Jessica Enright

Deleting Edges to Restrict the Size of an Epidemic: A New Application for Treewidth

Motivated by applications in network epidemiology, we consider the problem of determining whether it is possible to delete at most k edges from a given input graph of small treewidth so that the maximum component size in the resulting graph is at most h. While this problem is NP-complete in general, we provide evidence that many of the real-world networks of interest are likely to have small treewidth, and we describe an algorithm which solves the problem in time

A descriptive analysis of the growth of unrecorded interactions amongst cattle-raising premises in Scotland and their implications for disease spread

Owh^{2w}n

Building a Better Mouse Maze

Owh2wn on an input graph having n vertices and whose treewidth is bounded by a fixed constant w.

Games on interval and permutation graph representations

Calculation of expected outbreak size of a simple contagion on a known contact network is a common and important epidemiological task, and is typically carried out by computationally intensive simulation. We describe an efficient exact method to calculate the expected outbreak size of a contagion on an outbreak-invariant network that is a directed and acyclic, allowing us to model all dynamically changing networks when contagion can only travel forward in time. We describe our algorithm and its use in pseudocode, as well as showing examples of its use on disease relevant, data-derived networks.

Deleting edges to restrict the size of an epidemic in temporal networks.

BackgroundIndividual animal-level reporting of cattle movements between agricultural holdings is in place in Scotland, and the resulting detailed movement data are used to inform epidemiological models and intervention. However, recent years have seen a rapid increase in the use of registered links that allow Scottish farmers to move cattle between linked holdings without reporting.ResultsBy analyzing these registered trade links as a number of different networks, we find that the geographical reach of these registered links has increased over time, with many holdings linked indirectly to a large number of holdings, some potentially geographically distant. This increase was not linked to decreases in recorded movements at the holding level. When combining registered links with reported movements, we find that registered links increase the size of a possible outward chain of infection from a Scottish holding. The impact on the maximum size is considerably greater than the impact on the mean.ConclusionsWe outline the magnitude and geographic extent of that increase, and show that this growth both has the potential to substantially increase the size of epidemics driven by livestock movements, and undermines the extensive, invaluable recording within the cattle tracing system in Scotland and, by extension, the rest of Great Britain.

Changing times to optimise reachability in temporal graphs.

In many populations, the patterns of potentially infectious contacts are transients that can be described as a network with dynamic links. The relative timescales of link and contagion dynamics and the characteristics that drive their tempos can lead to important differences to the static case. Here, we propose some essential nomenclature for their analysis, and then review the relevant literature. We describe recent advances in they apply to infection processes, considering all of the methods used to record, measure and analyse them, and their implications for disease transmission. Finally, we outline some key challenges and opportunities in the field.

Counting small subgraphs in multi-layer networks.

Mouse Maze is a Flash game about Squeaky, a mouse who has to navigate a subset of the grid using a simple deterministic rule, which naturally generalises to a game on arbitrary graphs with some interesting chaotic dynamics. We present the results of some evolutionary algorithms which generate graphs which effectively trap Squeaky in the maze for long periods of time, and some theoretical results on how long he can be trapped. We then discuss what would happen to Squeaky if he couldnt count, and present some open problems in the area.