Course detail
Biological system modelling
FEKT-NMOBAcad. year: 2010/2011
Biological (medical and ecological) system, desriction of its properties. Planning experiments with biological systems. Theoretical approaches used for modelling biologcial systems (compartmental systems, deterministic chaos, fractals, theory of catastrophes, celular systems). Description of basic biological models - models of population dynamics, epidemiological and psychological models, models of biochemical processes, models of tissue structure, examples of basic models of human organism (cardiovascular system, endocrine system, etc.)
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Planned learning activities and teaching methods
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Aims
Specification of controlled education, way of implementation and compensation for absences
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Basic literature
Murray, J.D.:Mathematical Biology,Springer Verlag, Berlin 1989. (EN)
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Syllabus
Experiments with biological objects. Experiment planning and evaluation.
Continuous models of single species populations, Malthus equation, logistic equation, Hutchinson equation, possibilities for further modifications.
Discrete models of single species populations -Leslie's model, analogons of continuous models, deterministic chaos, delayed discrete models.
Models for interactive populations, predator-prey models, models for competitive and mutualistic populations, Kolmogorov model.
Multicompartmental analysis - principles, models of biochenical processes in human body.
Epidemiological models - SIR models and their analysis, models of veneral diseases, models of AIDS dynamics, geographical models of epidemies.
Discrete models of celular structures - celular automata. Artificial life. Spreading of excitation through tissues of living organisms, models of movement in multimember populations, analysis of celular automata.
Fractals, fundamental terms, principles. Basic fractal models. Morphological biological models - morphology of cardiovascular and respiratory systems.
Theory of catastrophes, fundamental vocabulary, principles. Definitions of basic catastrophes. Behavioral and psychological models.
Models of sybsystems of the human body - cardiovascular system (blood pressure, model of systemic circulation, Windkessel models).
Neurokardiovascular system - models of heart rate variability, baroreflex models. Regulation of gastric acidity regulation.
Models of blood glucose regulation - physiological background, regulation by kidney, regulation by insuline, regulation by glucagon.
Exercise in computer lab
Teacher / Lecturer
Syllabus
Continuous model of single species populations
Discrete models of single species populations, Leslie's model
Discrete logistic equation and deterministic chaos
Predator-prey models
Epidemic models