Modelling & Simulation

Lecturer:

Marcel Jiřina (gar.), Jiří Potůček

Tutor:

Petr Hošek, Jiří Potůček

Supervisor:

Department of Biomedical Informatics

Synopsis:

Modelling and simulation - fundamentals. Compartmental models. Models of population dynamics - single species population, interacting population, continuous models, discrete models.

Models with age distribution. Epidemic models - model of SIR structure, criss-cross models, models of venereal diseases.

Requirements:

participation in the exercises (max. 5 points),

processing of 2 separate tasks (max. 20 points),

examination - examples, Prof. Jiřina (maximum 50 points)

examination - theoretical questions, Ing. Potůček (max 25 points).

Syllabus of lectures:

1. Modelling and simulation - fundamentals. Aims and consequences of modelling and simulation. Parameter identification. Experiments.

2. Objective reality, dynamical system. Models and their description. Formal and informal description.

3. Equilibrium states and their stability. Compartmental models and their mathematical description.

4. Design of compartmental models. Examples of compartmental model applications in biology and medicine.

5. Continuous models of single-species population. Mathus model and its analysis.

6. Continuous logistic model with contant and variable parameters, analysis of their solutions.

7. Continuous logistic model with catching. Continuous models of single species with delay and their analysis.

8. Discrete models of single-species population and their analysis. Graphical solution of the diference equation. Deterministic chaos. Atractor.

9. Disrete models of single-species population with delay. Models with age structure - Leslie model. Models of interacting populations. Predator-prey model and its analysis.

10. Kolmogorov model. Model predator-prey with delay. Model of competition. Model of symbiosis.

11. Epidemic models. Model SIR. Kermack-McKendrick model and its analysis. Condition infection speadin, estimation of maximum number of infectives, estimation of number of victims.

12. SI ans SIS models and their analysis. Model SIR with mediators and vaccination. Models SEIR ans their analysis.

13. Modelling veneral diseases - criss-cross model and its analysis. Model of AIDS.

14. Model of phyrmacokinetics.

Syllabus of tutorials:

1. MATLAB - Simulink. Introduction to programing in Simulink. Demonstration of graphical programing.

2. Methodology of design and analysis of mathematical models. Model of blood glukose regulation.

3. Compartmental models - principle and model design. Model of food-intake control.

4. Compartmental models - models with variable parameters (continuous and discrete), analysis of stability.

5. Models for single species - continuous Mathus model, analysis, experiments with model parameters in MATLAB-Simulink.

6. Models for single species - continuous logistic model, analysis, experiments with model parameters in MATLAB-Simulink.

7. Implementation of delay into the single species model in MATLAB-Simulink.

8. Discrete models for single-species populations (Malthus and logistic models), simulation and analysis in Simulink.

9. Discrete model of single-species population with age distribution - Leslie model, simulation and analysis in Simulink.

10. Models of interacting populations. Predator-prey model, design, simulation and analysis in Simulink.

11. Models of interacting populations. Predator-prey model with delay. Design, simulation and analysis in Simulink. Analysis of equilibrium states and their stability.

12. Epidemic models. SIR model, design of the structure, simulation in Simulink, analysis of model behaviour. SIR model with mediators and vaccination.

13. Model sof generál diseases (criss-cross model), model of AIDS spreading. Model structure design and simulation in Simulink, analysis.

14. Identification of SIR model parameters by means of Newton?s method.

Study Objective:

To provide students with capability to design simple mathematical models of real biological systems and to theoretically analyse their properties, to implement the designed models in MATLAB and/or SIMULINK, to do basic simulation experiments and to assess results of the experiments.

Study materials:

1]Murray, J.D.: Mathematical Biology. Berlin, Springer Verlag 1993.,

[2]Carson,E., Cobelli,C.: Modelling Methodology for Physiology and Medicine. S.Diego, AP 2001

Note:

Time-table for winter semester 2011/2012:

Time-table is not available yet

Time-table for summer semester 2011/2012:

	06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00
Mon
Tue	roomKL:C-4 Jiřina M. 16:00–17:50 (lecture parallel1) Kladno FBMI Malý sál
Fri	roomKL:B-501 Hošek P. 12:00–13:50 (lecture parallel1 parallel nr.1) Kladno FBMI Počítačová učebna BMIroomKL:B-316 Hošek P. 14:00–15:50 (lecture parallel1 parallel nr.2) Kladno FBMI Počítačová učebna
Thu
Fri

The course is a part of the following study plans:

• Bakalářský studijní obor Biomedicínská informatika - prezenční (compulsory course)
• Bakalářský studijní obor Biomedicínská informatika - prezenční (compulsory course)