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1. Introduction When a previously unknown infectious disease emerges, initial options for control are limited. In the absence of an effective treatment or vaccine, policies are restricted to case management (such as isolation of known cases and quarantine of their contacts) and contact precautions for identifiable high-risk groups. Due to limitations in public health resources and concern about personal freedoms and economic impacts, policy-makers face decisions regarding the relative importance of such efforts. This paper identifies priorities and tradeoffs for control of the newly identified coronavirus that is causing an epidemic of Severe Acute Respiratory Syndrome (SARS) worldwide, particularly in parts of Asia. Our analysis focuses on the role of hospitals and healthcare workers (HCWs) in disease transmission by dividing the threatened population (city or region) into two groups: a hospital community and the community- at-large. Hospitals have been widely recognized as the highest-risk settings for SARS transmission (Drazen 2003, Lee 2003). Currently HCWs have comprised roughly 63% of SARS cases in Hanoi, 51% in Toronto, 42% in Singapore, 22% in Hong Kong, and 18% in mainland China (Booth et al. 2003, Hong Kong Department of Health 2003, Leo et al 2003, Twu et al 2003, World Health Organization 2003a). Healthcare settings and HCWs are thus an obvious focus for SARS control efforts, with particular concern for preventing leakage of the disease from hospitals back into surrounding communities. We present a model of a nascent SARS outbreak in a community and its hospital, addressing the relative benefits of case management and contact precautions for containing the disease. This situation holds great relevance because travel from 45
egions with on-going epidemics has the potential to seed new outbreaks worldwide (Twu et al. 2003). Of greatest concern are countries with poor health infrastructure, and the possibility of a seasonal re-emergence of SARS in the Northern hemisphere’s next winter. Furthermore, although our model is parametrized for SARS, the lessons learned will be useful in future outbreaks of novel infectious diseases or pandemic flu strains. Our analysis is based on a stochastic model, because chance events can greatly influence the early progression of an outbreak. We pay particular attention to capturing realistic distributions for the incubation and symptomatic periods associated with SARS, because the natural history of disease progression is less likely to vary between epidemics than are the mixing and transmission patterns. Disease control measures are described by explicit parameters, so their respective contributions to containment can be teased apart (see Table 1). Rates of hospitalizing infected community members and HCWs are denoted by hc and hh, respectively, and q is the rate of quarantining exposed individuals in the community following contact tracing. The transmission rate for case- isolated individuals is modified by a factor κ, reflecting measures such as respiratory isolation and negative pressure rooms, and transmission by quarantined individuals is modified by γ. Hospital-wide contact precautions, such as the use at all times of sterile gowns, filtration masks, and gloves, modify within-hospital transmission by a factor η. A final parameter ρ describes efforts to reduce contact between off-duty HCWs and the community. Control parameters are thus divided into those describing case management measures (hc, hh, q, γ, κ) and those describing contact precautions (η and ρ). 46
Page 1 and 2:
Disease transmission in heterogeneo
Page 3 and 4: Abstract Disease transmission in he
Page 5 and 6: variation is quantified from outbre
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: Chapter Three Curtailing transmissi
Page 57 and 58: transmission to the general communi
Page 59 and 60: and Ih), as well as from off-duty t
Page 61 and 62: ours—see Diekmann & Heesterbeek (
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
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quantity p0, the proportion of case
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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
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
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McCallum, H., N. Barlow and J. Hone
Page 201 and 202:
Taylor, H. M. and S. Karlin (1998).
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