Modelling & Simulation
- Garant předmětu:
- Department of Biomedical Informatics
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.
- Syllabus of lectures:
1. Basic concepts of simulation. Aims and consequences of modeling and simulation. The methodology of model development. Parameter identification. Experiments. Objective reality, dynamical systems, mathematical and simulation. Models and their description. Informal and formal description. Forms of mathematical description of continuous and discrete systems.
2. Continuous and discrete models of single populations. Malthus continuous model. Continuous logistic model with constant and variable parameters. Analysis of the solution. Continuous models of single populations of late. Discrete models of single populations. Discrete variants of Malthusian and logistic model. Discrete models of single populations of late. Models with age structure - Leslie's model.
3. Models of interacting populations. Predator-prey model. Analysis model of Lotka - Volterra. Kolmogorov model. Model predator - prey delays. Models of interacting populations. Models of competition. Models of cooperation.
4. Epidemiological models - basic epidemiological models. SIR model. Kermackův - McKendrik model - derivation. Conditions for the spread of the epidemic, estimate the maximum number of patients, estimate the number of victims. SI models, the SIS .. SIR model with vaccination and vector. Models of Seir.
5. Epidemiological models - models of disease dynamics veneral. Derivation of the Cross model. Analysis of the solution. Model the spread of AIDS.
6. Detailed block diagram of the process of modeling biological systems. The methodology of model development. Inverse problem of vector-optimization parameters
7. Detailed block diagram of the process of modeling biological systems-complete. Quality estimation of model parameters, or a new proposal. additional experiment. Importance of the sensitivity function in the design of a new experiment.
8. Compartmental models. Derivation of the mathematical description compartmenal systems. Modeling compartmental models. Examples compartmental use in biology and medicine.
9. Pharmacokinetics - linear pharmacokinetic models, examples of models, nonlinear pharmacokinetic models. PHEDSIM, analysis and use.
10. Optimal pharmacotherapy - MWPharm system analysis and application.
11. Compartment modeling systems - a model of kinetics of labeled aldosterone.
12. Model of regulation of heart rate during physical stress, analysis, practical application and training process.
13. Model glucose regulation, regulatory model stomach acidity.
- 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.,
Carson,E., Cobelli,C.: Modelling Methodology for Physiology and Medicine. S.Diego, AP 2001
- Further information:
- No time-table has been prepared for this course
- The course is a part of the following study plans:
- Biomedical Informatics - full-time study (compulsory course)