A systematic review of mathematical models of mosquito-borne pathogen transmission: 1970-2010

Mathematical models of mosquito-borne pathogen transmission originated in the early twentieth century to provide insights into how to most effectively combat malaria. The foundations of the Ross–Macdonald theory were established by 1970. Since then, there has been a growing interest in reducing the public health burden of mosquito-borne pathogens and an expanding use of models to guide their control. To assess how theory has changed to confront evolving public health challenges, we compiled a bibliography of 325 publications from 1970 through 2010 that included at least one mathematical model of mosquito-borne pathogen transmission and then used a 79-part questionnaire to classify each of 388 associated models according to its biological assumptions. As a composite measure to interpret the multidimensional results of our survey, we assigned a numerical value to each model that measured its similarity to 15 core assumptions of the Ross–Macdonald model. Although the analysis illustrated a growing acknowledgement of geographical, ecological and epidemiological complexities in modelling transmission, most models during the past 40 years closely resemble the Ross–Macdonald model. Modern theory would benefit from an expansion around the concepts of heterogeneous mosquito biting, poorly mixed mosquito-host encounters, spatial heterogeneity and temporal variation in the transmission process.

Recasting the theory of mosquito-borne pathogen transmission dynamics and control

Mosquito-borne diseases pose some of the greatest challenges in public health, especially in tropical and sub-tropical regions of theworld. Efforts to control these diseases have been underpinned by a theoretical framework developed for malaria by Ross and Macdonald, including models, metrics for measuring transmission, and theory of control that identifies key vulnerabilities in the transmission cycle. That framework, especially Macdonald’s formula for R0 and its entomological derivative, vectorial capacity, are nowused to study dynamics and design interventions for many mosquito-borne diseases. A systematic review of 388 models published between 1970 and 2010 found that the vast majority adopted the Ross–Macdonald assumption of homogeneous transmission in a well-mixed population. Studies comparing models and data question these assumptions and point to the capacity to model heterogeneous, focal transmission as the most important but relatively unexplored component in current theory. Fine-scale heterogeneity causes transmission dynamics to be nonlinear, and poses problems for modeling, epidemiology and measurement. Novel mathematical approaches show how heterogeneity arises from the biology and the landscape on which the processes of mosquito biting and pathogen transmission unfold. Emerging theory focuses attention on the ecological and social context formosquito blood feeding, themovement of both hosts and mosquitoes, and the relevant spatial scales for measuring transmission and for modeling dynamics and control.

Scott A. Shane : winner of the Global Award for Entrepreneurship Research

Scott A. Shane is the 2009 winner of the Global Award for Entrepreneurship Research. In this article we discuss and analyze Shane’s most important contributions to the field of entrepreneurship. His contribution is extraordinarily broad in scope, which makes it difficult to pinpoint one or a few specifics that we associate with Shane’s scholarship. Instead, they can be summarized in the following three points. First, he has influenced what we view as central aspects of entrepreneurship. Shane has been a leading figure in redirecting the focus on entrepreneurship research itself. Second, he has influenced how we view entrepreneurship. Shane’s research is arguably theory driven and it applies and develops theoretical lenses that greatly improve our understanding of entrepreneurship. Third, he has contributed to how we conduct entrepreneurship research. Shane has been a forerunner in examining relevant units of analysis that are difficult to sample; research designs and databases specifically designed for studying entrepreneurial processes; and sophisticated analytical methods. This has contributed to advancing the methodological rigor of the field. Summing them up, the contributions are very impressive indeed.

Thomas Young's contribution to visual optics : the Bakerian lecture "On the mechanism of the eye"

Thomas Young (1773-1829) carried out major pioneering work in many different subjects. In 1800 he gave the Bakerian Lecture of the Royal Society on the topic of the “mechanism of the eye”: this was published in the following year (Young, 1801). Young used his own design of optometer to measure refraction and accommodation, and discovered his own astigmatism. He considered the different possible origins of accommodation and confirmed that it was due to change in shape of the lens rather than to change in shape of the cornea or an increase in axial length. However, the paper also dealt with many other aspects of visual and ophthalmic optics, such as biometric parameters, peripheral refraction, longitudinal chromatic aberration, depth-of-focus and instrument myopia. These aspects of the paper have previously received little attention. We now give detailed consideration to these and other less-familiar features of Young’s work and conclude that his studies remain relevant to many of the topics which currently engage visual scientists.

Modelling cell separation during plant organ abscission

A simple mathematical model is presented to describe the cell separation process that plants undertake in order to deliberately shed organs. The focus here is on modelling the production of the enzyme polygalacturonase, which breaks down pectin that provides natural cell-to-cell adhesion in the localised abscission zone. A coupled system of three ordinary differential equations is given for a single cell, and then extended to hold for a layer of cells in the abscission zone. Simple observations are made based on the results of this preliminary model and, furthermore, a number of opportunities for applied mathematicians to make contributions in this subject area are discussed.

Hydrodynamic and thruster model validation for autonomous underwater vehicles

From Pontryagin’s Maximum Principle to the Duke Kahanamoku Aquatic Complex; we develop the theory and generate implementable time efficient trajectories for a test-bed autonomous underwater vehicle (AUV). This paper is the beginning of the journey from theory to implementation. We begin by considering pure motion trajectories and move into a rectangular trajectory which is a concatenation of pure surge and pure sway. These trajectories are tested using our numerical model and demonstrated by our AUV in the pool. In this paper we demonstrate that the above motions are realizable through our method, and we gain confidence in our numerical model. We conclude that using our current techniques, implementation of time efficient trajectories is likely to succeed.

Bushfire sustainability : Strategies for reconciling bushfire and biodiversity with daily life

This exhibition and catalogue provides a visual record of student work exhibited at the Australian Institute of Architects offices in Brisbane from November 15 to 29, 2010. The exhibition features the final design outcomes of the inaugural Bushfire Sustainability unit conducted at QUT in semester two, 2010. The core objective of this unit was to develop our students’ skills in collaborative practice in design, research and presentation. The theme of ‘bushfire sustainability’ was chosen because living sustainably in bushfire prone landscapes presents a number of problems, the nature of which might only be resolved via multidisciplinary collaboration among the design disciplines. The students involved represent the disciplines of Interior Design, Landscape Architecture, Industrial Design, Architecture and Sustainability – all from within the School of Design at QUT. 55 students, mostly in their third year of study, worked in teams of five (one from each discipline) to design one of a number of homes in highly bushfire prone sites in either Western Australia or SE Queensland. This year level and the interdisciplinary mix are perhaps the best placed to resolve these problems: being unrestrained from the burdens of professional practice and technical overload they retain the potential for innovative, lateral thinking across the range of spatial scales and philosophical perspectives associated with inhabitation of bushfire prone landscapes. It is envisaged that, through the ‘vehicle’ of this design research, that the students’ work will contribute to understandings of how creative design disciplines might respond to this significant national problem, which hitherto has been attended to primarily by engineering and the sciences.

Review of Collaboration and Interdisciplinarity in the Republic of Letters : Essays in Honour of Richard G. Maber, edited by Paul Scott.

This volume brings together a number of essays that seek to explore the nature of early modern scholarship, ostensibly with special regard to the themes of interdisciplinarity and collaboration. As one might expect, the essays thus cover a gamut of topics – political manoeuvring, philosophical debates, gift-giving and dramatic performance – and each study is important and useful in its own right. As a whole, however, this collection serves more as a starting point for an exploration of its themes, than as an authoritative overview of the subject at hand.

Thomas Young’s contributions to geometrical optics

In addition to his work on physical optics, Thomas Young (1773-1829) made several contributions to geometrical optics, most of which received little recognition in his time or since. We describe and assess some of these contributions: Young’s construction (the basis for much of his geometric work), paraxial refraction equations, oblique astigmatism and field curvature, and gradient-index optics.

Thomas Young’s investigations in gradient-index optics

Purpose: James Clerk Maxwell is usually recognized as being the first, in 1854, to consider using inhomogeneous media in optical systems. However, some fifty years earlier Thomas Young, stimulated by his interest in the optics of the eye and accommodation, had already modeled some applications of gradient-index optics. These applications included using an axial gradient to provide spherical aberration-free optics and a spherical gradient to describe the optics of the atmosphere and the eye lens. We evaluated Young’s contributions. Method: We attempted to derive Young’s equations for axial and spherical refractive index gradients. Raytracing was used to confirm accuracy of formula. Results: We did not confirm Young’s equation for the axial gradient to provide aberration-free optics, but derived a slightly different equation. We confirmed the correctness of his equations for deviation of rays in a spherical gradient index and for the focal length of a lens with a nucleus of fixed index surrounded by a cortex of reducing index towards the edge. Young claimed that the equation for focal length applied to a lens with part of the constant index nucleus of the sphere removed, such that the loss of focal length was a quarter of the thickness removed, but this is not strictly correct. Conclusion: Young’s theoretical work in gradient-index optics received no acknowledgement from either his contemporaries or later authors. While his model of the eye lens is not an accurate physiological description of the human lens, with the index reducing least quickly at the edge, it represented a bold attempt to approximate the characteristics of the lens. Thomas Young’s work deserves wider recognition.