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McCallum et al. 2002), and a similar goal is being pursued using correlation techniques for network models of disease (Bauch and Rand 2000; Ferguson and Garnett 2000; Eames and Keeling 2002). In exploring the relation between partnership dynamics and the classical frequency-dependent treatment of transmission, we have understood more clearly both the meaning of the classical model and the proper limits of its application. We have also extended theoretical results to include changes of contact behavior due to illness, so that this well-recognized effect can be incorporated into simple, analytic models when biological evidence requires it. 31
Table 1. Results for epidemics with infection-induced changes in behavior Case 1 2 3 4 Rates, κ kS=kI=k lSS=lSI=lII=l kS≠kI lSS=lSI=lII=l kS=kI=k lSS≠lSI≠lII kS≠kI lSS≠lSI≠lII 1 2 + π φκ(s,i) k k + l π π S I Ss I + π i π 1 1 2 2 4 a si 2 1− π π π S 2 2 ( π s + i) a( ) ⎟⎞ S πI 4 πSπ I ⎠ ⎜⎛ πSs + πIi + − si ⎝ kS kI Here s=S/N, i=I/N, π S = and π I = , and k + l k + l S SI I I SI 1− R 2 l ⎛ ⎞ ⎛ ⎞ ⎛ ⎞ SI lSI lSI lSI lSI a = ⎜ ⎜1− ⎟ + ⎜ ⎜1− ⎟ + ⎜ ⎜1− ⎟ . If kS=kI, then πS=πI≡π. kI ⎝ lSS ⎠ kS ⎝ lII ⎠ ⎝ lSSlII ⎠ R 0 is shown in Equation (5). 32 1− R 1− I i• 1 R0 1 + 1 πS ( − ) π S 0 π π 2 1− aπ R0 1− 2 R − aπ R 0 πS 0 + 1 π I 1− aπ π R S I 0 πS ( − ) − aπ Sπ I R0 π I I 0
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: addressed here. Our treatment consi
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 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
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
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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
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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
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* and for ν < ν : ∞ ∫ ν C 1
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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.
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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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