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specific from population-wide measures, and proves that stopping all transmission by some individuals controls epidemics better than partial reduction in everyone’s transmission (for a given reduction in R0). Returning to outbreak data, we see that changes in transmission patterns observed upon imposition of control are more consistent with individual-specific measures. Through the interplay of developing theory, analyzing empirical data, and addressing applied problems, the work contained in this dissertation constitutes some measure of progress in our understanding of disease transmission in heterogeneous populations. Much more remains to be understood, including some direct links between the studies presented here. Community-hospital spread of SARS should be re- addressed in light of the marked individual variation in SARS transmission patterns and their demonstrated impact on invasion dynamics. Theory incorporating the individual reproductive number should be extended to populations with structural heterogeneity (i.e. multiple distinct groups), and generalized beyond the invasion scenarios described by branching process models. Individual-level heterogeneity in pairing behavior could be introduced to a pair-formation model, perhaps leading to situations where only part of the population satisfies the timescale approximation required for frequency- dependent incidence to represent pair-based transmission. In all cases, more and better empirical datasets are needed to test our theoretical ideas. The struggle against infectious diseases will not abate in the foreseeable future, so epidemic modelers must continue to advance our science in order to contribute meaningfully to the fight. 9
Chapter Two Frequency-dependent incidence in sexually-transmitted disease models: portrayal of pair-based transmission and effects of illness on contact behaviour J.O. Lloyd-Smith, W.M. Getz, and H.V. Westerhoff 10
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: Hoffmann 2004; Shen et al. 2004)—
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 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
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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
Page 83 and 84:
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
Page 115 and 116:
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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