Modelling and Simulation Fundamentals

Lecturer:

Tutor:

Supervisor:

Department of Biomedical Technology

Synopsis:

Basic notions and principles of system modelling generally. Theoretical and applied analysis of qualities of models representing various medical, biochemical, epidemiological, ecological, and biological systems. Population modelling. Epidemiological models. Models of pharmacokinetics.

Requirements:

Assessment: sufficient participation in exercises (75%) and an oral presentation of a selected model

Examination: written - required at least 50 points of 100

Syllabus of lectures:

1Basic notions of modelling and simulation. General techniques. Procedure of model creation and of simulation experiments. [1], pp. 3-10

2Biological systems and their properties. Experiments with biological systems. Models and their description. [1], pp. 11-21

3Matematical model. Formal description of a system. Equations as models. [1], pp. 22-23

4Compartment models. [1], pp. 24-31

5Single species population models. Continuous models (Malhus´s, logistic), continuos models with delay. [1], pp. 32-45

6Single species population models - discrete models. Discrete models with delay. [1], pp. 46-61

7Two-species population models. Predator-prey model [1], pp. 62-73

8Two-species population models. Competition models. Cooperating populations model (symbiosis) [1], pp. 74-79

9Epidemiological models. Basicí ckoncept. Models SIR, SI, SIS, SEIR [1], pp. 80-90

10Veneric diseases dynamics models. [1], pp. 91-95

11Modalké modelling of pharmacokinetics. [1], pp. 102-104

12Distribution of metabolites in an organism. General model of pharmaceuticals effects. [1], pp. 105-115

13Parameters identification. Criterial function, optimization algorithms. [1], pp. 116-129

14Reserve

Syllabus of tutorials:

1Deriving of medelling laws from generally known models.

2Experiment planning. Forrester´s model of the world. Relations between the government and people. Synthesis and deckomposition.

3Examples of simple mathematical models from veryday life.

4Drug secretion. Food intake system. Iodine distribution in mammal organisms.

5Examples of models based on the logistic function.

6Age-structured population models (Leslie´s model)

7Practical examples (dynamics of predator-prey population dynamics)

8Predator-prey models with delay.

9Flu epidemic in an English boy´s boarding school; plague epidemic in Bombay

10AIDS development model for a homosexual population

11Some simple problems of drug distribution.

12Pharmacokinetics models examples.

13Special software for modelling and simulations

14Reserve

Study Objective:

To show students the methodology how to develop models of selected biological systems.

Study materials:

Basic:

[1] Jiří Holčík: Modelování a simulace biologických systémů, Nakladatelství ČVUT, Praha, 2006, 133 str., ISBN 80-01-03470-4

Supplementary:

[2] J. Mazumdar: An Introduction to Mathematical Physiology and Biology, Second

Edition, Cambridge University Press, 1999, ISBN 978-0-521-64675-8

[3] Vincent C. Rideout, Mathematical and Computer Modeling of Physiological Systems, Prentice-Hall, 1991, ISBN 978-0135633540

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans:

• Navazující magisterský studijní obor Systémová integrace procesů ve zdravotnictví - prezenční (compulsory elective course)