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individuals and a hospital of 3,000 individuals (c.f. Dwost et al 2003). In the appendix we assess sensitivity of our results to absolute population size, and also to the relative size of the two pools. 3. Results and Discussion Stochastic epidemics and the reproductive number Epidemics with reproductive number R less than 1 tend to fade out, because on average each infection does not replace itself. When R is greater than 1, the epidemic is expected to grow, although if the number of cases is small then random events can lead to fadeout of the disease, particularly if R is close to 1. (Note that these statements apply equally to the basic reproductive number, R0, and the effective reproductive number under a control strategy, R). Sample simulations of our model exhibit this basic trend (Figure 2A), as we see fadeout for four of five simulations corresponding to R=1.2, two of five for R=1.6 and one of five for R=2. Also note the variability in epidemic timing and rate of growth between realizations of our stochastic model. Because fadeout is an imprecise concept, we frame our results in terms of “epidemic containment”, which we define as eradication of the disease within 200 days of the first case, subject to the additional criterion that fewer than 1% of the population ever become infected. (This criterion is needed because a highly virulent disease can pass through a population within 200 days and still infect a large proportion of individuals before extinguishing itself.) The probability of containment in our model decreases with increasing R (Figure 2B), but is still significantly larger than zero for R~5. (This relationship can be defined precisely for stochastic models simpler than 51
ours—see Diekmann & Heesterbeek (2000).) We note from Figure 2B that even control measures which do not reduce R below 1 can have a substantial probability of succeeding, provided they are imposed when the number of cases is small. Effect of case isolation To identify control strategies sufficient to contain a SARS outbreak, we consider parameter combinations which reduce the effective reproductive number to 1. We plot R=1 contours for a range of R0 values in 2-dimensional parameter spaces (Figures 2C- E); parameter regions to the left of the lines give R
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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
Page 9 and 10: Engineering Research Council of Can
Page 11 and 12: Epidemic modelers face an essential
Page 13 and 14: casual contact (DCC), common usage
Page 15 and 16: HCW, and patient pools) and dynamic
Page 17 and 18: Hoffmann 2004; Shen et al. 2004)—
Page 19 and 20: Chapter Two Frequency-dependent inc
Page 21 and 22: principles and reach robust conclus
Page 23 and 24: partnership, disease and demographi
Page 25 and 26: transmission to incorporate this ph
Page 27 and 28: This result can be understood intui
Page 29 and 30: Garnett 2002). We simulated epidemi
Page 31 and 32: 4. Infection-induced changes in pai
Page 33 and 34: susceptible population (Diekmann an
Page 35 and 36: epidemics, since they bring R0 clos
Page 37 and 38: equired.) For slower-moving, chroni
Page 39 and 40: addressed here. Our treatment consi
Page 41 and 42: Table 1. Results for epidemics with
Page 43 and 44: (Equations 3 and A4); the lighter l
Page 45 and 46: Figure 2 A) B) Total proportion inf
Page 47 and 48: Appendix Derivation of SI pair dens
Page 49 and 50: As described in Section 2, our goal
Page 51 and 52: can be calculated as the product of
Page 53 and 54: Chapter Three Curtailing transmissi
Page 55 and 56: egions with on-going epidemics has
Page 57 and 58: transmission to the general communi
Page 59: and Ih), as well as from off-duty t
Page 63 and 64: In all cases (Figure 2C, 2D), we id
Page 65 and 66: Sensitivity to quarantining rate (s
Page 67 and 68: precautions in the hospital (η→1
Page 69 and 70: Preventing generalized community tr
Page 71 and 72: everywhere. These robust conclusion
Page 73 and 74: 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
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elatively mild variation in ν, sho
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cannot make inferences based on the
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low k extinction happens within the
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measured by the variance-to-mean ra
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succeed (Figure 3B). For a given re
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to lower infectiousness. Other rele
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observations for the diseases exami
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Pneumonic plague 6 outbreaks N=74 A
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s surveillance data. 90% CI: Bootst
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Figure captions Figure 1 Evidence f
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Figure 4 Impact of control measures
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Figure 2 Other Measles Influenza Ru
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Figure 4 C Reproductive number, R 1
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epresenting transmission yields a g
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We rescaled the AICc by subtracting
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for which the median of bootstrap e
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transmission due to the most infect
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an integer Z (99) such that FPoisso
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fv(u). Demographic stochasticity in
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original process is eliminated with
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For RA control, with a random propo
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∞ ( , ) ∫ ( ) ( ). k−1 −t w
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* and for ν < ν : ∞ ∫ ν C 1
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Contrib(control policy) = Pr(contai
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ange of the first disease generatio
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Figure S1 MLE estimates of k 10 1 0
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Figure S2 (cont) D E F k=inf k=4 k=
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Figure S4 Relative frequency 0.4 0.
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SARS (March 12) and the imposition
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Transmission was predominantly by i
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Monkeypox, Zaire 1980-1984 (Jezek e
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Rubella, Hawaii 1970 (Hattis et al.
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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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