Models in Biology and Epidemiology
FEKT-AMODAcad. year: 2018/2019
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.
Learning outcomes of the course unit
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
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
Recommended optional programme components
Recommended or required reading
JIŘÍK,R.: Modely v biologii a epidemiologii. El. skripta VUT v Brně, 2006. (CS)
Holčík, J., Fojt, O.: Modelování biologických systémů (Vybrané kapitoly), skripta VUT v Brně, 2001. (CS)
Pazourek,J.: Simulace biologických systémů. GRADA, Praha 1992. (CS)
V. Eck, M. Razím, Biokybernetika, skripta ČVUT v Praze, 1998. (CS)
Murray, J.D.:Mathematical Biology,Springer Verlag, Berlin 1989. (EN)
ALLMAN, E.S., RHODES, J.A.: Mathematical Models in Biology: An Introduction. Cambridge University Press, 2004. (EN)
Planned learning activities and teaching methods
Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Teaching methods include lectures and computer laboratories (modeling in Matlab and Simulink). Course is taking advantage of e-learning (Moodle) systém.
Assesment methods and criteria linked to learning outcomes
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.
Language of instruction
1. Modeling and Simulation - basic concepts, classification of models
2. Modeling and Simulation - identification of model parameters, ways of describing the model
3. Mathematical and computer models - mathematical model analysis, computer modeling and simulation
4. Models of single populations - continuous: Malthus, Pearl-Verhulst and Hutchinson
5. Models of single populations - discrete: Malthus, Pearl-Verhulst, Leslie and Hutchinson
6. Models of interacting populations - predator-prey models: Lotka-Volterra and Kolmogorov
7. Models of interacting populations - models of competition and symbiosis
8. Models of cardiovascular system - hemodynamic parameters, Windkessel models
9. Models of action potential pulse - Hodgkin-Huxley model
10. Models of respiratory system - mechanical ventilation
11. Pharmacokinetic models - compartment model of diffusion, the pharmacokinetic parameters, single-compartment models
12. Pharmacokinetic models - two-compartment and three-compartment models
13. Epidemiological models - the SIR model, SEIR, SI and SIS.
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.
Specification of controlled education, way of implementation and compensation for absences
Computer exercises are compulsory, properly excused exercises absences can be substitute at another time after consultation with the teacher.