A rigorous approach to investigating common assumptions about disease transmission: Process algebra as an emerging modelling methodology for epidemiology

Changing scale, for example the ability to move seamlessly from an individual-based model to a population-based model, is an important problem in many fields. In this paper we introduce process algebra as a novel solution to this problem in the context of models of infectious disease spread. Process algebra allows us to describe a system in terms of the stochastic behaviour of individuals, and is a technique from computer science. We review the use of process algebra in biological systems, and the variety of quantitative and qualitative analysis techniques available. The analysis illustrated here solves the changing scale problem: from the individual behaviour we can rigorously derive equations to describe the mean behaviour of the system at the level of the population. The biological problem investigated is the transmission of infection, and how this relates to individual interaction

Molecular Infectious Disease Epidemiology: Survival Analysis and Algorithms Linking Phylogenies to Transmission Trees

Recent work has attempted to use whole-genome sequence data from pathogens to reconstruct the transmission trees linking infectors and infectees in outbreaks. However, transmission trees from one outbreak do not generalize to future outbreaks. Reconstruction of transmission trees is most useful to public health if it leads to generalizable scientific insights about disease transmission. In a survival analysis framework, estimation of transmission parameters is based on sums or averages over the possible transmission trees. A phylogeny can increase the precision of these estimates by providing partial information about who infected whom. The leaves of the phylogeny represent sampled pathogens, which have known hosts. The interior nodes represent common ancestors of sampled pathogens, which have unknown hosts. Starting from assumptions about disease biology and epidemiologic study design, we prove that there is a one-to-one correspondence between the possible assignments of interior node hosts and the transmission trees simultaneously consistent with the phylogeny and the epidemiologic data on person, place, and time. We develop algorithms to enumerate these transmission trees and show these can be used to calculate likelihoods that incorporate both epidemiologic data and a phylogeny. A simulation study confirms that this leads to more efficient estimates of hazard ratios for infectiousness and baseline hazards of infectious contact, and we use these methods to analyze data from a foot-and-mouth disease virus outbreak in the United Kingdom in 2001. These results demonstrate the importance of data on individuals who escape infection, which is often overlooked. The combination of survival analysis and algorithms linking phylogenies to transmission trees is a rigorous but flexible statistical foundation for molecular infectious disease epidemiology.Comment: 28 pages, 11 figures, 3 table

TECHNICAL BARRIERS TO TRADE: A CASE STUDY OF PHYTOSANITARY BARRIERS AND U.S. - JAPANESE APPLE TRADE

Concern about the use if technical barriers as restrictions to trade has increased since the World Trade Organization Agreement on Agriculture. In this analysis, we quantify the phytosanitary barriers to U.S. apple exports to Japan by calculating tariff-rate equivalents. We examine the trade and welfare impacts of removing phytosanitary barriers and tariffs under two assumptions regarding transmission of the bacterial disease fire blight: first, that transmission via commercial fruit is not possible, and second, that it can occur. The disease losses required to eliminate the grains to trade are estimated to be much larger than those experienced in other countries.International Relations/Trade,

Graph Theory and Networks in Biology

In this paper, we present a survey of the use of graph theoretical techniques in Biology. In particular, we discuss recent work on identifying and modelling the structure of bio-molecular networks, as well as the application of centrality measures to interaction networks and research on the hierarchical structure of such networks and network motifs. Work on the link between structural network properties and dynamics is also described, with emphasis on synchronization and disease propagation.Comment: 52 pages, 5 figures, Survey Pape

Measuring comovements by regression quantiles

This paper develops a rigorous econometric framework to investigate the structure of codependence between random variables and to test whether it changes over time. Our approach is based on the computation - over both a test and a benchmark period - of the conditional probability that a random variable yt is lower than a given quantile, when the other random variable xt is also lower than its corresponding quantile, for any set of prespecified quantiles. Time-varying conditional quantiles are modeled via regression quantiles. The conditional probability is estimated through a simple OLS regression. We illustrate the methodology by investigating the impact of the crises of the 1990s on the major Latin American equity markets returns. Our results document significant increases in equity return co-movements during crises consistent with the presence of financial contagion. JEL Classification: C14, C22, G15codependence, conditional quantiles, semi-parametric

Dynamical Systems on Networks: A Tutorial

We give a tutorial for the study of dynamical systems on networks. We focus especially on "simple" situations that are tractable analytically, because they can be very insightful and provide useful springboards for the study of more complicated scenarios. We briefly motivate why examining dynamical systems on networks is interesting and important, and we then give several fascinating examples and discuss some theoretical results. We also briefly discuss dynamical systems on dynamical (i.e., time-dependent) networks, overview software implementations, and give an outlook on the field.Comment: 39 pages, 1 figure, submitted, more examples and discussion than original version, some reorganization and also more pointers to interesting direction

Mathematical models in the evaluation of health programmes.

Modelling is valuable in the planning and evaluation of interventions, especially when a controlled trial is ethically or logistically impossible. Models are often used to calculate the expected course of events in the absence of more formal assessments. They are also used to derive estimates of rare or future events from recorded intermediate points. When developing models, decisions are needed about the appropriate level of complexity to be represented and about model structure and assumptions. The degree of rigor in model development and assessment can vary greatly, and there is a danger that existing beliefs inappropriately influence judgments about model assumptions and results

A class of pairwise models for epidemic dynamics on weighted networks

In this paper, we study the $SIS$ (susceptible-infected-susceptible) and $SIR$ (susceptible-infected-removed) epidemic models on undirected, weighted networks by deriving pairwise-type approximate models coupled with individual-based network simulation. Two different types of theoretical/synthetic weighted network models are considered. Both models start from non-weighted networks with fixed topology followed by the allocation of link weights in either (i) random or (ii) fixed/deterministic way. The pairwise models are formulated for a general discrete distribution of weights, and these models are then used in conjunction with network simulation to evaluate the impact of different weight distributions on epidemic threshold and dynamics in general. For the $SIR$ dynamics, the basic reproductive ratio $R_0$ is computed, and we show that (i) for both network models $R_{0}$ is maximised if all weights are equal, and (ii) when the two models are equally matched, the networks with a random weight distribution give rise to a higher $R_0$ value. The models are also used to explore the agreement between the pairwise and simulation models for different parameter combinations

Hotspots: Modelling capacity for vector-borne disease risk analysis in New Zealand: A case study of Ochlerotatus camptorhynchus incursions in New Zealand

This Hotspots case study of Oc. camptorhynchus in New Zealand forms part of the wider aims and objectives of the Hotspots project. The overall aims of the case study were: 1. To evaluate the performance of the Hotspots model as a risk analysis tool for Oc. camptorhynchus; 2. To use and learn from the experience of the various incursions of Oc. camptorhynchus in order to critically assess and improve the model; 3. To gain experience in using the model for risk analysis for Oc. camptorhynchus in particular, and in so doing, also develop experience applicable to risk analysis for other vectors of concern (Table 1); and, 4. To develop an experience and knowledge base as well as guidelines for future use of the model in its various applications related to biosecurity, surveillance and risk assessment and management