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
Number of ECTS credits
Mode of study
Guarantor
Entry knowledge
• 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
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 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
Prerequisites and corequisites
Basic literature
JIŘÍK,R.: Modely v biologii a epidemiologii. El. skripta VUT v Brně, 2006. (CS)
Recommended reading
V. Eck, M. Razím, Biokybernetika, skripta ČVUT v Praze, 1998. (CS)
Elearning
Classification of course in study plans
- Programme BPC-BTB Bachelor's 3 year of study, summer semester, compulsory
Type of course unit
Lecture
Teacher / Lecturer
Syllabus
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
Teacher / Lecturer
Syllabus
2. Models of single species populations
3. Models of two species populations
4. Models of cardiovascular system
5. Pharmacokinetical models
6. Epidemiological models
Elearning