-average-coreness group. And we calculate early detection days for transitivity by multiplying the coefficient and confidence intervals in Table S13 by the difference in transitivity between the above-average-transitivity group and the below-average-transitivity group.
Table S1: Summary Statistics for Friend Group and Random Group
Friend GroupRandom GroupMann-Whitney U MeanS.D.MeanS.D.pNFlu Diagnosis by Medical Staff0.0750.2640.0780.2690.876744Self-Reported Flu Symptoms0.3250.4690.3100.4630.678744In Degree1.4350.6630.4330.6640.000744Out Degree2.6890.5432.6110.6720.306744Betweenness Centrality (Percentile)0.5590.2710.4230.2940.000744K-Coreness1.6730.5531.4140.5650.000744Transitivity0.1420.2310.1480.2740.039721Popularity Index4.0530.9823.9671.0220.195744Self-Reported H1N1 Vaccine0.2000.4000.1880.3910.685744H1N1 Vaccine at UHS0.1150.3200.1100.3130.812744Self-Reported Seasonal Flu Vaccine0.4990.5280.4730.5060.595744Seasonal Flu Vaccine at UHS0.3880.4880.4010.4910.719744Female0.7200.4500.6270.4840.007744Sophomore0.1760.3820.2350.4250.049744Junior0.2590.4390.2380.4270.522744Senior0.3220.4680.2760.4480.172744Varsity Athlete0.0920.2890.1130.3170.345744Friend group N=425, random group N=325. The Mann Whitney U p value indicates the probability that values for the friends and random groups were drawn from the same distribution.
Table S2: Correlates of Getting Flu by December 31, 2009
Medical Staff Flu DiagnosesSelf-Reported Flu SymptomsCorrelationpCorrelationpFlu Diagnosis by Medical Staff------0.400.00Self-Reported Flu Symptoms0.400.00------Member of Friend Group-0.010.880.020.68In Degree0.010.780.080.02Out Degree-0.010.750.010.84Betweenness Centrality0.020.670.030.36K-Coreness0.040.280.090.02Transitivity-0.030.460.050.19Popularity Index-0.030.460.010.86Self-Reported H1N1 Vaccine-0.040.28-0.030.41H1N1 Vaccine at UHS-0.010.850.050.19Self-Reported Seasonal Flu Vaccine0.010.750.040.33Seasonal Flu Vaccine at UHS0.050.200.050.16Female0.020.510.060.10Sophomore0.040.230.040.22Junior-0.060.090.080.02Senior-0.060.12-0.070.07Varsity Athlete0.040.30-0.040.31P values indicate probability the Pearson correlation is 0. Lack of consistent correlation suggests none of the independent variables influence overall cumulative risk of flu.
Table S3: Effect of Being in the Friend Group on Cumulative Flu Incidence, Diagnoses by Medical Staff
Model 1Model 2Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Friend Group-13.91.7-16.6-19.9-15.72.1-19.3-12.4 H1N1 Vaccination32.07.317.643.8 Seasonal Flu Vaccination-0.82.2-5.61.3 Female-8.52.2-12.2-3.2 Sophomore25.22.920.132.1 Junior66.73.161.272.8 Senior57.62.554.362.3 Varsity Athlete-5.73.0-12.0-1.7 Constant69.41.566.972.143.02.838.247.2Scale Variable:24.71.222.926.726.71.119.523.3Residual Standard Error0.20310.2022Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show friend group gets diagnosed with the flu by medical staff about 15 days earlier than the random group, and controlling for other factors does not affect the significance of the estimate.
Table S4: Effect of Being in the Friend Group on Cumulative Flu Incidence, Self-Reported Data
Model 3Model 4Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Friend Group-3.20.6-4.3-2.2-2.50.6-3.6-1.6 H1N1 Vaccination12.51.210.114.8 Seasonal Flu Vaccination2.80.51.83.9 Female-9.00.7-10.3-7.7 Sophomore-5.30.8-6.9-4.0 Junior-7.30.6-8.5-6.2 Senior6.90.85.68.2 Varsity Athlete6.60.85.18.2 Constant123.90.6122.9125.2126.21.0124.1128.6Scale Variable:36.80.436.137.434.90.334.435.5Residual Standard Error0.34810.3463Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the self-reported cumulative incidence of flu in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show the friend group self-reports flu symptoms about 3 days earlier than the random group, and controlling for other factors does not affect the significance of the estimate.
Table S5: Effect of Self-Reported Popularity on Cumulative Flu Incidence
Model 5(Medical Staff Diagnoses)Model 6(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Self-Reported Popularity3.61.02.26.0-1.30.2-1.7-0.8 Constant47.44.237.752.5127.21.1124.8128.7Scale Variable:25.51.223.427.636.80.436.237.5Residual Standard Error0.20320.3481Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results self-reported popularity has an inconsistent effect on timing of the flu.
Table S6: Effect of Being in the Friend Group on Cumulative Flu Incidence, Controlling for Self-Reported Popularity
Model 7(Medical Staff Diagnoses)Model 8(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Friend Group-14.52.4-19.4-11.0-3.10.5-4.1-2.2 Self-Reported Popularity4.11.02.15.5-1.30.3-1.8-0.7 Constant53.54.248.161.8128.91.2127.2131.4Scale Variable:24.71.023.026.336.80.436.237.6Residual Standard Error0.20310.3480Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show the friend group gets the flu significantly earlier, even when controlling for a self-reported measure of popularity.
Table S7: Effect of Network In Degree on Cumulative Flu Incidence
Model 9(Medical Staff Diagnoses)Model 10(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: In Degree-5.71.3-8.1-3.6-8.00.4-8.5-7.3 Constant67.81.465.470.3130.20.7128.6131.3Scale Variable:25.21.322.827.836.80.535.937.6Residual Standard Error0.20320.3470Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that individuals with high in-degree tend to get the flu earlier than others.
Table S8: Effect of Network Out Degree on Cumulative Flu Incidence
Model 11(Medical Staff Diagnoses)Model 12(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Out Degree7.51.84.711.22.50.41.53.2 Constant42.24.832.949.5115.21.3113.3118.3Scale Variable:25.51.223.027.436.80.436.037.4Residual Standard Error0.20320.3481Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that the number of friends a person nominates actually delays the average onset of flu.
Table S9: Effect of Betweenness Centrality on Cumulative Flu Incidence
Model 13(Medical Staff Diagnoses)Model 14(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Betweenness Centrality-16.58.3-28.3-1.9-22.91.9-27.2-20.0 Constant62.91.160.965.0123.20.5122.1123.9Scale Variable:25.51.123.327.536.80.435.937.4Residual Standard Error0.20320.3479Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that individuals with high betweenness centrality tend to get the flu earlier than others.
Table S10: Effect of Betweenness Centrality on Cumulative Flu Incidence With Controls
Model 15(Medical Staff Diagnoses)Model 16(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Betweenness Centrality-15.08.4-27.3-0.4-16.61.8-19.5-13.5 In Degree-4.21.3-6.2-1.4-7.60.4-8.3-6.9 Out Degree7.81.75.411.43.40.52.64.3 Constant46.74.737.054.0121.61.3118.9124.3Scale Variable:25.31.223.227.536.70.435.937.4Residual Standard Error0.20310.3468Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that betweenness centrality remains a significant predictor of early flu onset even when controlling for degree variables.
Table S11: Effect of K-Coreness on Cumulative Flu Incidence
Model 13(Medical Staff Diagnoses)Model 14(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: K-Coreness-3.41.8-6.9-0.2-6.30.5-7.1-5.3 Constant67.42.862.671.7132.00.9130.1133.4Scale Variable:25.70.923.827.036.80.436.037.4Residual Standard Error0.20320.3478Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that individuals with high k-coreness tend to get the flu earlier than others.
Table S12: Effect of K-Coreness on Cumulative Flu Incidence With Controls
Model 15(Medical Staff Diagnoses)Model 16(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: K-Coreness-4.72.4-8.7-0.0-1.50.6-2.6-0.6 In Degree-4.31.4-6.5-1.8-7.50.4-8.2-6.8 Out Degree8.51.94.511.43.20.52.44.1 Constant51.65.143.162.5123.51.4121.3125.8Scale Variable:25.41.223.328.336.70.435.937.4Residual Standard Error0.20310.3469Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 744 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that k-coreness remains a significant predictor of early flu onset even when controlling for degree variables.
Table S13: Effect of Transitivity on Cumulative Flu Incidence
Model 17(Medical Staff Diagnoses)Model 18(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Transitivity31.94.823.543.515.01.612.718.5 Constant56.91.553.559.0153.91.2151.3155.8Scale Variable:24.80.823.326.640.50.739.141.7Residual Standard Error0.20460.2873Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 721 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that individuals with low transitivity tend to get the flu earlier than others.
Table S14: Effect of Transitivity on Cumulative Flu Incidence with Controls
Model 19(Medical Staff Diagnoses)Model 20(Self Reports)Coef.S.E.Lower 95% C.I.Upper 95% C.I.Coef.S.E.Lower 95% C.I.Upper 95% C.I.Location Variables: Transitivity34.94.225.142.022.81.819.125.6 In Degree-3.61.2-5.4-1.0-4.60.5-5.6-3.8 Out Degree17.62.213.721.317.30.716.119.0 Constant13.26.02.221.1109.71.9106.9112.8Scale Variable:25.01.023.126.939.40.738.141.0Residual Standard Error0.20450.2860Nonlinear least squares estimates of parameters in a cumulative logistic function fit to the cumulative incidence of flu diagnosed by medical staff (left model) and self-reported (right model) in 721 subjects, each followed for 122 days. Location variable coefficients can be interpreted as the shift that occurs in days with respect to a unit increase in the independent variable. Standard errors and confidence intervals are bootstrapped. Results show that transitivity remains a significant predictor of early flu onset even when controlling for degree variables.
REFERENCES for SUPPORINTING INFORMATION
PAGE
PAGE 24
. Freeman LC (1977) Set of measures of centrality based on betweenness. Sociometry 40:35-41.
. Batagelj V, Mrvar A (2006) PAJEK: Program for Analysis and Visualization of Large Networks, version 1.14
. Kamada T, Kawai C (1989) An algorithm for drawing general undirected graphs. Information Processing Letters 31:113-120.
. Scott BA, Judge TA (2009) The popularity contest at work: who wins, why, and what do they receive? J Applied Psych 94: 2033.
. Bates DM, Watts DG. Nonlinear Regression Analysis and Its Applications (New York: Wiley, 1988)
. Huet S, Bouvier A, Poursat MA, Jolivet E (2003) Statistical tools for nonlinear regression: a practical guide with S-PLUS and R examples. (Berlin: Springer).
. Turnbull BW (1976) The empirical distribution function with arbitrarily grouped, censored and truncated data. J. R. Statist. Soc. B 38: 290-295.
#$% ' 3 9 : L ~
j
ȼȳrch'qhqCJOJQJ^J h'qhqCJOJQJ^JaJhqCJOJQJh'qhqCJOJQJh'qhqCJH*OJQJhqCJH*OJQJhqH*OJQJh'qhqH*OJQJh'qhqOJQJhqOJQJ"hhq5OJQJ\mH sH hhqmH sH hqmH sH &#$%i9
g.)1!!d#3`gdq3gdq$a$gdq6$a$gdqgdqgdqj
bop!!!!!>"H"""d#f#o###$$)$*$A$B$ʺʺʺʶʺʭʺʺʺʶʺʤxjE
hhqUVaJjhhqUaJjhhq0J/UaJhhqaJhhqaJhqhhq6hhq5hhqh+hqPJh'qhqCJOJQJ^JhqCJOJQJh'qhqCJOJQJ)B$C$D$y$z$$$$$$$$$$$$$%%1%2%?%@%D%E%X%Y%Z%[%%%%%%%%&&&+&3&@&G&R&d&ڡІڀyppppph-#hqaJ
hq6aJ
hqaJhhq6H*aJj hhqEHUaJjfG
hhqUVaJjhhqEHUaJjE
hhqUVaJhhq6aJhhqaJjhhqUaJjhhqEHUaJ,d#%()Q+U-..;1D1*3W5Z6r6:<*>B>`>x>;B**B~BB1$x$Ifa$gdq0gdqgdq3`gdq3gdqd&i&m&s&&&&'''3'B'C'y'z'((((( (,())^+_+,,,,,*-+-,-R-S-U---..z/{/////;1D1غ{{hhq5hhq0J^Jjh3hqU^JjhhqU^Jjhhq0J/U^Jhhq^Jjhhq0J/Uhhq6hhqhqhhq
hq6aJh-#hqaJ
hqaJ0D1\3^3'4(4)4W5g5Z6[6n6o6p6q6x6y6{66666666667 777,7-7r7t7v7w788 8888v9x9-:.:/:3:4:5::::::ɼ jlhhq6 jshhq6 jahhq6hhq6H*jdhhqEHUjeWG
hhqUVjhhqUhq jrhhq6hhq6hhq6:::::::::::::&;';;;<<<<p=q=*>+>>>?>@>A>`>a>t>u>v>w>>>??a@c@u@~@@@@@@@@A4A5A=A͇ hq6jhhqEHUjG
hhqUVjhhqEHUj2G
hhqUVjhhqUhqjhhq0J/Uhhq6H*hhq6hhqhhqH*5=A]AfAAA;B>B?B}B~BBBBBBBCCDCECqCrCCCCCCCCCC
DDDDDEDxDyDDDDD3E4ErEsEEEŽťxhA/5hq hq6hhqmH sH +hhq6CJOJQJ^JaJmH sH .hhq6>*CJOJQJ^JaJmH sH hhq6hhq6>*hhqOJQJhhqOJQJ\hhqOJQJmH sH hqhhq/BBBBBBBBBBUkd ($$Iflr@q!$%%%644
lap1$x$Ifa$gdq BBBBB%kd)$$Ifl֞@Fq!$%%%%%644
lap21$x$Ifa$gdqBBBBBBCC1$x$Ifa$gdq1x$IfgdqCC"C3(1x$Ifgdqkd0*$$Ifl֞@Fq!$%%%%%644
lap2"C(C.C4C:C@CDC1$x$Ifa$gdqDCECOC3(1x$IfgdqkdX+$$Ifl֞@Fq!$%%%%%644
lap2OCUC[CaCgCmCqC1$x$Ifa$gdqqCrC}C3(1x$Ifgdqkdr,$$Ifl֞@Fq!$%%%%%644
lap2}CCCCCCC1$x$Ifa$gdqCCC3(1x$Ifgdqkd-$$Ifl֞@Fq!$%%%%%644
lap2CCCCCCC1$x$Ifa$gdqCCC3(1x$Ifgdqkd.$$Ifl֞@Fq!$%%%%%644
lap2CCCD
DDD1$x$Ifa$gdqDD"D3(1x$Ifgdqkd/$$Ifl֞@Fq!$%%%%%644
lap2"D(D.D4D:D@DDD1$x$Ifa$gdqDDEDVD3(1x$Ifgdqkd0$$Ifl֞@Fq!$%%%%%644
lap2VD\DbDhDnDtDxD1$x$Ifa$gdqxDyDD3(1x$Ifgdqkd1$$Ifl֞@Fq!$%%%%%644
lap2DDDDDDD1$x$Ifa$gdqDDD3(1x$Ifgdqkd3$$Ifl֞@Fq!$%%%%%644
lap2DDDDDDD1$x$Ifa$gdqDDE3(1x$Ifgdqkd(4$$Ifl֞@Fq!$%%%%%644
lap2EEE#E)E/E3E1$x$Ifa$gdq3E4EPE3(1x$IfgdqkdB5$$Ifl֞@Fq!$%%%%%644
lap2PEVE\EbEhEnErE1$x$Ifa$gdqrEsEzE3(1x$Ifgdqkd\6$$Ifl֞@Fq!$%%%%%644
lap2zEEEEEEE1$x$Ifa$gdqEEE3(1x$Ifgdqkdv7$$Ifl֞@Fq!$%%%%%644
lap2EEEEEEE1$x$Ifa$gdqEEEEEFFPFQF^F_FrFsFFFGG>GvGwGGGGGGG!H"H@HAHaHbHHHHHHHHHHHHHHHHHHH)I*ISITIIIIIIIIIJh28khq hq6+hhq6CJOJQJ^JaJmH sH .hhq6>*CJOJQJ^JaJmH sH hhq6>*hqhhq6hhqmH sH hhq>EEE3(1x$Ifgdqkd8$$Ifl֞@Fq!$%%%%%644
lap2EEEEEEE1$x$Ifa$gdqEEE3(1x$Ifgdqkd9$$Ifl֞@Fq!$%%%%%644
lap2EFF
FFFF1$x$Ifa$gdqFF.F3(1x$Ifgdqkd:$$Ifl֞@Fq!$%%%%%644
lap2.F4F:F@FFFLFPF1$x$Ifa$gdqPFQFG>G3.)0gdq2gdqkd;$$Ifl֞@Fq!$%%%%%644
lap2>G?G[GvGwGxGGGGG~rkd=$$IflFYn&%%%I44
lap1$x$Ifa$gdq GGGGGGG\QCCCC1$x$Ifa$gdq1x$Ifgdqkd=$$IflrY1 n&%%%%%#I44
lap2GGGGGGG\QCCCC1$x$Ifa$gdq1x$Ifgdqkd>$$IflrY1 n&%%%%%#I44
lap2GGHHHH!H\QCCCC1$x$Ifa$gdq1x$Ifgdqkd?$$IflrY1 n&%%%%%#I44
lap2!H"H,H1H6H;H@H\QCCCC1$x$Ifa$gdq1x$Ifgdqkd@$$IflrY1 n&%%%%%#I44
lap2@HAHLHRHWH\HaH\QCCCC1$x$Ifa$gdq1x$IfgdqkdsA$$IflrY1 n&%%%%%#I44
lap2aHbHyH~HHHH\QCCCC1$x$Ifa$gdq1x$IfgdqkdZB$$IflrY1 n&%%%%%#I44
lap2HHHHHHH\QCCCC1$x$Ifa$gdq1x$IfgdqkdAC$$IflrY1 n&%%%%%#I44
lap2HHHHHHH\QCCCC1$x$Ifa$gdq1x$Ifgdqkd(D$$IflrY1 n&%%%%%#I44
lap2HHHHHHH\QCCCC1$x$Ifa$gdq1x$IfgdqkdE$$IflrY1 n&%%%%%#I44
lap2HHIII$I)I\QCCCC1$x$Ifa$gdq1x$IfgdqkdE$$IflrY1 n&%%%%%#I44
lap2)I*I>IDIIINISI\QCCCC1$x$Ifa$gdq1x$IfgdqkdF$$IflrY1 n&%%%%%#I44
lap2SITIwI|IIII\QCCCC1$x$Ifa$gdq1x$IfgdqkdG$$IflrY1 n&%%%%%#I44
lap2IIIIIII\QCCCC1$x$Ifa$gdq1x$IfgdqkdH$$IflrY1 n&%%%%%#I44
lap2IIIIIII\QCCCC1$x$Ifa$gdq1x$IfgdqkdI$$IflrY1 n&%%%%%#I44
lap2IIIIIII\QCCCC1$x$Ifa$gdq1x$IfgdqkdyJ$$IflrY1 n&%%%%%#I44
lap2IIIJ
JJJ\QCCCC1$x$Ifa$gdq1x$Ifgdqkd`K$$IflrY1 n&%%%%%#I44
lap2JJJ"J'J-J2J\QCCCC1$x$Ifa$gdq1x$IfgdqkdGL$$IflrY1 n&%%%%%#I44
lap2JJ2J3JXJYJZJ
KKqKKKKKKKKKKLL
LLLLLL3L4LJLNLaLbLLLLLLLLLLLLLLLMMM梍~~~~ hq5hhq56(hhqCJOJQJ^JaJmH sH hhq5+hhq6CJOJQJ^JaJmH sH .hhq6>*CJOJQJ^JaJmH sH hhq6>*hqhhq6hhqhhqmH sH 12J3JCJHJMJSJXJ\QCCCC1$x$Ifa$gdq1x$Ifgdqkd.M$$IflrY1 n&%%%%%#I44
lap2XJYJ
KqKrKzKK\WRI==1$$Ifa$gdq 1$Ifgdq0gdq2gdqkdN$$IflrY1 n&%%%%%#I44
lap2KKKKKKKKKKK1$$Ifa$gdqqkd
O$$IflF$%%aa644
lap
KK
kdO$$Ifl !$%%%~%%~6$$$$44
lap2KKKKKKKKKK1$$Ifa$gdq 1$Ifgdq KK
kdP$$Ifl !$%%%~%%~6$$$$44
lap2KL
LLLL#L'L-L3L1$$Ifa$gdq 1$Ifgdq 3L4L
kd$R$$Ifl !$%%%~%%~6$$$$44
lap24LJLKLLLMLNLSLWL\LaL1$$Ifa$gdq 1$Ifgdq aLbL
kdNS$$Ifl !$%%%~%%~6$$$$44
lap2bLLLLLLLLLL1$$Ifa$gdq 1$Ifgdq LL
kdxT$$Ifl !$%%%~%%~6$$$$44
lap2LLLLLLLLLL1$$Ifa$gdq 1$Ifgdq LL
kdU$$Ifl !$%%%~%%~6$$$$44
lap2LLLLLLLLLL1$$Ifa$gdq 1$Ifgdq LL
kdV$$Ifl !$%%%~%%~6$$$$44
lap2LLLLLLLLMM1$$Ifa$gdq 1$Ifgdq MM
kdW$$Ifl !$%%%~%%~6$$$$44
lap2MMMMMMM M%M*M1$$Ifa$gdq 1$Ifgdq MM*M+M@MDMXMYMgMkMlMoMpMtMuMyMMMMMMMMMMMMMMMMCPDPPPPQQQQ%Q&Q8Q^Q_QuQyQQQQQQQQQşӉ+hhq6CJOJQJ^JaJmH sH .hhq6>*CJOJQJ^JaJmH sH hhq5OJQJ\hhq6>*hqhhq6(hhqCJOJQJ^JaJmH sH hhqhhq56*M+M
kd Y$$Ifl !$%%%~%%~6$$$$44
lap2+M@MAMBMCMDMIMMMSMXM1$$Ifa$gdq 1$Ifgdq XMYM
kdJZ$$Ifl !$%%%~%%~6$$$$44
lap2YMgMlMpMuMzMMMMM1$$Ifa$gdq 1$Ifgdq MM
kdt[$$Ifl !$%%%~%%~6$$$$44
lap2MMMMMMMMMM1$$Ifa$gdq 1$Ifgdq MM
kd\$$Ifl !$%%%~%%~6$$$$44
lap2MMMMMCPPPPPyto0gdq2gdqqkd]$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq PPPPPPPPPPQ1$$Ifa$gdqqkdr^$$IflF$%%aa644
lap
QQ
kd_$$Ifl !$%%%~%%~6$$$$44
lap2QQQQ Q!Q"Q#Q$Q%Q1$$Ifa$gdq 1$Ifgdq %Q&Q
kdT`$$Ifl !$%%%~%%~6$$$$44
lap2&Q8Q=QAQFQKQPQTQYQ^Q1$$Ifa$gdq 1$Ifgdq ^Q_Q
kda$$Ifl !$%%%~%%~6$$$$44
lap2_QuQvQwQxQyQ~QQQQ1$$Ifa$gdq 1$Ifgdq QQ
kdb$$Ifl !$%%%~%%~6$$$$44
lap2QQQQQQQQQQ1$$Ifa$gdq 1$Ifgdq QQ
kdc$$Ifl !$%%%~%%~6$$$$44
lap2QQQQQQQQQQ1$$Ifa$gdq 1$Ifgdq QQQQQRRRR/R0R*hhq5hhq6(hhqCJOJQJ^JaJmH sH hhq@QQ
kd
e$$Ifl !$%%%~%%~6$$$$44
lap2QQQQQQQRRR1$$Ifa$gdq 1$Ifgdq RR
kd4f$$Ifl !$%%%~%%~6$$$$44
lap2RRRRRR!R%R*R/R1$$Ifa$gdq 1$Ifgdq /R0R
kd^g$$Ifl !$%%%~%%~6$$$$44
lap20RR?R@RDRHRLRPR1$$Ifa$gdq 1$Ifgdq PRQR
kdh$$Ifl !$%%%~%%~6$$$$44
lap2QRfRgRhRiRjRnRrRvRzR1$$Ifa$gdq 1$Ifgdq zR{R
kdi$$Ifl !$%%%~%%~6$$$$44
lap2{RRRRRRRRRR1$$Ifa$gdq 1$Ifgdq RR
kdj$$Ifl !$%%%~%%~6$$$$44
lap2RRRRRRRRRR1$$Ifa$gdq 1$Ifgdq RR
kdl$$Ifl !$%%%~%%~6$$$$44
lap2RSSSSMUUUUUyto0gdq2gdqqkd0m$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq UUUUUUUVVV%V1$$Ifa$gdqqkdm$$IflF$%%aa644
lap
%V&V
kdn$$Ifl !$%%%~%%~6$$$$44
lap2&V;VV?V@VAVBVCV1$$Ifa$gdq 1$Ifgdq CVDV
kdo$$Ifl !$%%%~%%~6$$$$44
lap2DVbVfVjVnVrVwV{VVV1$$Ifa$gdq 1$Ifgdq VV
kdp$$Ifl !$%%%~%%~6$$$$44
lap2VVVVVVVVVV1$$Ifa$gdq 1$Ifgdq VV
kdr$$Ifl !$%%%~%%~6$$$$44
lap2VVVVVVVVVV1$$Ifa$gdq 1$Ifgdq VV
kdHs$$Ifl !$%%%~%%~6$$$$44
lap2V
WWWW+YYYYYyto0gdq2gdqqkdrt$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq YYYYYYZZZZ.Z1$$Ifa$gdqqkdu$$IflF$%%aa644
lap
YY.Z/ZAZDZLZMZ_ZZZZZZZ[[[9[:[R[`[a[]]]^^^^r^s^^^^^^^^^^^^_5_6_N_\_]_tauaaaaaaaaHbIb[b^bfbgbϺᳺᳺᳺ׳ᳺϺ᯳ᳺ׳ᳺϺhhq5OJQJ\hqhhq(hhqCJOJQJ^JaJmH sH hhq5hhq6>*hhq6+hhq6CJOJQJ^JaJmH sH ?.Z/Z
kdu$$Ifl !$%%%~%%~6$$$$44
lap2/ZDZEZFZGZHZIZJZKZLZ1$$Ifa$gdq 1$Ifgdq LZMZ
kdv$$Ifl !$%%%~%%~6$$$$44
lap2MZ_ZeZiZoZuZzZ~ZZZ1$$Ifa$gdq 1$Ifgdq ZZ
kd6x$$Ifl !$%%%~%%~6$$$$44
lap2ZZZZZZZZZZ1$$Ifa$gdq 1$Ifgdq ZZ
kd`y$$Ifl !$%%%~%%~6$$$$44
lap2ZZZZZZZZZ[1$$Ifa$gdq 1$Ifgdq [[
kdz$$Ifl !$%%%~%%~6$$$$44
lap2[[[[![&[+[/[4[9[1$$Ifa$gdq 1$Ifgdq 9[:[
kd{$$Ifl !$%%%~%%~6$$$$44
lap2:[R[Y[`[a[]]]^^yto0gdq2gdqqkd|$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq ^^ ^&^+^:^I^O^T^c^r^1$$Ifa$gdqqkd}$$IflF$%%aa644
lap
r^s^
kd2~$$Ifl !$%%%~%%~6$$$$44
lap2s^^^^^^^^^^1$$Ifa$gdq 1$Ifgdq ^^
kdj$$Ifl !$%%%~%%~6$$$$44
lap2^^^^^^^^^^1$$Ifa$gdq 1$Ifgdq ^^
kd$$Ifl !$%%%~%%~6$$$$44
lap2^^^^^^^^^^1$$Ifa$gdq 1$Ifgdq ^^
kd́$$Ifl !$%%%~%%~6$$$$44
lap2^____"_'_+_0_5_1$$Ifa$gdq 1$Ifgdq 5_6_
kd$$Ifl !$%%%~%%~6$$$$44
lap26_N_U_\_]_taaaaayto0gdq2gdqqkd $$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq aaaabbb%b*b9bHb1$$Ifa$gdqqkdʄ$$IflF$%%aa644
lap
HbIb
kdt$$Ifl !$%%%~%%~6$$$$44
lap2Ib^b_b`babbbcbdbebfb1$$Ifa$gdq 1$Ifgdq fbgb
kd$$Ifl !$%%%~%%~6$$$$44
lap2gbwb{bbbbbbbb1$$Ifa$gdq 1$Ifgdq gbwbbbbbbbcc c.c/c/e5ePeQeeeeeeee(f)f;f>fFfGfcfffffffffg$g%gHiIiiiiiiii/j0jBjEjMjNjjjjjjjjjjjhhq5+hhq6CJOJQJ^JaJmH sH hhq5OJQJ\hhq6>*(hhqCJOJQJ^JaJmH sH hhqhhq6Abb
kd$$Ifl !$%%%~%%~6$$$$44
lap2bbbbbbbbbb1$$Ifa$gdq 1$Ifgdq bb
kd$$Ifl !$%%%~%%~6$$$$44
lap2bbbbbbbbcc1$$Ifa$gdq 1$Ifgdq cc
kd8$$Ifl !$%%%~%%~6$$$$44
lap2c c'c.c/cPeeeeeyto0gdq2gdqqkdb$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq eeeeeeef
ff(f1$$Ifa$gdqqkd$$IflF$%%aa644
lap
(f)f
kd$$Ifl !$%%%~%%~6$$$$44
lap2)f>f?f@fAfBfCfDfEfFf1$$Ifa$gdq 1$Ifgdq FfGf
kd$$Ifl !$%%%~%%~6$$$$44
lap2Gfcfifmfsfxf~ffff1$$Ifa$gdq 1$Ifgdq ff
kd&$$Ifl !$%%%~%%~6$$$$44
lap2ffffffffff1$$Ifa$gdq 1$Ifgdq ff
kdP$$Ifl !$%%%~%%~6$$$$44
lap2ffffffffff1$$Ifa$gdq 1$Ifgdq ff
kdz$$Ifl !$%%%~%%~6$$$$44
lap2fgg$g%gHiiiiiyto0gdq2gdqqkd$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq iiiiiijjj j/j1$$Ifa$gdqqkdN$$IflF$%%aa644
lap
/j0j
kd$$Ifl !$%%%~%%~6$$$$44
lap20jEjFjGjHjIjJjKjLjMj1$$Ifa$gdq 1$Ifgdq MjNj
kd0$$Ifl !$%%%~%%~6$$$$44
lap2Njjjpjtjzjjjjjj1$$Ifa$gdq 1$Ifgdq jj
kdh$$Ifl !$%%%~%%~6$$$$44
lap2jjjjjjjjjj1$$Ifa$gdq 1$Ifgdq jj
kd$$Ifl !$%%%~%%~6$$$$44
lap2jjjjjjjjjj1$$Ifa$gdq 1$Ifgdq jj
kd$$Ifl !$%%%~%%~6$$$$44
lap2jkkkkk%k)k/k5k1$$Ifa$gdq 1$Ifgdq jk5k6kFklkmkkkkmmmmmnnn9nAnQnRnnnnnnnnnnnnnnnnnnnnnnnnnnn o
oooooooo!o"o%o&o)oÿ hq6hhq5+hhq6CJOJQJ^JaJmH sH hqhhq5OJQJ\hhq6>*(hhqCJOJQJ^JaJmH sH hhqhhq6=5k6k
kd$$Ifl !$%%%~%%~6$$$$44
lap26kFkKkOkTkYk^kbkgklk1$$Ifa$gdq 1$Ifgdq lkmk
kd$$Ifl !$%%%~%%~6$$$$44
lap2mkkkkkmnn9nQnyto0gdq2gdqqkd:$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq QnRnSnYn^nmn|nnnnn1$$Ifa$gdqqkd$$IflF$%%aa644
lap
nn
kd$$Ifl !$%%%~%%~6$$$$44
lap2nnnnnnnnnn1$$Ifa$gdq 1$Ifgdq nn
kdƞ$$Ifl !$%%%~%%~6$$$$44
lap2nnnnnnnnnn1$$Ifa$gdq 1$Ifgdq nn
kd$$Ifl !$%%%~%%~6$$$$44
lap2n ooooo"o&o,o2o1$$Ifa$gdq 1$Ifgdq )o,o1o2o3oCoGoHoKoLoPoQoUo_ocoiojooooootquq~qqqqqqqqqrr/r0rrrrrrrrrrrrrrrrrrrrrrrΚΕ hq6hhq5+hhq6CJOJQJ^JaJmH sH hhq5OJQJ\hOhq6hhq6hhq6>*(hhqCJOJQJ^JaJmH sH hqhhq:2o3o
kd($$Ifl !$%%%~%%~6$$$$44
lap23oCoHoLoQoVo[o_odoio1$$Ifa$gdq 1$Ifgdq iojo
kdR$$Ifl !$%%%~%%~6$$$$44
lap2joooooqqqr/ryto0gdq2gdqqkd|$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq /r0r1r7r*hhq6(hhqCJOJQJ^JaJmH sH hqhhqJrr
kdH$$Ifl !$%%%~%%~6$$$$44
lap2rrrrrrss ss1$$Ifa$gdq 1$Ifgdq ss
kdr$$Ifl !$%%%~%%~6$$$$44
lap2ss#s's+s0s4s8s**~~*hhq6=vvvvvvvvvvv1$$Ifa$gdqqkḓ$$IflF$%%aa644
lap
vv
kdv$$Ifl !$%%%~%%~6$$$$44
lap2vvvvvvvvvv1$$Ifa$gdq 1$Ifgdq vv
kd$$Ifl !$%%%~%%~6$$$$44
lap2vwwww"w'w+w0w5w1$$Ifa$gdq 1$Ifgdq 5w6w
kd$$Ifl !$%%%~%%~6$$$$44
lap26wDwIwMwRwWw]wawgwmw1$$Ifa$gdq 1$Ifgdq mwnw
kd$$Ifl !$%%%~%%~6$$$$44
lap2nw~wwwwwwwww1$$Ifa$gdq 1$Ifgdq ww
kd:$$Ifl !$%%%~%%~6$$$$44
lap2wwwwwy1z2zUzmzyto0gdq2gdqqkdd$$IflF$%%aa644
lap1$$Ifa$gdq 1$Ifgdq mznzozuzzzzzzzzz1$$Ifa$gdqqkd$$IflF$%%aa644
lap
zz
kd$$Ifl !$%%%~%%~6$$$$44
lap2zzzzzzzzzz1$$Ifa$gdq 1$Ifgdq zz
kd$$Ifl !$%%%~%%~6$$$$44
lap2zzzz{{
{{{{1$$Ifa$gdq 1$Ifgdq {{
kd($$Ifl !$%%%~%%~6$$$$44
lap2{({-{1{6{;{@{D{I{N{1$$Ifa$gdq 1$Ifgdq N{O{
kdR$$Ifl !$%%%~%%~6$$$$44
lap2O{_{d{h{m{r{w{{{{{1$$Ifa$gdq 1$Ifgdq {{
kd|$$Ifl !$%%%~%%~6$$$$44
lap2{{{{{{{{{{1$$Ifa$gdq 1$Ifgdq {{
kd$$Ifl !$%%%~%%~6$$$$44
lap2{{{{{{{{{{1$$Ifa$gdq 1$Ifgdq {{
kdм$$Ifl !$%%%~%%~6$$$$44
lap2{||||T~U~V~W~~~~ytooffdd3`gdq0gdq2gdqqkd$$IflF$%%aa644
lap1$$Ifa$gdq 1$IfgdqX~~~~~~~~~~~~~~~~~~~~~~~~~~~~~-34ᷱ᠓unfnunhghq6hghqjhghq0J/H*Uhq0JHOJQJmHnHuhBDhq0JHOJQJ!jhBDhq0JHOJQJU
hq0JHjhq0JHUh"hqOJQJhchqOJQJhq0JHOJQJhqjhqUhEhq5\hEhq5$~~~~~~~~~~~~~~~~~~~~~~~~~~"h]hgdq"&`#$gdq
gdq~~~~~3`gdq:gdq"h]hgdq"&`#$gdq4setʀnhEhq5\hghq6hghq6^Jhghq^J
hq^Jjhghq0J/H*Uhghqhqhhq630 001hP:pq/ =!"#$%Dd
Th\
c$A??#"`BE=>4Ψ+FD0Tۘp 7Ѓ`YsE=>4Ψ+F!AXJ|sxeQK/Q<"!XWӰvfhtr0чtV$c]H K\BOy{HI0I4]}1D=ʘJ ~`nWĎZ}~;AHȁI*4ۯzAj;Mm֫n
roPz%wo~ yu^da.9%&(DV*AEdKmfT*Y7rWte]\{
BW,;e7\ojlb6d{D3t:l%PM3L;Ya}Q`H;y1IIb"1I|V )Or c|!н+~ @XJ|xuRQk`=K֮1n0XֆRl1j:K|WA؟{> 3> {tGnɗsn9@pYYE"RQhfӽ)5+MeiFwoC$Ũs\2{x%'|JЌDhO43~^|i84ϗ2\v!on`D s''b'aO:-j"??( ]EЎS_^"K,R6Aӏ}ri̫{^b_eE--wו(f
>u]0j+V-4mǪ]ݞg|Sp02.;;0rT;:Hb3ujٜ3-p(Vd\eؚl`"~/AkcII-&?0at!7,7Dd
||\
c$A??#"`BY:EPot0T:o{Y:EPot:aa00|xmR/Q۶*ۭa|F V,V7K7,JD½7\E.IԼj*U7o~73O,I8&Q4>6"yL[u`ZLCl?1Vo.+.P"2!g߮xO]yEs}\tJPzqAb[ff;ͭ1t{ЇD${Y/ 5g<>}GF:k@C{^(;Hn9t}h῍hJNϪ[ ͋Ӫ8z'f-42ALݰ8êښVLMIU3y{35=60mjSL "n "t
FƓX
Q{#;o}
C``00xuRN@}NHvB9"0Hm% kUX n!!(Js$8q *T!ނ9!af7*y^7 $QHDQE/.#>bO(""^>8*\<`K KzEdʅ3*~e.k&~߶.L9OpkΰIM<Ψ˰wb Pn>֫^\A_)$svbT.-]#I,P.VfACUι)_U/@6gM
kȟ&la`bRht3>xXደ302t;rÎZy~w5;guASҚ$kHY}_Nr`E:,u@:Sw9&p.aoNru[kR#Dd
P
SA?" BcsÁY TcsÁ@#PgxVOoDoPC[Ej/Qڱ╨Ԉ"6MH'ڋl*cW@P_cÛ{v6
vwo|n%B+?Ε^btɨ|A z]~p'OCB XJ-|z:<]#=A sFUQ<+])]5QA|DYD'z Dǟ^qUysF~ᤎxŋue%#}$y9F:)|KMSd-{@g[}'D}!3qOrgS1'f x8Qw.f[`sJC+Z5PΠ]f&NSCqWz#ۡa2RSKYk%Mya|ٞ@]vyU}1ܥ^
D#ݷc(d lt܇3mR k1u&8]0FŘ$Mo|=TIDCH6NơNT
3%mWj30_
&sd=}t-oܻ̽N4JKAJhxh?:~?RDyK
!"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefghijklmnopqrstuvwxyz{|}~
!"#$%&'()*+,-./0123456789:;<=>?@ABCEFGHIJK_PSTUVWYXZ[\]^`abcdefghijklmnopqrstuvwxyz{|}~Root Entry# F)Gvi}KRData
DWordDocument"2ObjectPool% Ii}KFvi}K_1174120372FSIi}KIi}KOle
CompObjiObjInfo
!$%(+,-.0123456789;
FMathType 5.0 EquationMathType EFEquation.DSMT49q(<DSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A
sikEquation Native _1174120452FTJi}KjJi}KOle
CompObj
i
FMathType 5.0 EquationMathType EFEquation.DSMT49q(<dDSMT5WinAllBasicCodePagesTimes New RomanSymbolCourier NewMT Extra!/ED/APG_APAPAE%B_AC_AE*_HA@AHA*_D_E_E_A
sijkObjInfo
Equation Native _1200449230FSJi}K×Ji}KOle
FMicrosoft EquationDNQEEquation.3j
xj
=sijk
sikijk
CompObjNObjInfoEquation Native _1200445285FeJi}KJi}KOle
CompObjNObjInfoEquation Native FMicrosoft EquationDNQEEquation.3
Pit
=l1+e-t+a+bXit()s
()-1_1200463154FXJi}KmJi}KOle
CompObj NObjInfo"FMicrosoft EquationDNQEEquation.3
pt
=l)e-t+a()s
s1+e-t+a()s
()FMicrosoft EquationDNQEEEquation Native #_1200463031FKi}KKi}KOle
&CompObj 'Nquation.3
pt
=l)e-t+a+bfriend()s
s1+e-t+a+bfriend()s
()
՜.+,D՜.+,ObjInfo!)Equation Native *1Table{SummaryInformation($\yKNhttp://jhfowler.ucsd.edu/flunet_v3.movDd
P
SA?" B
l<chvF` T
l<chvF``p(8xWoD{nڪU{Kc7RMHH"Z )Y|(T
jr"nm_' 85= -+7oLESGtZ?8^"__ѮG~|
dF\w:t͢d/^O1B8E)z^ )Aƹ3:jاx9&t6xtѴsAsذ(+26> C,lhk4*5TyMظk ٥Qz6G5|r,bt
|OkVJ6-\Qv9QW <0 ƿc%4p
"bȩ-7ey:yc5#[ea?rܥa"ɣ[YBH\$y,#D_>ߣU;bx^$3:!K2
O9g@c@vI0ohݴ'-t^2=J<(\iM }lj[b9NA|3
JpU5}[o_)/TH:KɟB?ĪkMY99{\3onl̩ yD=qP-%A]h|R*JRD5W|j̱laf%QqLU's2oKՠdw2oHRFKVr'*Bm?ׁ0WEdOL(8Z>Z5]j4M)uL4ːMq}@o_%W l)C+@Su5XQ:}Pr-O_V'A:@ȕ* 7A88I5%Qش``kFTXKq*pZGL>Tw%q@ᶶ9D1eY];aq- hZTK7\ۅ}X~[
wV={ wGߟl;4[m]Y hʘ& HLmn{pRlnK4(9 jF}Ieɰ[`ԊR_Z.-\At<)Ȍ5Sgv'*ɩkll9x[/Oqq\
Xfr||IIu3+-xsu2}^Pf'n;4rJrw/wNW#9B^:w;A.w??N!^gIm
>Dd
HP
SA?" B;
n^_t2mv& Tn;
n^_t2m*"$<xXoD{!ğu HHHagznJH)pE?@H܀? $.47cz7V}yfg~$_yrrYŏ|FrQUR}ɇQ<|a? iA"d䄐#SB
M`[b,I1J0<~
v#-FCȒN]F`K.[B_ ӂh>qR+(UKe"q1"'B=78fOY2kx]v5|hM/Ct7%#*2J(_\_&{o> Ɵd
j`P1O~Da3r&:tx-s=w̗ws6TM> Shu(;y5f~,*%y
N)57, FiNoH,L!'WFSpD(/@ڢQ:Q"j0pOqR'QR#ȿz z8ќvВG&
CJv)lݥnM+'lA/K#yYmiE#JĚuʡ~::Thx Vi΅0z((-ZJڤU =ˣjSX@
g^2ɾp8J~PMY`Q/ۚO62+]
ߤQuh!S,*jaU^y(%ȡJ
\!䶄5*qYiPn#K_P{^/X,J4|:,crfQnnb|@0s゛QpsG]U#&8gLG?1?0ٔI3ܯsI(Wd)DOKWRɛxSśJޱT;b5msUP1\ddC0ӓ>˰%ܵ\OgQZ'{2Le`sR5CMj,kG)#FanDZZvd6`Aɘo|WU)}&$YRױz/!,)Z\BdSQ`2w0nlUQ`d4ry8Հw3DR`v1e
xF 8K
g9X*T]l,R)*tU-O緯@ Ї*ʐ@M/~#
yspQ`qlT"&6Wz
0C-FLj
bɇ{d|}`qS NBX{Ӳ&A;Y:
rg]8hꐇX0耛m%Q^p|m٧F=--0CG^418b= 3T:lq9=[36sĶVաm^Oda>/))YRr~H\[|p6f__}xb^k+ѨF Ɋ~iVhjxshF.ۗ[LQNormal CJPJ^J_HaJmH sH tH RR.N Heading 1$$@&a$5OJPJQJ^JaJL@L.N Heading 2$@&5OJPJQJ^JaJPP.N Heading 3$@&5CJOJPJQJ^JaJHH.N Heading 4$@&OJPJQJ^JaJRR.N Heading 5$$@&a$6OJPJQJ^JaJDA`DDefault Paragraph FontRi@RTable Normal4
l4a(k (No ListXX.NHeading 1 Char#5CJOJQJ^JaJmHsHtH XX.NHeading 2 Char#5CJOJQJ^JaJmHsHtH XX.NHeading 3 Char#5CJOJQJ^JaJmHsHtH T!T.NHeading 4 Char CJOJQJ^JaJmHsHtH X1X.NHeading 5 Char#6CJOJQJ^JaJmHsHtH HBHIBalloon TextCJOJQJ^JaJNQN;qBalloon Text CharCJOJQJ^JaJPaP;qBalloon Text Char4CJOJQJ^JaJPqP;qBalloon Text Char3CJOJQJ^JaJPP;qBalloon Text Char2CJOJQJ^JaJ:U@:A Hyperlink>*B*^Jphj/j}'zDefault7$8$H$5B*CJOJPJQJ^J_HaJmH nHphsH tH>>5
Footnote TextCJaJTTCFootnote Text CharCJ^JaJmHsHtH D&D5Footnote ReferenceH*^J\\IBalloon Text Char1 CJOJQJ^JaJmHsHtH DDList Paragraph
^m$4@4!r}VHeader
!FF r}VHeader CharCJ^JaJmHsHtH 4 @"4#r}VFooter
"
!F1F"r}VFooter CharCJ^JaJmHsHtH JVAJisFollowedHyperlink>*B*^JphXCRX&.NBody Text Indent%5CJOJPJQJ^JaJfaf%.NBody Text Indent Char#5CJOJQJ^JaJmHsHtH JQrJ(.NBody Text 3'CJOJPJQJ^JaJXX'.NBody Text 3 Char CJOJQJ^JaJmHsHtH jRj*.NBody Text Indent 2)hdx^hCJOJPJQJ^JaJff).NBody Text Indent 2 Char CJOJQJ^JaJmHsHtH .W.qUStrong
5\^JN^NqUNormal (Web),dd[$\$OJQJ^J4+4.( j0Endnote Text-JJ-( j0Endnote Text CharCJPJ^JaJ>*@>
( j0Endnote ReferenceH*0O0i!TBLTTL05CJNONi!TBLROW1dhCJOJQJ^JaJmH sH &O"&i!TBLFN2Po2Pp37dh`7 CJOJPJQJ_HmH sH tH 2BB25r Body Text4xDQD4rBody Text CharCJPJ^JaJ<Oab<rarttitle65CJ OJQJ"ar"raug7&a&raff86&a2&rabs95,Oa,rbibcit:x&a&rack;CJ*ar*rmeth1hd<00rmeth1ttl=50a0rreceived>CJ,,rcorr?5CJ0a0rLEGEND@OJQJ0a0rfootnoteACJ*"*rsec1ttlB(a2(rfd
C
9! B rBXD$R$rsuppE0O1b0rp-niF`.r.rmeth1
G7`7.)@.cPage NumberPK!K[Content_Types].xmlj0Eжr(]yl#!MB;BQޏaLSWyҟ^@
Lz]__CdR{`L=r85v&mQ뉑8ICX=H"Z=&JCjwA`.Â?U~YkG/̷x3%o3t\&@w!H'"v0PK!֧6_rels/.relsj0}Q%v/C/}(h"O
= C?hv=Ʌ%[xp{۵_Pѣ<1H0ORBdJE4b$q_6LR7`0̞O,En7Lib/SeеPK!kytheme/theme/themeManager.xmlM
@}w7c(EbˮCAǠҟ7՛K
Y,
e.|,H,lxɴIsQ}#Ր ֵ+!,^$j=GW)E+&
8PK!\theme/theme/theme1.xmlYOoE#F{o'NDuر i-q;N3'
G$$DAč*iEP~wq4;{o?g^;N:$BR64Mvsi-@R4mUb V*XX!cyg$w.Q"@oWL8*Bycjđ0蠦r,[LC9VbX*x_yuoBL͐u_.DKfN1엓:+ۥ~`jn[Zp֖zg,tV@bW/Oټl6Ws[R?S֒7 _כ[֪7 _w]ŌShN'^Bxk_[dC]zOլ\K=.:@MgdCf/o\ycB95B24SCEL|gO'sקo>W=n#p̰ZN|ӪV:8z1fk;ڇcp7#z8]Y/\{t\}}spķ=ʠoRVL3N(B<|ݥuK>P.EMLhɦM .co;əmr"*0#̡=6Kր0i1;$P0!YݩjbiXJB5IgAФa6{P g֢)҉-Ìq8RmcWyXg/u]6Q_Ê5H
Z2PU]Ǽ"GGFbCSOD%,p
6ޚwq̲R_gJSbj9)ed(w:/ak;6jAq11_xzG~F<:ɮ>O&kNa4dht\?J&l O٠NRpwhpse)tp)af]
27n}mk]\S,+a2g^Az
)˙>E
G鿰L7)'PK!
ѐ'theme/theme/_rels/themeManager.xml.relsM
0wooӺ&݈Э5
6?$Q
,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-!K[Content_Types].xmlPK-!֧61_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!\theme/theme/theme1.xmlPK-!
ѐ'
theme/theme/_rels/themeManager.xml.relsPK]
H!u"d%/0G2v_G,cfvPPv
(6669j
B$d&D1:=AEJMQYgbj)orNvX~4FHIKLMNl$?Bd#BBBC"CDCOCqC}CCCCCD"DDDVDxDDDDDE3EPErEzEEEEEEEF.FPF>GGGG!H@HaHHHHH)ISIIIIIJ2JXJKKKKK3L4LaLbLLLLLLLMM*M+MXMYMMMMMPQQ%Q&Q^Q_QQQQQQQRR/R0RPRQRzR{RRRRRU%V&VCVDVVVVVVVY.Z/ZLZMZZZZZ[[9[:[^r^s^^^^^^^5_6_aHbIbfbgbbbbbcce(f)fFfGfffffffi/j0jMjNjjjjjjj5k6klkmkQnnnnnnn2o3oiojo/rrrrrrrss@sAsxsysssvvvvv5w6wmwnwwwmzzzzz{{N{O{{{{{{{~~GJOPQRSTUVWXYZ[\]^_`abcdefghijkmnopqrstuvwxyz{|}~
!"#%&'()*+,-./0123456789:;<=>@A+-w.BD"#<#D,X,Z,33373K3M3v:::X:::$(/29!! ?B$O oj?uB$77zWg&Q釺M!n
B$$?*Ne^Pa{D@ 0(
B
S ?H0(
vYsYs
%
Ydcd~C!H!x!~!
'';(F(,,,,,,[-^-r4}44445%505a5i5555566w88889=D=g=o=[@_@@@EEEEJJJJNNNNRR S$SVVVVR?wX"de3NDN3DxTe F7^`CJOJQJo(^`CJOJQJo(opp^p`CJOJ QJ o(@@^@`CJOJ QJ o(^`CJOJ QJ o(^`CJOJ QJ o(^`CJOJ QJ o(^`CJOJ QJ o(PP^P`CJOJ QJ o(^`^Jo(.^`^J.pL^p`L^J.@^@`^J.^`^J.L^`L^J.^`^J.^`^J.PL^P`L^J.hh^h`^Jo(.hh^h`56o(*hH.
^`hH.
pL^p`LhH.
@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PL^P`LhH.hh^h`56o(*hH.
^`hH.
pL^p`LhH.
@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PL^P`LhH.^`^Jo(.^`^J.pLp^p`L^J.@@^@`^J.^`^J.L^`L^J.^`^J.^`^J.PLP^P`L^J.hh^h`56o(*hH.
^`hH.
pL^p`LhH.
@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PL^P`LhH.^`OJPJQJo(^`OJQJo(op^p`OJ QJ o(@^@`OJQJo(^`OJQJo(o^`OJ QJ o(^`OJQJo(^`OJQJo(oP^P`OJ QJ o(^`^Jo(.^`^J.pL^p`L^J.@^@`^J.^`^J.L^`L^J.^`^J.^`^J.PL^P`L^J.hh^h`56o(*hH.
^`hH.
pL^p`LhH.
@^@`hH.
^`hH.
L^`LhH.
^`hH.
^`hH.
PL^P`LhH.hh^h`^Jo(.^`56o(*hH.
^`hH.
L^
`LhH.
w
^w
`hH.
G^G`hH.
L^`LhH.
^`hH.
^`hH.
L^`LhH.QU~e3NDwX"&F7{4R?DxT . "+ T . dd ;[))V\q7U7V7c7p7777777777777777777777888888&8,82888>8D8H8I8T8Z8`8f8l8r8v8w8888888888888888888999999-93999?9E9K9O9P9k9q9w9}99999999999999999::
::':-:3:9:?:E:I:J:Q:W:]:c:i:o:s:t:~::::::::::::::::::::::::;;;;;#;';(;;<<2<M<N<O<[<]<i<k<l<<<<<<<<<<<<<<<<<<<==
====#=)=.=3=8=9=P=U=Z=_=d=e=p=u=z====================>>>> >%>*>+>N>S>X>]>b>c>>>>>>>>>>>>>>>>>>>>>>>>>>>>? ?
???$?*?/?0??H@I@Q@Y@Z@[@a@f@u@@@@@@@@@@@@@@@@@@@@@@@@A
AA!A"A#A$A%A*A.A3A8A9AWAXAYAZA[A`AdAiAmAnAzA{A|A}A~AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAABBBBBBB B$B*B/B0B>BCBGBLBQBVBZB_BdBeBuBzB~BBBBBBBBBBBBEyEzEEEEEEEEEEEEEEEEEEEEEEEEFFFF"F'F+F0F5F6FLFMFNFOFPFUFYF^FcFdFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFGGGGGGGGGG#G'G(G=G>G?G@GAGEGIGMGQGRG`GfGjGpGvG|GGGGGGGGGGGGGGGGGGG$JnJoJJJJJJJJJJJJJJKKKKKKKKKK9K=KAKEKIKNKRKWK\K]KkKpKtKyK~KKKKKKKKKKKKKKKKKKKKNwNxNNNNNNNNNNNNOOOOOOO O!O"O#O$O6OWNWRWVWZW_WcWgWkWoWpW~WWWWWWWWWWWWWWWWWWWWWWXX'ZoZpZZZZZZZZZZZZZ[[[[[[[[[[[:[@[D[J[O[U[Y[_[e[f[t[y[}[[[[[[[[[[[[[[[[[[[[[[^v^w^^^^^^^^^^^^______ _!_"_#_$_%_A_G_K_Q_V_\_`_f_l_m_|__________________________```
``"`&`+`0`5`9`>`C`D`\`c`j`k`bbbc(c)c*c0c5cDcScYc^cmc|c}ccccccccccccccccccccccccccccd d
ddd#d(d-d2d6d;d@dAdYd`dgdhdffffggggg"g1g7glDlElUlZl^lclhlmlqlvl{l|lllllno o,oDoEoFoLoQo`ooouozooooooooooooooooooooooooopp
pppp p%p&p6p;p?pDpIpNpRpWp\p]pkppptpxp}ppppppppppppppppppppWs[s`sesjsssvvvDDDDDDDDDDD@X-.v@
@<@8t@Unknown
GTimes New Roman5Symbol3Arial5Monaco;Helvetica7CambriaCLucida Grande9 CodeHei?1)Courier New;)Wingdings"h!!lk_0"r:hh4dt2qH?^0SMONITORING UNDERGRADUATE SOCIAL NETWORKS FOR EARLY WARNING REGARDING A FLU OUTBREAK
Tom KeeganJames Fowler<
~~