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Lecturer(s)
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Revilla Rimbach Tomas Augusto, Ph.D.
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Course content
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Contents of lectures: 1. Dynamical Systems: Discrete and continuous time. Equilibrium, cycles and chaos. 2. Models of Structured Populations: basic reproductive ratio, (st)age-structure, etc. 3. Models of Interactions: Lotka-Volterra models, local stability, graphical analysis. 4. Stochastic Models: birth-death processes, environmental and demographic stochasticity. 5. Infectious Disease Modeling: SIR models, within-host dynamics, immune system. 6. Biochemistry: chemical kinetics, pharmacodynamics, enzymes. 7. Physiology: Hodgkin-Huxley and Fitzhugh-Nagumo models of nerve impulse. 8. Genetics and Natural Selection: Hardy-Weinberg law, mutations, selection dynamics. 9. Conflict and cooperation: game theory, evolutionary stable strategy, kin selection. 10. Networks: gene and neural networks, food webs. Topology and robustness. 11. Spatio-Temporal Dynamics: morphogenesis, tumor dynamics, metapopulations. Content of practicals: 1. Quantitative and qualitative methods 2. Graphical methods 3. Computer simulations (Matlab/Octave, R)
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Learning activities and teaching methods
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Monologic (reading, lecture, briefing), Dialogic (discussion, interview, brainstorming), Work with multi-media resources (texts, internet, IT technologies)
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Learning outcomes
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Introduce mathematical modelling of biological phenomena. The scope comprises various levels of organization, from molecular and physiological, to populations and ecosystems. Emphasis on dynamical processes in discrete or continuous time, and the application of qualitative and computational methods.
Student gets an overview of models used in biology, will be able to formulate, analyze, and interpret them.
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Prerequisites
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Basic knowledge of calculus and probability.
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Assessment methods and criteria
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Student performance assessment, Combined exam, Interim evaluation
Tutorials: 5 tests of 20 points each; student must score 50 points minimum. Exam: individual homework project
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Recommended literature
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Allman, Elizabeth Spencer; Rhodes, John Anthony. Mathematical models in biology : an introduction. 1st ed. Cambridge : Cambridge University Press, 2004. ISBN 0-521-52586-1.
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Bacaër, Nicolas. A Short History of Mathematical Population Dynamics. Springer London, 2011.
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Batschelet, Edward. Introduction to mathematics for life scientists. 3rd ed. Berlin : Springer, 1979. ISBN 3-540-09648-5.
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Bodine, Lenhart&Gross. Mathematics for the Life Sciences. 2014.
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Edelstein-Keshet, Leah. Mathematical models in biology. 1st ed. Boston, MA : McGraw-Hill, 1988. ISBN 0-07-554950-6.
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