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Mathematics and Statistics Group

Seminar Programme: Winter/Spring 2017 - ALL WELCOME

All seminars take place on Tuesdays at 3pm in the Cottrell Building, room 4B96 (Except where stated otherwise).

For further details please contact:

Date Speaker Title
7 Feb
Prof Andy White
‌School of Mathematical and Computer Sciences
Heriot Watt University
Mathematical Modelling Tools for Red Squirrel Conservation
Since its introduction into the UK, c1900, the grey squirrel has replaced the native red squirrel throughout most of England and Wales, and in parts of Scotland and Ireland. There is strong evidence that grey squirrels are superior competitors in many habitats and also that a shared virus, squirrelpox, plays a critical role in red squirrel decline. ODE and PDE frameworks, parameterised to represent the red/grey/squirrelpox system, will be examined to understand the impact of squirrelpox on red and grey squirrel population dynamics and the spread of squirrelpox following grey invasion. Squirrelpox is endemic in grey populations in England and Wales but has only recently been reported in Southern Scotland. A spatial, individual based version of the model will be outlined and used to assess the spread of squirrelpox through squirrel populations in Southern Scotland. These findings are being used to inform current red squirrel conservation policy.
21 Feb
Dr Joe Collis
‌School of Mathematical Sciences
University of Nottingham
Bayesian calibration, validation and uncertainty quantification for predictive modelling of tumour growth
Over recent years the fields of validation, verification and uncertainty quantification (VVUQ) have become vitally important in the predictive modelling of complex physical systems for safety critical engineering applications. In order for computational model outputs to be viewed as sufficiently reliable for application to the clinic (in particular predictive therapy planning), it is natural to suppose that parametric and structural uncertainties must be quantified, as they are for predictive models of other safety critical phenomena. In this talk, we consider the calibration and validation of an uncertain, Gompertzian model of tumour growth through a pedagogical example. In this example, we introduce, and subsequently apply, VVUQ techniques not commonly employed in the field of continuum mechanical cancer modelling to in vitro experimental data. Finally, we highlight some of the mathematical and computational challenges involved in the development of patient specific computational models of tumour growth and response to therapy.
28th Feb
Dr Morag Macpherson
Computing Science and Mathematics
University of Stirling
(joint work with Adam Kleczkowski, Ben White and Nick Hanley)
A bioeconomic model of precautionary and reactive control of an invasive species incursion
Invasive species are a threat to forests worldwide. With the frequency of invasions likely to increase, a key policy question is how to reduce their, potentially irreversible, impact on the environment. Traditionally management practices of invasive species are reactive (e.g. felling or spraying); however recently there has been a shift to developing precautionary practices (e.g. border control). Precautionary practices decrease the rate of an invasive species arriving, which subsequently may reduce – or even mitigate – future market and non-market losses. We are interested in understanding how the availability of a reactive strategy alters the optimal level of precautionary control. To address this, we create a novel generalisable, bioeconomic model to examine under what economic and epidemiological conditions it is optimal to deploy precautionary control to a forest so that the losses associated with the invasion are minimised. We show, using policy plots, that the optimal level of precautionary control is sensitive to the primary and secondary rate of invasion and the damage (loss) caused by the invasion: an increase in time of invasion arrival, spread of invasion, and damage, increases the optimal level of precautionary control, when a reactive strategy is not available. However, when a reactive strategy is available, it becomes optimal to not deploy precautionary control for high rates of primary and secondary invasion, and instead deploy the reactive strategy after the invasion is detected. This highlights the importance of considering how reactive and precautionary management strategies can be used together so as to minimise the effect of invasive species on forests. Our model can easily be generalised to describe control of invasive species.
21st Mar
Iona Paterson
Computing Science and Mathematics
University of Stirling
Optimising antibiotic dosage regimens to treat bacterial infections
For too long have antibiotic dosage regimes against bacterial infections followed the traditional approach of a giving a fixed dose X per day for N days. With the rise of antibiotic resistance, the need to find better, more efficient strategies is essential. Here we combine mathematical modelling of a bacterial infection (including resistance), with genetic algorithms from computational optimisation, to find optimal dosage regimes. These regimes improve the treatment success while also minimising total antibiotic usage.
2nd May
Dr Alan Terry
School of Science and Sport
University of the West of Scotland
Predator–prey models with component Allee effect for predator reproduction
We present four predator-prey models with component Allee effect for predator reproduction. Using numerical simulation results for our models, we describe how the customary definitions of component and demographic Allee effects, which work well for single species models, can be extended to predators in predator-prey models by assuming that the prey population is held fixed. We also find that when the prey population is not held fixed, then these customary definitions may lead to conceptual problems. After this discussion of definitions, we explore our four models, analytically and numerically. Each of our models has a fixed point that represents predator extinction, which is always locally stable. We prove that the predator will always die out either if the initial predator population is sufficiently small or if the initial prey population is sufficiently small. Through numerical simulations,we explore co-existence fixed points. In addition, we demonstrate, by simulation, the existence of a stable limit cycle in one of our models. Finally, we derive analytical conditions for a co-existence trapping region in three of our models, and show that the fourth model cannot possess a particular kind of co-existence trapping region. We punctuate our results with comments on their real-world implications; in particular, we mention the possibility of prey resurgence from mortality events, and the possibility of failure in a biological pest control program.

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