Tools to study trends in community structure: Application to fish and livestock trading networks

Partitioning of contact networks into communities allows groupings of epidemiologically related nodes to be derived, that could inform the design of disease surveillance and control strategies, e.g. contact tracing or design of 'firebreaks' for disease spread. However, these are only of merit if they persist longer than the timescale of interventions. Here, we apply different methods to identify concordance between network partitions across time for two animal trading networks, those of salmon in Scotland (2002-2004) and livestock in Great Britain (2003-2004). Both trading networks are similar in that they moderately agree over time in terms of their community structures, but this concordance is higher - and therefore community structure is more consistent - when only the 'core' network of nodes involved in trading over the whole time series is considered. In neither case was higher agreement found between partitions close together in time. These measures differ in their absolute values unless appropriate standardisation is applied. Once standardised, the measures gave similar values for both network type

Comparison of the activities of students with different fever onsets.

<p>Students are grouped into those who never had symptoms, had fever onset by 14^th May, or fever onset 15^th May or later. The behavior of students with onset by 14^th May is similar to that of students who never became symptomatic.</p

Upper school activity levels by grade.

<p>A comparison of the activities of healthy upper school students during the school closure. Activity level in grades 11 and 12 was higher than in grades 9 and 10. Averages are given numerically.</p

Absenteeism by grade in upper and lower school before and after the school closure.

<p>Note different vertical axes. The lower school had significantly higher absenteeism. The mean and standard deviation about that mean for the same period of the previous year is shown in solid and dotted lines respectively.</p

Work missed by caretaker.

<p>The fraction of students reporting no ILI whose caretaker stayed home from work for the given number of days. About 9% of healthy upper school students reported a caretaker staying home from work at least one day, while about 30% of healthy lower school parents report a caretaker staying home at least one day.</p

Upper school activity frequency.

<p>A comparison of the frequency distribution of different activities among healthy upper school students.</p

Lower school activity levels by grade.

<p>Levels of activity in healthy students are lower than reported by upper school students.</p

A hexagonal mesh showing the spatial units of the Great Britain human movement database.

<p>A subset of the data covering the city of Stoke-on-Trent is shown. For an example hexagon magnified on the right, coloured segments correspond to the proportion of the residents in different demographic categories, considering only individuals older than 34 years of age. The top hexagon shows age ranges in years and the bottom hexagon shows employment status (UE  =  unemployed, FT  =  full-time employed and PT  =  part-time employed). The gray shaded areas on the map indicate urban areas and the blue lines indicate major roads.</p

A–C. The deviation in DIC for different locations of the infection source for the Stoke-on-Trent outbreak.

<p>The three levels of richness of the human movement data are shown are shown: A. Level 1, B. Level 2, C. Level 3. The deviation in DIC is calculated as the difference from the lowest DIC value for the given data richness level. The red lines intersect at the location of the true infection source. Town features are not shown to preserve anonymity. <b>D.</b> The number of individuals with a non-zero probability of visiting locations in Stoke-on Trent during a week, predicted by the GBHM database. The pink arrow indicates the preferred source hexagon obtained using the GBHM database to describe human movement (data richness Level 2). Grey lines indicate major roads.</p

The DIC value for different locations of the infection source for the outbreaks in A. Stoke-on-Trent, B. Hereford and C. Barrow-in-Furness.

<p>The three levels of richness of the human movement data are shown: Level 1 (red squares), Level 2 (blue circles) and Level 3 (green triangles).</p