Andrew Stacey

Borrelia burgdorferi Promotes the Establishment of Babesia microti in the Northeastern United States

Babesia microti and Borrelia burgdorferi, the respective causative agents of human babesiosis and Lyme disease, are maintained in their enzootic cycles by the blacklegged tick (Ixodes scapularis) and use the white-footed mouse (Peromyscus leucopus) as primary reservoir host. The geographic range of both pathogens has expanded in the United States, but the spread of babesiosis has lagged behind that of Lyme disease. Several studies have estimated the basic reproduction number (R 0) for B. microti to be below the threshold for persistence (<1), a finding that is inconsistent with the persistence and geographic expansion of this pathogen. We tested the hypothesis that host coinfection with B. burgdorferi increases the likelihood of B. microti transmission and establishment in new areas. We fed I. scapularis larva on P. leucopus mice that had been infected in the laboratory with B. microti and/or B. burgdorferi. We observed that coinfection in mice increases the frequency of B. microti infected ticks. To identify the ecological variables that would increase the probability of B. microti establishment in the field, we integrated our laboratory data with field data on tick burden and feeding activity in an R 0 model. Our model predicts that high prevalence of B. burgdorferi infected mice lowers the ecological threshold for B. microti establishment, especially at sites where larval burden on P. leucopus is lower and where larvae feed simultaneously or soon after nymphs infect mice, when most of the transmission enhancement due to coinfection occurs. Our studies suggest that B. burgdorferi contributes to the emergence and expansion of B. microti and provides a model to predict the ecological factors that are sufficient for emergence of B. microti in the wild.

Multi-scaling analysis of a logistic model with slowly varying coefficients

All single-species differential-equation population models incorporate parameters which define the model - for example, the rate constant, r, and carrying capacity, K, for the Logistic model. For constant parameter values, an exact solution may be found, giving the population as a function of time. However, for arbitrary time-varying parameters, exact solutions are rarely possible, and numerical solution techniques must be employed. In this work, we demonstrate that for a Logistic model in which the rate constant and carrying capacity both vary slowly with time, an analysis with multiple time scales leads to approximate closed form solutions that are explicit, are valid for a range of parameter values and compare favourably with numerically generated ones.

Optical properties of retinal photoreceptors and the Campbell effect

In 1958, Campbell observed that certain artificial pupil displacements could considerably change acuity (measured by viewing gratings) while others had very little effect. He sought an explanation of the small retinal contribution to those effects that was consistent with the Stiles-Crawford effect. This paper suggests an explanation that satisfies that requirement using a waveguide model of the retinal cones. We show that the waveguiding properties of the receptors make them sensitive to obliquely incident exciting waves and this provides some support for the hypothesis that both the Stiles-Crawford and Campbell effects are manifestations of the same underlying waveguide nature of the receptors.

A simple model for the establishment of tick-borne pathogens of Ixodes scapularis: A global sensitivity analysis of R0

The basic reproduction number of a pathogen, R0, determines whether a pathogen will spread (R0>1), when introduced into a fully susceptible population or fade out (R0<1), because infected hosts do not, on average, replace themselves. In this paper we develop a simple mechanistic model for the basic reproduction number for a group of tick-borne pathogens that wholly, or almost wholly, depend on horizontal transmission to and from vertebrate hosts. This group includes the causative agent of Lyme disease, Borrelia burgdorferi, and the causative agent of human babesiosis, Babesia microti, for which transmission between co-feeding ticks and vertical transmission from adult female ticks are both negligible. The model has only 19 parameters, all of which have a clear biological interpretation and can be estimated from laboratory or field data. The model takes into account the transmission efficiency from the vertebrate host as a function of the days since infection, in part because of the potential for this dynamic to interact with tick phenology, which is also included in the model. This sets the model apart from previous, similar models for R0 for tick-borne pathogens. We then define parameter ranges for the 19 parameters using estimates from the literature, as well as laboratory and field data, and perform a global sensitivity analysis of the model. This enables us to rank the importance of the parameters in terms of their contribution to the observed variation in R0. We conclude that the transmission efficiency from the vertebrate host to Ixodes scapularis ticks, the survival rate of Ixodes scapularis from fed larva to feeding nymph, and the fraction of nymphs finding a competent host, are the most influential factors for R0. This contrasts with other vector borne pathogens where it is usually the abundance of the vector or host, or the vector-to-host ratio, that determine conditions for emergence. These results are a step towards a better understanding of the geographical expansion of currently emerging horizontally transmitted tick-borne pathogens such as Babesia microti, as well as providing a firmer scientific basis for targeted use of acaricide or the application of wildlife vaccines that are currently in development.

Spatial-frequency response of a photoreceptor and its wavelength dependence. I. Coherent sources

The response of an isolated model foveal cone to a coherent sinusoidal intensity source is explored with use of the methods of photoreceptor optics. The dielectric waveguide model of a foveal cone that was previously used to explain the Stiles-Crawford effect and its wavelength dependence [Vision Res. 13, 1115 (1973)] is applied to photoreceptor excitation by coherent gratings with variable spatial frequency and light wavelength. The results indicate that the photoreceptors themselves contribute to visual acuity through a wavelength-dependent response at each spatial frequency. In particular, the isolated photoreceptor has a characteristic low-pass spatial-frequency-filter effect for wavelengths between 410 and 654 nm (where two waveguide modes are carried) and a flat response for wavelengths greater than 654 nm (the single-mode region).

Spatial-frequency response of a photoreceptor and its wavelength dependence. II. Partially coherent sources

The response of an isolated model foveal cone to a partially coherent sinusoidal intensity source is explored with the methods of photoreceptor optics. This extends the work with coherent sinusoidal intensity sources reported in part one [J. Opt. Soc. Am. A11, 1193 (1994)]. The dielectric waveguide model of a foveal cone previously used to discuss the origin of the Stiles–Crawford effect and its wavelength dependence is applied to photoreceptor excitation by a partially coherent sinusoidal intensity source with variable spatial frequency and light wavelength. The results indicate that the photoreceptors themselves contribute to visual acuity through a wavelength-dependent response at each spatial frequency and that the response is dependent on the spatial coherence of the source. In particular the isolated photoreceptor has a characteristic low-pass-spatial-frequency filter effect for wavelengths between 410 nm and 654 nm (where two waveguide modes are carried). The coherent and the incoherent response curves are separated by differing amounts depending on the wavelength of the light. For wavelengths greater than 654 nm (the single-mode region) the incoherent curve also has the shape of a characteristic low-pass-spatial-frequency filter, while the coherent curve shows a flat response. The results are used to discuss human eye modulation-transfer-function measurements.

Action research to improve methods of delivery and feedback in an Access Grid Room environment

This article describes a qualitative study which was undertaken to improve the delivery methods and feedback opportunity in honours mathematics lectures which are delivered through Access Grid Rooms. Access Grid Rooms are facilities that provide two-way video and audio interactivity across multiple sites, with the inclusion of smart boards. The principal aim was to improve the student learning experience, given the new environment. The specific aspects of the course delivery that the study focused on included presentation of materials and provision of opportunities for interaction between the students and between students and lecturers. The practical considerations in the delivery of distance learning are well documented in the literature, and similar problems arise in the Access Grid Room environment; in particular, those of limited access to face-to-face interaction and the reduction in peer support. The nature of the Access Grid Room classes implies that students studying the same course can be physically situated in different cities, and possibly in different countries. When studying, it is important that students have opportunity to discuss new concepts with others; particularly their peers and their lecturer. The Access Grid Room environment also presents new challenges for the lecturer, who must learn new skills in the delivery of materials. The unique nature of Access Grid Room technology offers unprecedented opportunity for effective course delivery and positive outcomes for students, and was developed in response to a need to be able to interact with complex data, other students and the instructor, in real-time, at a distance and from multiple sites. This is a relatively new technology and as yet there has been little or no studies specifically addressing the use and misuse of the technology. The study found that the correct placement of cameras and the use of printed material and smart boards were all crucial to the student experience. In addition, the inclusion of special tutorial type sessions were necessary to provide opportunities to students for one-on-one discussion with both lecturer and other students. This study contributes to the broader understanding of distance education in general and future Access Grid Room course delivery in particular.