Edge-Based Compartmental Modeling for Infectious Disease Spread Part III: Disease and Population Structure

We consider the edge-based compartmental models for infectious disease spread introduced in Part I. These models allow us to consider standard SIR diseases spreading in random populations. In this paper we show how to handle deviations of the disease or population from the simplistic assumptions of Part I. We allow the population to have structure due to effects such as demographic detail or multiple types of risk behavior the disease to have more complicated natural history. We introduce these modifications in the static network context, though it is straightforward to incorporate them into dynamic networks. We also consider serosorting, which requires using the dynamic network models. The basic methods we use to derive these generalizations are widely applicable, and so it is straightforward to introduce many other generalizations not considered here

Beyond clustering: mean-field dynamics on networks with arbitrary subgraph composition

Clustering is the propensity of nodes that share a common neighbour to be connected. It is ubiquitous in many networks but poses many modelling challenges. Clustering typically manifests itself by a higher than expected frequency of triangles, and this has led to the principle of constructing networks from such building blocks. This approach has been generalised to networks being constructed from a set of more exotic subgraphs. As long as these are fully connected, it is then possible to derive mean-field models that approximate epidemic dynamics well. However, there are virtually no results for non-fully connected subgraphs. In this paper, we provide a general and automated approach to deriving a set of ordinary differential equations, or mean-field model, that describes, to a high degree of accuracy, the expected values of system-level quantities, such as the prevalence of infection. Our approach offers a previously unattainable degree of control over the arrangement of subgraphs and network characteristics such as classical node degree, variance and clustering. The combination of these features makes it possible to generate families of networks with different subgraph compositions while keeping classical network metrics constant. Using our approach, we show that higher-order structure realised either through the introduction of loops of different sizes or by generating networks based on different subgraphs but with identical degree distribution and clustering, leads to non-negligible differences in epidemic dynamics

How South Pacific mangroves may respond to predicted climate change and sea level rise

In the Pacific islands the total mangrove area is about 343,735 ha, with largest areas in Papua New Guinea, Solomon Islands, Fiji and New Caledonia. A total of 34 species of mangroves occur, as well as 3 hybrids. These are of the Indo-Malayan assemblage (with one exception), and decline in diversity from west to east across the Pacific, reaching a limit at American Samoa. Mangrove resources are traditionally exploited in the Pacific islands, for construction and fuel wood, herbal medicines, and the gathering of crabs and fish. There are two main environmental settings for mangroves in the Pacific, deltaic and estuarine mangroves of high islands, and embayment, lagoon and reef flat mangroves of low islands. It is indicated from past analogues that their close relationship with sea-level height renders these mangrove swamps particularly vulnerable to disruption by sea-level rise. Stratigraphic records of Pacific island mangrove ecosystems during sea-level changes of the Holocene Period demonstrate that low islands mangroves can keep up with a sea-level rise of up to 12 cm per 100 years. Mangroves of high islands can keep up with rates of sea-level rates of up to 45 cm per 100 years, according to the supply of fluvial sediment. When the rate of sea-level rise exceeds the rate of accretion, mangroves experience problems of substrate erosion, inundation stress and increased salinity. Rise in temperature and the direct effects of increased CO2 levels are likely to increase mangrove productivity, change phenological patterns (such as the timing of flowering and fruiting), and expand the ranges of mangroves into higher latitudes. Pacific island mangroves are expected to demonstrate a sensitive response to the predicted rise in sea-level. A regional monitoring system is needed to provide data on ecosystem changes in productivity, species composition and sedimentation. This has been the intention of a number of programs, but none has yet been implemented

Most vital segment barriers

We study continuous analogues of "vitality" for discrete network flows/paths, and consider problems related to placing segment barriers that have highest impact on a flow/path in a polygonal domain. This extends the graph-theoretic notion of "most vital arcs" for flows/paths to geometric environments. We give hardness results and efficient algorithms for various versions of the problem, (almost) completely separating hard and polynomially-solvable cases

Epidemics on contact networks: a general stochastic approach

Dynamics on networks is considered from the perspective of Markov stochastic processes. We partially describe the state of the system through network motifs and infer any missing data using the available information. This versatile approach is especially well adapted for modelling spreading processes and/or population dynamics. In particular, the generality of our systematic framework and the fact that its assumptions are explicitly stated suggests that it could be used as a common ground for comparing existing epidemics models too complex for direct comparison, such as agent-based computer simulations. We provide many examples for the special cases of susceptible-infectious-susceptible (SIS) and susceptible-infectious-removed (SIR) dynamics (e.g., epidemics propagation) and we observe multiple situations where accurate results may be obtained at low computational cost. Our perspective reveals a subtle balance between the complex requirements of a realistic model and its basic assumptions.Comment: Main document: 16 pages, 7 figures. Electronic Supplementary Material (included): 6 pages, 1 tabl

A monotonic relationship between the variability of the infectious period and final size in pairwise epidemic modelling

For a recently derived pairwise model of network epidemics with non-Markovian recovery, we prove that under some mild technical conditions on the distribution of the infectious periods, smaller variance in the recovery time leads to higher reproduction number, and consequently to a larger epidemic outbreak, when the mean infectious period is fixed. We discuss how this result is related to various stochastic orderings of the distributions of infectious periods. The results are illustrated by a number of explicit stochastic simulations, suggesting that their validity goes beyond regular networks

The experience of long-term opiate maintenance treatment and reported barriers to recovery: A qualitative systematic review

Background/Aim: To inform understanding of the experience of long-term opiate maintenance and identify barriers to recovery. Methods: A qualitative systematic review. Results: 14 studies in 17 papers, mainly from the USA (65%), met inclusion criteria, involving 1,088 participants. Studies focused on methadone prescribing. Participants reported stability; however, many disliked methadone. Barriers to full recovery were primarily ‘inward focused'. Conclusion: This is the first review of qualitative literature on long-term maintenance, finding that universal service improvements could be made to address reported barriers to recovery, including involving ex-users as positive role models, and increasing access to psychological support. Treatment policies combining harm minimisation and abstinence-orientated approaches may best support individualised recovery

Minimal symmetric Darlington synthesis

We consider the symmetric Darlington synthesis of a p x p rational symmetric Schur function S with the constraint that the extension is of size 2p x 2p. Under the assumption that S is strictly contractive in at least one point of the imaginary axis, we determine the minimal McMillan degree of the extension. In particular, we show that it is generically given by the number of zeros of odd multiplicity of I-SS*. A constructive characterization of all such extensions is provided in terms of a symmetric realization of S and of the outer spectral factor of I-SS*. The authors's motivation for the problem stems from Surface Acoustic Wave filters where physical constraints on the electro-acoustic scattering matrix naturally raise this mathematical issue