Course detail

Models in Biology and Epidemiology

FEKT-BPC-MBEAcad. year: 2024/2025

The course is dedicated to the modeling of biological systems. Students gain theoretical knowledge in the field of modeling terminology, classification of biological systems, modeling objectives, identification of model parameters and methods of its description. Students will gain practical skills in the design of a mathematical model, its analysis, practical implementation in MATLAB and Simulink and model simulation.

Language of instruction

Czech

Number of ECTS credits

4

Mode of study

Not applicable.

Guarantor

Ing. Martin Vítek, Ph.D.

Department

Department of Biomedical Engineering (UBMI)

Entry knowledge

The student who enters the course should be able to:
• Analyze simple electrical circuits using Ohm's law and Kirchhoff's laws
• Find the analytical solutions of simple differential equations
• Solve the system of equations using matrices
• Create a simple program in MATLAB that contains loops, conditions, and mathematical equations

Rules for evaluation and completion of the course

Computer exercises: 25 points - solving tasks during the exercise, the minimum for the credit and admission to the final examination is to obtain at least 10 points
Final exam: 75 points - exam is written and consists of three parts with 25 points each. The first part verifies the general theoretical knowledge of biological systems modeling, the second part verifies the theoretical knowledge and practical skills in the field of population models and the third part verifies the theoretical knowledge and practical skills in modeling of the human body systems.
For successful completion of the course, it is necessary to obtain from the written exam at least 35 points and in a total at least 50 points.

Computer exercises are compulsory, properly excused exercises absences can be substitute at another time after consultation with the teacher.

Aims

The aim of the course is to provide students the basic knowledge and skills in design of mathematical models of biological systems, their analysis, computer implementation and subsequent simulation.
The graduate of the course:
• Is able to identify the basic elements, links and state variables of biological systems
• Can describe the activity of biological systém using set of equations
• Can solve the system of differential equations using Euler's method and Runge-Kutta methods
• Is able to analyze the stability of equilibrium states of the model using the Jacobi matrix
• Can construct an implementation scheme of a model from the system of equations
• Can construct a system of equations from the model implementation scheme
• Is able to implement a computer model in MATLAB and Simulink
• Is able to simulate a computer model in MATLAB and Simulink
• Is able to discuss the results of a computer model simulation

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Holčík, J., Fojt, O.: Modelování biologických systémů (Vybrané kapitoly), skripta VUT v Brně, 2001. (CS)
JIŘÍK,R.: Modely v biologii a epidemiologii. El. skripta VUT v Brně, 2006. (CS)

Recommended reading

Pazourek,J.: Simulace biologických systémů. GRADA, Praha 1992. (CS)
V. Eck, M. Razím, Biokybernetika, skripta ČVUT v Praze, 1998. (CS)

Classification of course in study plans

  • Programme BPC-BTB Bachelor's 3 year of study, summer semester, compulsory

Type of course unit

 

Lecture

26 hod., optionally

Teacher / Lecturer

Ing. Martin Vítek, Ph.D.

Syllabus

1. Modelling and simulation - fundamental terms, classification of models
2. Modelling and simulation - identification of model parameters, ways of describing the model
3. Mathematical and computer models - analysis of the mathematical model, computer models and simulations
4. Models of single species populations - continuous: Malthus, Pearl-Verhulst and Hutchinson
5. Models of single species populations - discrete: Malthus, Pearl-Verhulst, Hutchinson and Leslie
6. Models of two species populations - predator-prey: Lotka-Volterra and Kolmogorov
7. Models of two species populations - competitive and mutualistic populations
8. Models of cardiovascular system - hemodynamic parameters, Windkessel models
9. Models of action potential impulse - Hodgkin-Huxley model
10. Models of respiratory system - mechanical ventilatory
12. Pharmacokinetical models - compartment model of diffusion, pharmacokinetic parameters, single compartment models
12. Pharmacokinetical models - two compartment models and three compartment models
13. Epidemiological models - models SIR, SEIR, SI a SIS

Exercise in computer lab

13 hod., compulsory

Teacher / Lecturer

Ing. Martin Mézl, Ph.D.
MUDr.Ing. Richard Ředina

Syllabus

1. Modelling and simulation
2. Models of single species populations
3. Models of two species populations
4. Models of cardiovascular system
5. Pharmacokinetical models
6. Epidemiological models