Special Topics in Software Engineering:

Mathematical Modelling and Simulation of Biological Systems

The aim of the course is to introduce students to application of ordinary differential equations, partial differential equations, partial functional differential equations and optimal control theory to model problems arising in biology and simulation of these mathematical models.

Students should be able to derive mathematical model of biological system and its simulation using Mathlab & Simulink.

Lecturer

Prof. Dr. Tibor Kmet, Constantine the Philosopher University, Slovakia
tkmet@ukf.sk

Dates

Contents

Topics will be chosen from the following list

• ordinary differential equations,
• partial differential equations,
• partial functional differential equations and optimal controltheory,
• steady state and fixed points,
• stability,
• numerical solution,
• creating a mathematical
• model,
• modelling and simulating dynamical systems,
• running simulation.

Exam

Students have to do a project (i.e. to develop a mathematical model of realistic biological system, stability analysis, application of optimal control problem and simulation of the mathematical model using Mathlab & Simulink)

Downloads

• Workbook.pdf
• ComplexModel2.pdf
• Complex.Model1.pdf

Software: Mathlab & Simulink

Literature:

1. D. J. Higham, N. J. Higham: Matlab Guide, SIAM, 2000.
2. Mathlab & Simulink Guide, The MathWorks, Inc. 2004
3. F. Brauer, C. Castillo-Cháves : Mathematical Models in population Biology and Epidemology, Springer, 2000.
4. P. Fishwick: Dynamic Modeling, SCS, 2002
5. J. Wu: Theory and applications of partial functional differential equations, Springer, Applied Math. Sciences, 1996