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Table 2. Impact of control measures on offspring distribution (for Z~NegB(R,k)) Outbreak SARS Beijing 2003 SARS Singapore 2003 Pneumonic plague Mukden 1946 Smallpox (V. major) v? Kuwait 1967 Symbols as in Table 1. N Before control During control ˆ R 0, mle (90% CI) 33 0.94 (0.27, 1.51) 57 1.63 (0.54,2.65) 12 2.00 (1.08, 2.75) 4 2.75 (1.00, 4.00) kmle ˆ (90% CI) 0.17 (0.10, 0.64) 0.16 (0.11,0.64) 2.63 (1.26, ∞) 2.64 (2.23, ∞) 119 N ˆ R c, mle (90% CI) 43 0.28 (0,0.84) b 114 0.68 (0.17, 1.14) 27 0.41 (0.11, 0.63) 23 0.91 (0, 1.57) b kmle ˆ (90% CI) 0.006 (0.006, ∞) u 0.071 (0.049, 0.41) 0.32 (0.12,2.15) 0.026 (0.012, ∞) u,b
Figure captions Figure 1 Evidence for variation in individual reproductive number ν. (A) Transmission data from SARS outbreak in Singapore, 2003 (Leo et al. 2003). Bars show observed frequency of Z, the number of individuals infected by each case; lines show maximum likelihood fits for Z~Poisson (squares), Z~geometric (triangles), and Z~negative binomial (circles). (A, inset) Probability density function (solid) and cumulative distribution function (dashed) for gamma-distributed ν (corresponding to Z~negative binomial) estimated from Singapore SARS data. (B) Proportion of all transmission due to the most infectious cases for six diseases of casual contact, based on ˆ values in Table 1. (C) Proportion of transmission due to the most infectious 20% of cases, for data drawn from single outbreaks (circles), multiple outbreaks (squares), and long-term surveillance (triangles). Dashed lines show proportions expected under the 20/80 rule (top) and homogeneity (bottom). Superscript v indicates a significant level of vaccination in the affected population; * indicates an outbreak that is probably exceptional for rubella. Figure 2 Superspreading events (SSEs). (A) Reported SSEs (diamonds) relative to estimated reproductive number R (squares) for twelve diseases of casual contact. Lines show 5-95 percentile range of Z~Poisson(R), and crosses show the 99 th percentile proposed as threshold definition for SSEs. Stars represent SSEs with more than one source case. Other diseases plotted in the top row are: a, Streptococcus group A; b, Lassa fever; c, Mycoplasma pneumonia; d, pneumonic plague; e, tuberculosis. See data in Table S1. 120 k mle
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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
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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 and 126: Pneumonic plague 6 outbreaks N=74 A
Page 127: s surveillance data. 90% CI: Bootst
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
Page 177 and 178: 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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