Modelling & Simulation
Code  Completion  Credits  Range  Language 

17PBIMS  Z,ZK  5  2P+2C  Czech 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Biomedical Informatics
 Synopsis:

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, crisscross models, models of venereal diseases.
 Requirements:
 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. Predatorprey 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 vectoroptimization parameters
7. Detailed block diagram of the process of modeling biological systemscomplete. 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 foodintake 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 MATLABSimulink.
6. Models for single species  continuous logistic model, analysis, experiments with model parameters in MATLABSimulink.
7. Implementation of delay into the single species model in MATLABSimulink.
8. Discrete models for singlespecies populations (Malthus and logistic models), simulation and analysis in Simulink.
9. Discrete model of singlespecies population with age distribution  Leslie model, simulation and analysis in Simulink.
10. Models of interacting populations. Predatorprey model, design, simulation and analysis in Simulink.
11. Models of interacting populations. Predatorprey 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 (crisscross 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.,
[2]Carson,E., Cobelli,C.: Modelling Methodology for Physiology and Medicine. S.Diego, AP 2001
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Biomedical Informatics  fulltime study (compulsory course)