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1.
Figure 7

Figure 7. From: Spread of infectious disease through clustered populations.

Replacing the edges {v,w} and {x,y} with {v,x} and {w,y} breaks the triangle and allows more infections, without affecting the degree distribution.

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
2.
Figure 3

Figure 3. From: Spread of infectious disease through clustered populations.

Different options for paths of length 2 between nodes u and v: (a) nuv=4, xuv=1; (b) nuv=4, xuv=0.

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
3.
Figure 11

Figure 11. From: Spread of infectious disease through clustered populations.

(a–d) 0,r with heterogeneous transmissibility and weighted edges on the EpiSimS network (black solid curve, unclustered 0; black dashed curve, 0,0; grey solid curve, 0,1; dotted curve, 0,2; dot-dashed curve, 0,3; grey dashed curve, 0,4).

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
4.
Figure 12

Figure 12. From: Spread of infectious disease through clustered populations.

Simulated (a) and (b) (symbols) for the weighted EpiSimS network compared with predictions in unclustered networks with the same edge weight distribution (curves).

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
5.
Figure 10

Figure 10. From: Spread of infectious disease through clustered populations.

(a) 0,r (black solid curve, unclustered 0; black dashed curve, 0,0; grey solid curve, 0,1; dotted curve, 0,2; dot-dashed curve, 0,3; grey dashed curve, 0,4) and (b) and for the weighted EpiSimS network with a homogeneous population.

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
6.
Figure 1

Figure 1. From: Spread of infectious disease through clustered populations.

A sample network and several stages of an outbreak. Nodes begin susceptible (small circles), become infected (large open circles), possibly infecting others along edges, and then recover (large filled circles). The outbreak finishes when no infected nodes remain.

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
7.
Figure 5

Figure 5. From: Spread of infectious disease through clustered populations.

The progression of 10 simulated epidemics for (a) T=0.1 and (b) T=0.2 in the EpiSimS network. (a) Nr+1/Nr against rank and (b) the cumulative fraction of the population infected are shown (dotted curve, unclustered 0 prediction; dashed curve, 0,1).

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
8.
Figure 8

Figure 8. From: Spread of infectious disease through clustered populations.

(a–e) calculated from EPNs for the heterogeneous examples of table 1 (black solid curve, unclustered 0; black dashed curve, 0,0; grey solid curve, 0,1; dotted curve, 0,2; dot-dashed curve, 0,3; grey dashed curve, 0,4). (f) 0,1 values for all of the different cases, including both unclustered 0 (solid curve) and homogeneous 0,1 (dotted curve) are compared.

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
9.
Figure 4

Figure 4. From: Spread of infectious disease through clustered populations.

(a,b) Comparison of first three asymptotic approximations for 0,1 from equation (3.1) with the exact value for the EpiSimS network. (b) The comparison at small T is shown (solid curve, exact 0,1; dotted curve, first approximation; dot-dashed curve, second approximation; dashed curve, third approximation).

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
10.
Figure 9

Figure 9. From: Spread of infectious disease through clustered populations.

Comparison of (a) and (b) observed from EPNs in the clustered EpiSimS network with heterogeneities (symbols) with that predicted by the unclustered theory (curves) using table 1. Each data point is based on a single EPN. For both and , Tin(v)=〈T〉 for all nodes, and so the unclustered prediction for is the same.

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
11.
Figure 6

Figure 6. From: Spread of infectious disease through clustered populations.

Probability and attack rate of epidemics for the (clustered) EpiSimS network (pluses) versus T, compared with the prediction derived from the degree distribution assuming no clustering. Each data point is from a single EPN (the variation in resulting from different EPNs is negligible).

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.
12.
Figure 2

Figure 2. From: Spread of infectious disease through clustered populations.

(a,b) Simulated values of the rank reproductive ratio for r=0, …, 4 using an EPN from the (fixed) EpiSimS network with a homogeneous population, compared with the unclustered prediction. (b) At small T, 0,10,4 match the unclustered prediction (black solid curve, unclustered 0 prediction; black dashed curve, 0,0; grey solid curve, 0,1; dotted curve, 0,2; dot-dashed curve, 0,3; grey dashed curve, 0,4). Each data point for 〈T〉≤0.5 is for 105 index cases in a single EPN, while each data point for T>0.5 is for 103 index cases. Noise becomes less significant at larger r.

Joel C. Miller. J R Soc Interface. 2009 December 6;6(41):1121-1134.

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