Effect of random sampling on tree balance for infection trees of an ER graph (red), WS graph (green) and BA graph (blue).

<p>The mean degree and the transmissibility are the same for all networks: and . The rewiring probability for the WS is . The solid lines show the median over simulations and the light and dark shaded areas the 95% and 50% quantiles respectively. The dotted lines show the median normalized Sackin index for fully sampled trees of size equivalent to the sample size.</p

Normalized Sackin index for epidemics occurring on Watts-Strogatz graphs with varying rewiring probability.

<p>The total size of the population is and the color shows the size of the epidemic outbreak. The network is constructed by connected each node to its 8 closest neighbors on a ring lattice, and then rewiring each link with a probability . At low rewiring and transmission probabilities, and respectively, the epidemic only infects a small portion of the population and thus the Sackin index remains fairly small. Imbalance is largest for values of close to the critical value where the epidemic transition occurs.</p

Numbers of patients seen in each clinical service during the four twelve-month periods studied.

<p>Abbreviations: OP, outpatients; IP, inpatients; ICU, intensive care units; ED, emergency departments.</p

Imbalance of the infection tree for contact networks generated by three different models.

<p>Panel A shows the Sackin index as a measure of tree imbalance. Panel B shows the size of the epidemic outbreak for each of the network models at different values of transmissibility . All three models have the same mean number of neighbors . For the BA model, each vertex added in the preferential attachment is connected to nodes in the existing network, resulting in a mean degree of 8. The WS networks start with a ring lattice where each node is connected to its 4 closest neighbors on each side. Every link is then rewired with probability . The light shaded area show the values lying between the 2.5-th and the 97.5-th percentile, the dark shaded area the values between the 25th and the 75th percentile and the solid lines are the mean of the simulations. Each data point corresponds to simulation runs on independent graphs. A plot showing the normalized Sackin index for these three network models can be found in the supporting <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1002413#pcbi.1002413.s009" target="_blank">text S2</a>.</p

Time evolution of the normalized Sackin index, for the networks generated by the ER (red), BA (blue) and WS (green) model respectively.

<p>For all models, the mean number of neighbors and the total population size . The epidemic parameters are . For the WS model, the rewiring probability is . epidemics on different networks were simulated for each of the three networks models. (A) Tree imbalance when all individuals that have been infected prior to the time are included in the tree. While both the ER and BA models saturate at a certain value of the normalized Sackin index, the WS model continues to grow exponentially with new infected individuals. (B) Only those individuals which are infectious at time are included in the tree.</p

Tree imbalance of the Swiss HIV phylogenetic tree and 100 bootstrap trees (candlestick).

<p>The solid red curve shows the behavior of the normalized Sackin index for a tree with randomly sampled leaves from the complete HIV tree. The blue curve is the normalized Sackin index of an epidemic in a susceptible population displaying random mixing. The size of the susceptible population is chosen uniformly from the interval . The total epidemic size is chosen uniformly from the interval . The removal rate was chosen to be and transmission rate such that . We simulated outbreaks for each of the sample sizes of . The light shaded areas show the credible intervals, the dark shaded areas the credible intervals. The individual data points are the values of the normalized Sackin index for the three largest transmission clusters: heterosexuals/intravenous drug users (HET/IDU) and two men having sex with men (MSM) clusters.</p

Percentage of tests performed with positive result, median duration of inpatient stay, mean age of all patients seen and mean age of patients tested, for each clinical service.

<p>As data were not significantly different between 2008–2009 and 2010–2011, they have been pooled for clarity.</p><p>Abbreviations: IQR, interquartile range; SD, standard deviation; N/A, not applicable; OP, outpatients; IP, inpatients; ED, emergency department.</p

HIV testing practices by clinical service and year.

<p>Figure shows the numbers of tests performed (A) and the testing rates (B) in each clinical service during each of the four twelve-month periods studied. Abbreviations: OP, outpatients; IP, inpatients; ICU, intensive care units; ED, emergency departments.</p

Sampling schemes of tree leaves. The grey lines represent the full transmission tree.

<p>The red dashed lines are the reconstructed coalescent events of the sampled branches. (A) Random sampling: branches are randomly selected from the complete tree. (B) Sampling up to time : all transmission events that happened before time are kept. (C) Sampling at time : only branches alive at a given time are kept and the coalescent events are reconstructed.</p

Imbalance (normalized Sackin index) of the infection tree for ER random graphs with varying number of average neighbors.

<p>The light shaded area show the values lying between the 2.5-th and 97.5-th percentile, the dark shaded area those between the 25th and 75th percentile. The dashed line is the expected value of the imbalance for a tree with the same number of leaves under the Yule model (equation (7)). The transmissibility is chosen . The inset show the same data points on a log-log scale.</p