Alison Gray

A stochastic differential equation SIS epidemic model

In this paper we extend the classical susceptible-infected-susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation (SDE) for the number of infectious individuals

Results of international standardised beekeeper surveys of colony losses for winter 2012-2013: analysis of winter loss rates and mixed effects modelling of risk factors for winter loss

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An Observational Study of Honey Bee Colony Winter Losses and Their Association with Varroa destructor, Neonicotinoids and Other Risk Factors

. We then prove that this SDE has a unique global positive solution

Almost sure exponential stability of backward Euler-Maruyama discretizations for hybrid stochastic differential equations

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Preliminary analysis of loss rates of honey bee colonies during winter 2015/16 from the COLOSS survey

and establish conditions for extinction and persistence of

EU sampling strategies for the detection of veterinary drug residues in aquaculture species: Are they working?

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Simulating posterior Gibbs distributions: a comparison of the Swendsen-Wang and Gibbs sampler methods

. We discuss perturbation by stochastic noise. In the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance. The results are illustrated by computer simulations, including two examples based on real-life diseases.

Morphological texture analysis using the texture evolution function

Summary This article presents results of an analysis of winter losses of honey bee colonies from 19 mainly European countries, most of which implemented the standardised 2013 COLOSS questionnaire. Generalised linear mixed effects models (GLMMs) were used to investigate the effects of several factors on the risk of colony loss, including different treatments for Varroa destructor, allowing for random effects of beekeeper and region. Both winter and summer treatments were considered, and the most common combinations of treatment and timing were used to define treatment factor levels. Overall and within country colony loss rates are presented. Significant factors in the model were found to be: percentage of young queens in the colonies before winter, extent of queen problems in summer, treatment of the varroa mite, and access by foraging honey bees to oilseed rape and maize. Spatial variation at the beekeeper level is shown across geographical regions using random effects from the fitted models, both before and after allowing for the effect of the significant terms in the model. This spatial variation is considerable.

Classification of Ordered Texture Images Using Regression Modelling and Granulometric Features

This article presents results of an analysis of honey bee losses over the winter of 2011-2012 in the Netherlands, from a sample of 86 colonies, located at 43 apiaries. The apiaries were selected using spatially stratified random sampling. Colony winter loss data were collected and related to various measures of colony strength recorded in summer, as well as data from laboratory analysis of sample material taken from two selected colonies in each of the 43 apiaries. The logistic regression model which best explained the risk of winter loss included, in order of statistical importance, the variables (1) Varroa destructor mite infestation rate in October 2011, (2) presence of the cyano-substituted neonicotinoids acetamiprid or thiacloprid in the first 2 weeks of August 2011 in at least one of the honey bee matrices honey, bees or bee bread (pollen), (3) presence of Brassica napus (oilseed rape) or Sinapis arvensis (wild mustard) pollen in bee bread in early August 2011, and (4) a measure of the unexplained winter losses for the postal code area where the colonies were located, obtained from a different dataset. We consider in the discussion that reduced opportunities for foraging in July and August because of bad weather may have added substantially to the adverse effects of acetamiprid and thiacloprid. A novel feature of this work is its use of postal code random effects from two other independent datasets collected in the annual national monitoring by questionnaires of winter losses of honey bees in the Netherlands. These were used to plan the sample selection and also in the model fitting of the data in this study. It should however be noted that the results of the present pilot study are based on limited data, which may consequently reveal strong factors but fail to demonstrate possible interaction effects.

A comparison of digital length estimators for image features

This is a continuation of the first authors earlier paper [1] jointly with Pang and Deng, in which the authors established some sufficient conditions under which the Euler-Maruyama (EM) method can reproduce the almost sure exponential stability of the test hybrid SDEs. The key condition imposed in [1] is the global Lipschitz condition. However, we will show in this paper that without this global Lipschitz condition the EM method may not preserve the almost sure exponential stability. We will then show that the backward EM method can capture the almost sure exponential stability for a certain class of highly nonlinear hybrid SDEs.