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Figure captions – appendix A Figure S1 Comparison of maximum likelihood and proportion of zeros estimates and 90% confidence intervals for the negative binomial shape parameter k. Each point corresponds to an outbreak for which we have full information on Z, so we are able to estimate ˆ and the corresponding bias-corrected bootstrap confidence interval. For k mle the same dataset, we then discarded all information except the mean and proportion of zeros and estimated ˆ and the binomial-bootstrap confidence interval. Figure S2 k pz Branching process results for Z~NegB(R0,k). (A) The probability generating function of the negative binomial distribution, plotted for R0=3 and different shape parameters k. The y-intercept of the pgf equals p0, the probability that an infected individual will infect nobody, and is a major factor in the rising probability of extinction as k decreases. The extinction probability q is determined by the point of intersection of the pgf with a line of slope 1 (dashed) through the origin. (B) The probability of stochastic extinction given introduction of a single infected individual, q, rises to 1 as kØ0 for any value of R0. (C) The probability of stochastic extinction by the n th generation of transmission, qn, for R0=3 and a range of k. Interestingly, for the third and subsequent generations, the k=1 case has the highest continuing probability of extinction. (D) Expected size of a minor outbreak (i.e. an outbreak that dies out spontaneously) versus R0. Curves for all k values are identical for R0
ange of the first disease generation with 100 cases; whiskers show 95-percentile range, and crosses show outliers. Percentages show the proportion of 10,000 simulated outbreaks that reached the 100-case threshold (i.e. roughly 1-q). (F) Growth rate of simulated outbreaks with R0=3. Both (E) and (F) are exactly analogous to Figure 3C except for different values of R0. Figure S3 Impact of control measures. (A) Accuracy of the approximation whereby the offspring distribution under random absolute (RA) control is represented by a negative binomial RA RA RA distribution, Z ~NegB( R , k ). Calculation of the proportion of overlap is described in the SOM text. (B) Precise and approximated NB offspring distributions under RA control for R0=3. From bottom to top, five curves for both the precise (red solid lines and circles) and approximate (black dotted lines and squares) distributions RA show k=0.1, 0.5, 1, 3, and 10. (C) The approximated shape parameter k decreases monotonically as control effort c increases. Curves depict uncontrolled k=1000 (blue), k=1 (green), and k=0.1 (red), for R0=1 (solid), R0=3 (dotted), and R0=10 (dashed). (D) Effect of control measures targeting the most infectious individuals. The plot is exactly analogous to Figure 3D, except that in the targeted control scenario individuals in the top 20% of infectiousness are ten-fold more likely to be controlled than those in the bottom 80%. c c c 150 c
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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
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Table 1. Summary of transmission an
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formulation of our model allows for
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Figure 3 (A) Increase in cumulative
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Figure 1 74
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Figure 3 (A) (B) (C) Cumulative num
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Appendix Sensitivity to population
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symptomatic HCWs is low. Indeed, th
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E I I I I m, i m, 1 m, 2 m , 3 m ,
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for a stochastic epidemic: the prob
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progress through the age sub-compar
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We therefore wish to characterize t
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Figure S4 Distribution of (A) incub
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Figure S2 (A) (C) 92 (B) (D)
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Figure S4 (A) (B) Proportion of cas
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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 and 128: s surveillance data. 90% CI: Bootst
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: Contrib(control policy) = Pr(contai
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
Page 179 and 180: Measles 250 Dance party ?M First ar
Page 181 and 182: SARS 187+ Apartment block 26M Amoy
Page 183 and 184: SARS 33 Hospital 62W Undiagnosed: S
Page 185 and 186: SARS 24/2* Home, emergency room, IC
Page 187 and 188: Streptococcus group A (type 1) 100+
Page 189 and 190: References Abbot, P. and L. M. Dill
Page 191 and 192: Caswell, H. (2001) Matrix Populatio
Page 193 and 194: Evatt, B. L., W. R. Dowdle, M. John
Page 195 and 196: Health Canada (2003) Summary of Sev
Page 197 and 198: Kretzschmar, M. (2000). Sexual netw
Page 199 and 200: McCallum, H., N. Barlow and J. Hone
Page 201 and 202: Taylor, H. M. and S. Karlin (1998).
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K - College of Natural Resources - University of California, Berkeley

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