Basic concepts. Aims and consequences of modeling and simulation. The methodology of modeling and simulation. Inverse problem. Proposal for a new, respectively. additional experiment. Compartmental models. Physiological models. Pharmacokinetics. Continuous and discrete models of population dynamics. Epidemiological models. Veneral disease models.
Contents:
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.
Recommended literature:
[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
Keywords:
biological system, modelling, simulation, population dynamics, epidemiology