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Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area, particularly models involving only two or three coupled differential equations. These models were amenable to students as well as interesting and relevant to students because they came from real research papers. I will describe the use of scenarios and case studies in lectures, and group projects for assessment. The scenarios and case studies were published in a textbook that I wrote. Scenarios, case studies and projects provided an opportunity to expose students to some novel applications of differential equations. One example is developed here as a Classroom Note: modelling the dynastic cycles in Chinese history. [ABSTRACT FROM AUTHOR]

This paper investigates the deposition of the tear film on the cornea of the human eye. The tear film is laid down by the motion of the upper eyelid and then subsequently flows and thins. Of particular interest is the stability of the tear layer and the development of dry patches on the cornea. While there has been significant research on the behaviour of tear films between blinks, this paper focuses on understanding the mechanisms which control the shape and thickness of the deposited film and how this affects the subsequent film behaviour. Numerical and analytical methods are applied to a lubrication model which includes the effects of surface tension, viscosity, gravity and evaporation. The model reveals the importance of the eyelid velocity, motion of the surface lipid layer and the storage of tear film between blinks. [ABSTRACT FROM AUTHOR]

An SEI metapopulation model is developed for the spread of an infectious agent by migration. The model portrays two age classes on a number of patches connected by migration routes which are used as host animals mature. A feature of this model is that the basic reproduction ratio may be computed directly, using a scheme that separates topography, demography, and epidemiology. We also provide formulas for individual patch basic reproduction numbers and discuss their connection with the basic reproduction ratio for the system. The model is applied to the problem of spatial spread of bovine tuberculosis in a possum population. The temporal dynamics of infection are investigated for some generic networks of migration links, and the basic reproduction ratio is computed—its value is not greatly different from that for a homogeneous model. Three scenarios are considered for the control of bovine tuberculosis in possums where the spatial aspect is shown to be crucial for the design of disease management operations. [Copyright &y& Elsevier]

Line distributions of Stokes flow singularities are used to model the flow around a slender body which is straddling a flat interface between two viscous fluids. Motion of the slender body parallel to the interface and normal to the interface is considered where the axis of symmetry of the slender body is always perpendicular to the undisturbed interface. Asymptotic approximations to the force distributions on the slender body are evaluated and the relative contributions of that part of the slender body in one fluid to the force distribution in the other fluid and of the interface interaction to the force distribution are examined. It is observed that a shielding region exists about the interface which is due to the interaction with that part of the slender body in the other fluid. Finally, for parallel motion, the first order interface deformation is calculated. [ABSTRACT FROM PUBLISHER]