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equired for the derivation means that pair-based STD transmission is portrayed accurately only for promiscuous populations and chronic, less-transmissible infections. Simulations define the limits of the classical model for two broad classes of STD. I then extend the derivation to include situations where infected individuals exhibit altered pairing behavior, presenting analytic expressions for the generalized frequency-dependent transmission rate, basic reproductive number (R0), and steady-state prevalence of an epidemic, for four cases of increasing behavioral complexity. Potentially significant effects of infection-induced changes in contact behavior are illustrated by simulating epidemics of bacterial and viral STDs. In Chapter 3, I investigate the stochastic invasion dynamics of an emerging disease in a community and its associated hospital, exploring for the first time the potential amplifying role of hospitals in an outbreak characterized by nosocomial spread. Severe acute respiratory syndrome (SARS) was transmitted extensively within hospitals, and healthcare workers comprised a large proportion of SARS cases worldwide. I evaluate contact precautions and case management (quarantine and isolation) as control measures for SARS, revealing that hospital infection control is the most potent measure and should be practiced by all individuals in affected hospitals, rather than only those interacting with known SARS cases. Delays of a few days in contact tracing and case identification severely degrade the utility of quarantine and isolation, and still more detrimental are delays between onset of an outbreak and implementation of control measures. If hospital-based transmission is not halted, measures which reduce community-healthcare worker contact are vital to preventing a widespread epidemic. These results have implications for future outbreaks of SARS or other emerging pathogens. In Chapter 4, I address the impact of individual-level variation in infectiousness, and resulting superspreading events (SSEs), on disease emergence. I introduce the “individual reproductive number”, a natural extension of the basic reproductive number R0 from a population average to a distribution incorporating individual variation. The degree of individual 2
variation is quantified from outbreak data for ten diseases of casual contact (including SARS, smallpox, plague and H5N1 avian influenza), showing conclusively that conventional models are inadequate to represent real transmission patterns. I provide the first in-depth discussion and analysis of SSEs, including an extensive review of their causes and a general, probabilistic definition that allows prediction of the proportion of cases causing SSEs for a given disease outbreak. I introduce a rigorous stochastic theory for disease invasions based on the individual reproductive number, and analyze it to demonstrate profound effects of individual variation on disease emergence. The model replicates real-world patterns, such as the explosive outbreaks characteristic of SARS in 2003—a test failed by conventional models. Finally, I present theory and data on outbreak control that distinguish between population-wide and individual-specific control measures. Data from four outbreaks are more consistent with individual-specific control, which is proven to be more effective at disease containment for a given reduction in R0. I show that targeting highly-infectious individuals substantially improves the efficiency of control, opening important research challenges in predicting individual infectiousness. 3
Page 1 and 2: Disease transmission in heterogeneo
Page 3: Abstract Disease transmission in he
Page 7 and 8: 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
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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
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quantity p0, the proportion of case
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model selection techniques, lending
Page 111 and 112:
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
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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