| CODE | MAT3755 | ||||||||
| TITLE | Advanced Mathematical Modeling in Biology | ||||||||
| UM LEVEL | 03 - Years 2, 3, 4 in Modular Undergraduate Course | ||||||||
| MQF LEVEL | 6 | ||||||||
| ECTS CREDITS | 5 | ||||||||
| DEPARTMENT | Mathematics | ||||||||
| DESCRIPTION | Mathematical Biology is a fast growing, well-recognized subject and one of the most exciting modern application of mathematics. The increasing use of mathematics in biology is inevitable as biology becomes more quantitative. This study-unit is focused on the development and analysis of advanced mathematical models which could be used to unravel the underlying mechanisms involved in biological processes. Through the specimen models discussed, students will be in a position to tackle the modelling of genuinely practical problems with realism. The study unit will cover: - Biological motion: macroscopic theory of motion, directed motion, steady state equations and transit times, biological invasions, travelling wave solutions of general reaction-diffusion equations, spatial spead of epidemics; - Molecular and cellular biology: neural modelling, immunology and AIDS; - Pattern formation: Turing instability and biffurcations, activator-inhibitor systems, biffurcations with domain size, mechanochemical models, morphogenesis; - Tumour modelling: phenomenological models, nutrients and the diffusion-limited stage, moving boundary problems, growth promoters and inhibators, vascularisation, metastasis, immune system response. Study-unit Aims: The aim of this study-unit is to provide a toolkit of advanced modelling techniques with numerous examples drawn from population and developmental ecology, evolution, epidemiology and other areas. Students will acquire a practical and realistic view of biological modelling as well as developing advanced mathematical techniques (applications of analytic and numerical methods for partial differential equations and ordinary differential equations, spectral theory, stochastic processes, Perron-Frobenius theory, etc.) needed to get approximative quantitative solutions and will thereby realise the importance of relating the models and the results to the real biological problems under study. Learning Outcomes: 1. Knowledge & Understanding: By the end of the study-unit the student will be able to: - Demonstrate understanding and knowledge of the nature and setup of realistic mathematical representations of important biological phenomena; - Interpret the mathematical results in terms of insights and predictions in a biological context. 2. Skills: By the end of the study-unit the student will be able to:# - Use ordinary and partial differential equations to model biological motion, spatial spread of epidemics, immunologic mechanisms, morphogenesis and tumours; - Select, explain and apply quantitative and qualitative techniques to analyse these models and evaluate critically their accuracy and appropriateness; - Use other mathematical techniques (numerical methods, stochastic approaches, etc.) to answer problems that arise in Biology; - Demonstrate enhanced transferable/professional skills such as problem solving, information technology, self-management and learning. Main Text/s and any supplementary readings: - N. F. Britton: Essential Mathematical Biology (Springer undergraduate mathematics series), Springer-Verlag London Limited, 2003. - D. S. Jones and B. D. Sleeman: Differential Equations and Mathematical Biology (Chapman & Hall/CRC mathematical biology and medicine series), Chapman and Hall/CRC, 2003. - R. B.Hoyle: Pattern formation: an introduction to methods, Cambridge: Cambridge University, 2006. - J. DiStefano III: Dynamic Systems Biology Modeling and Simulation, Academic Press, 2015. |
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| ADDITIONAL NOTES | Follows from: MAT3750, MAT3715 | ||||||||
| STUDY-UNIT TYPE | Lecture and Independent Study | ||||||||
| METHOD OF ASSESSMENT |
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| LECTURER/S | Cristiana Sebu |
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The University makes every effort to ensure that the published Courses Plans, Programmes of Study and Study-Unit information are complete and up-to-date at the time of publication. The University reserves the right to make changes in case errors are detected after publication.
The availability of optional units may be subject to timetabling constraints. Units not attracting a sufficient number of registrations may be withdrawn without notice. It should be noted that all the information in the description above applies to study-units available during the academic year 2023/4. It may be subject to change in subsequent years. |
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