Mathematical modelling in biology and medicine 1100-5FM12

http://www.fuw.edu.pl/~jarekz/MODELOWANIE/Modelowanie.html

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.

Mode

Classroom

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

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 criteria

Written exam

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 .

Additional information

Information on level of this course, year of study and semester when the course unit is delivered, types and amount of class hours - can be found in course structure diagrams of apropriate study programmes. This course is related to the following study programmes:

Applications of Physics in Biology and Medicine, second cycle programme

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1100-5FM12 in USOSweb