Mathematical modelling in biology and medicine

General data

Course ID:	1100-5FM12
Erasmus code / ISCED:	(unknown) / (unknown)
Course title:	Mathematical modelling in biology and medicine
Name in Polish:	Modelowanie matematyczne procesów w biologii i medycynie
Organizational unit:	Faculty of Physics
Course groups:	(in Polish) ZFBM, II stopień; Fizyka medyczna
Course homepage:	http://www.fuw.edu.pl/~jarekz/MODELOWANIE/Modelowanie.html
ECTS credit allocation (and other scores):	(not available) Basic information on ECTS credits allocation principles: the annual hourly workload of the student’s work required to achieve the expected learning outcomes for a given stage is 1500-1800h, corresponding to 60 ECTS; the student’s weekly hourly workload is 45 h; 1 ECTS point corresponds to 25-30 hours of student work needed to achieve the assumed learning outcomes; weekly student workload necessary to achieve the assumed learning outcomes allows to obtain 1.5 ECTS; work required to pass the course, which has been assigned 3 ECTS, constitutes 10% of the semester student load. view allocation of credits
Language:	Polish
Prerequisites (description):	Student can: - anayze functions - solve ordinary differential equations - solve simple diference equations Student can use Matlab for: - writting own scipts and functions - plot functions Suggested courses: mathematical analysis II, numerical methods, course Matlab 1103-217
Mode:	Classroom
Short description:	The lecture prepares to constructing and analyzing mathematical models relevant for problems encountered in biology, ecology, medicine and neuroscience
Full description:	The subject consists of lecture and exercises. The lecture prepares to constructing and analyzing mathematical models relevant for problems encountered in biology, ecology, medicine and neuroscience. Syllabus: 1) Models in biology. 2) Elements of qualitative theory of spatially homogenous differential equations (fixed points, bifurcations, limit cycles, phase portrait) 3) Discrete and continuous models of populations growth and interactions. 4) Kinetics of chemical reaction with enzymes. 5) Biologically realistic modeling of neurons : a) Compartmental modeling of neurons: Hodgkin-Huxley model, Fitzhugh-Nagumo model, Integrate and fire, leaky integrator model, b) Lumped models of neural populations: Wilson and Cowana model, Freeman model 6) Elements of qualitative theory of spatially inhomogeneous differential equations: a) Model of infection spread b) Model of tumor growth The exercises are devoted to the analysis of selected models, both analitically and numericaly.
Bibliography:	1. Murray, James Dickson Mathematical biology. Berlin : Springer, cop. 1989. 2. Černavskij, Dmitrij Sergeevič. Modelowanie matematyczne w biofizyce [translated by. Ewa Skrzypczak]. Warszawa: Państ. Wydaw. Naukowe, 1979. 3. Lecture scripts and examples: http://brain.fuw.edu.pl/~jarek/MODELOWANIE/Modelowanie.html .
Learning outcomes:	Student can: - identify popular models used in biology and medicine - discuss qualitative behavior of discrete and continuous models of one or two dimensions spatially homogeneous - illustrates numerically behavior of discrete and continuous models
Assessment methods and assessment criteria:	Written exam

This course is not currently offered.

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Copyright by University of Warsaw.