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Measles v95 US 1997-1999 N=165 s Measles v95? Canada 1998-2001 N=49 s Table notes P G NB P G NB 27.8 9.6 0 12.9 3.5 0 0 0.01 0.99 0 0.15 0.85 0.63 # (0.47,0.80) # 0.82 # (0.72,0.98) # 0.23 (0.13,0.40) b 0.21 (0.09,0.52) b 0.81 (0.70,0.92) 0.83 (0.64,0.96) Upper portion, results based on full distribution of Z; lower portion, only mean of Z and proportion of zeros known. Data and analysis described in appendices A and B. ∆AICc: Akaike information criterion, modified for small sample size, relative to lowest score. Akaike weight: approximate probability that model is the best of models considered. ˆ ˆ R 0,mle and k mle: maximum likelihood estimates of mean and shape parameter of negative binomial distribution, from full distribution of Zobs. ˆ ˆ R 0,pz and k pz : estimates of mean and shape parameter of negative binomial distribution, from mean and proportion of zeros of Zobs. t20: proportion of transmission due to most infectious 20% of cases, calculated from k . ˆ vXX significantly vaccinated population; XX = proportion vaccinated, ( ? value estimated or unknown). * outbreak probably atypical of disease. † incomplete or inaccurate tracing suspected. N = number of infectious individuals in dataset. 117
s surveillance data. 90% CI: Bootstrap confidence intervals, based on 10000 resamples and bias-corrected percentile method. # value calculated in source report; raw data not available. 95% confidence intervals reported. b confidence interval determined directly from binomial distribution. u upper limit of confidence interval determined by assumption that ˆ →∞ for bootstrap datasets with no non-zero values of Z. 118 k pz
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Disease transmission in heterogeneo
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Abstract Disease transmission in he
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variation is quantified from outbre
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ACKNOWLEDGEMENTS I’ve been fortun
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Engineering Research Council of Can
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Epidemic modelers face an essential
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casual contact (DCC), common usage
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HCW, and patient pools) and dynamic
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Hoffmann 2004; Shen et al. 2004)—
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Chapter Two Frequency-dependent inc
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principles and reach robust conclus
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partnership, disease and demographi
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transmission to incorporate this ph
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This result can be understood intui
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Garnett 2002). We simulated epidemi
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4. Infection-induced changes in pai
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susceptible population (Diekmann an
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epidemics, since they bring R0 clos
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equired.) For slower-moving, chroni
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addressed here. Our treatment consi
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Table 1. Results for epidemics with
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(Equations 3 and A4); the lighter l
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Figure 2 A) B) Total proportion inf
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Appendix Derivation of SI pair dens
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As described in Section 2, our goal
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can be calculated as the product of
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Chapter Three Curtailing transmissi
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egions with on-going epidemics has
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transmission to the general communi
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and Ih), as well as from off-duty t
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ours—see Diekmann & Heesterbeek (
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In all cases (Figure 2C, 2D), we id
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Sensitivity to quarantining rate (s
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precautions in the hospital (η→1
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Preventing generalized community tr
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everywhere. These robust conclusion
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increasingly significant contributi
Page 75 and 76: hospitals or wards. Future work on
Page 77 and 78: Table 1. Summary of transmission an
Page 79 and 80: formulation of our model allows for
Page 81 and 82: Figure 3 (A) Increase in cumulative
Page 83 and 84: Figure 1 74
Page 85 and 86: Figure 3 (A) (B) (C) Cumulative num
Page 87 and 88: Appendix Sensitivity to population
Page 89 and 90: symptomatic HCWs is low. Indeed, th
Page 91 and 92: E I I I I m, i m, 1 m, 2 m , 3 m ,
Page 93 and 94: for a stochastic epidemic: the prob
Page 95 and 96: progress through the age sub-compar
Page 97 and 98: We therefore wish to characterize t
Page 99 and 100: Figure S4 Distribution of (A) incub
Page 101 and 102: Figure S2 (A) (C) 92 (B) (D)
Page 103 and 104: Figure S4 (A) (B) Proportion of cas
Page 105 and 106: 1. Introduction During the global e
Page 107 and 108: quantity p0, the proportion of case
Page 109 and 110: model selection techniques, lending
Page 111 and 112: elatively mild variation in ν, sho
Page 113 and 114: cannot make inferences based on the
Page 115 and 116: low k extinction happens within the
Page 117 and 118: measured by the variance-to-mean ra
Page 119 and 120: succeed (Figure 3B). For a given re
Page 121 and 122: to lower infectiousness. Other rele
Page 123 and 124: observations for the diseases exami
Page 125: Pneumonic plague 6 outbreaks N=74 A
Page 129 and 130: Figure captions Figure 1 Evidence f
Page 131 and 132: Figure 4 Impact of control measures
Page 133 and 134: Figure 2 Other Measles Influenza Ru
Page 135 and 136: Figure 4 C Reproductive number, R 1
Page 137 and 138: epresenting transmission yields a g
Page 139 and 140: We rescaled the AICc by subtracting
Page 141 and 142: for which the median of bootstrap e
Page 143 and 144: transmission due to the most infect
Page 145 and 146: an integer Z (99) such that FPoisso
Page 147 and 148: fv(u). Demographic stochasticity in
Page 149 and 150: original process is eliminated with
Page 151 and 152: For RA control, with a random propo
Page 153 and 154: ∞ ( , ) ∫ ( ) ( ). k−1 −t w
Page 155 and 156: * and for ν < ν : ∞ ∫ ν C 1
Page 157 and 158: Contrib(control policy) = Pr(contai
Page 159 and 160: ange of the first disease generatio
Page 161 and 162: Figure S1 MLE estimates of k 10 1 0
Page 163 and 164: Figure S2 (cont) D E F k=inf k=4 k=
Page 165 and 166: Figure S4 Relative frequency 0.4 0.
Page 167 and 168: SARS (March 12) and the imposition
Page 169 and 170: Transmission was predominantly by i
Page 171 and 172: Monkeypox, Zaire 1980-1984 (Jezek e
Page 173 and 174: Rubella, Hawaii 1970 (Hattis et al.
Page 175 and 176: tracing, with the stated goal of de
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Table S1. Superspreading events in
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Measles 250 Dance party ?M First ar
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SARS 187+ Apartment block 26M Amoy
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SARS 33 Hospital 62W Undiagnosed: S
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SARS 24/2* Home, emergency room, IC
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Streptococcus group A (type 1) 100+
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References Abbot, P. and L. M. Dill
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Caswell, H. (2001) Matrix Populatio
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Evatt, B. L., W. R. Dowdle, M. John
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Health Canada (2003) Summary of Sev
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Kretzschmar, M. (2000). Sexual netw
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McCallum, H., N. Barlow and J. Hone
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Taylor, H. M. and S. Karlin (1998).
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