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Figure 3 A) B) C) Steady−state prevalence Total proportion infected Total proportion infected 1 0.8 0.6 0.4 0.2 k S k I l SI l or l SS II 0 0.01 0.1 1 10 100 Rate of pair formation or breakup 0.7 0.6 0.5 0.4 0.3 0.2 0.1 Bacterial STD 0 0 1 Time (years) 2 1 0.8 0.6 0.4 0.2 Viral STD +25% +50% −25% −50% No change in k I −70% −90% +50% +25% No change in k I −25% −50% −70% −90% 0 0 5 10 15 20 25 Time (years) 37
Appendix Derivation of SI pair density * Here we present a general derivation of the steady-state SI pair density P , including the results shown in Sections 2 and 4. We begin with the standard one-sex formulation of a pair-formation/epidemic model, extended such that pair-entry rates ky and break-up rates lyz (where y,z=S or I) can vary as a function of infection status (c.f. Dietz and Hadeler 1988): dX dt dX dt dP I SS SI II S dt dP dt dP dt = −k = −k = = = 1 2 1 2 1 2 I k k S I S S X X m k m I m SI II S + 2l SS + 2l X X X I S S II SS − l + − l P 1 2 II P II SS SS P + l I II + l P SS k m SI IS SI P X + β P SI I pair SI + σP −σX SI − l P + σX SI SI I SI I − 2µ P P − µ X SS − 2σP + λ − µ X − β II I pair + µ P SI S − 2µ P ( 2P + P ) ( 2P + P ) II + µ II −σP SI SS SI + 2σP II SI − 2µ P Parameters and variables are defined in the caption to Figure 1. The factors of ½ reflect that it takes two individuals to make a partnership (i.e. one unit of Pyz is equivalent to two units of XS or XI), and the factors of 2 in µ and σ terms reflect events that arise from transitions undergone by either member of a pair. Note that mixed partnerships (PSI) are formed both by XS individuals “choosing” XI individuals and vice versa; the two separate terms are essential to maintaining constant population size. We assume that population density has reached equilibrium, and set λ=µN. This derivation pertains to populations where pair formation and dissolution occur on faster timescales than disease and demographic processes (i.e. pairing rate parameters ky and lyz are significantly greater than epidemic rates βpair, σ and µ). We 38 SI SI (A1)
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: Figure 2 A) B) Total proportion inf
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
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We therefore wish to characterize t
Page 99 and 100:
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
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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
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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