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Deterministic and Stochastic Epidemic Models
Staněk, Jakub ; Štěpán, Josef (advisor) ; Hlubinka, Daniel (referee) ; Dohnal, Gejza (referee)
Kermack-McKendrick model and its version with vaccination are presented. First, we introduce a model with vaccination and then a numerical study that includes comparison of di erent vaccination strategies and searching for optimal vaccination strategy is presented. We proceed to introduce a stochastic model with migration and consequently we suggest its generalization and prove the existence and uniqueness of a solution to the stochastic di erential equation (henceforth SDE) describing this model. Three stochastic versions of Kermack-McKendrick model with vaccination are suggested and compared. A procedure of nding the optimal vaccination strategy is presented. We also prove the theorem on the existence and uniqueness of a solution to the SDE that drives a model with multiple pathogens. Finally, the stochastic di erential equation describing the general model is presented. We study properties of a solution to this SDE and present sufficient conditions for the existence of a solution that is absorbed by the natural barrier of the model.
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The influence of computer games on aggressiveness
STANĚK, Jakub
This Bachelor Thesis deals with study of influence of computer games on aggression. The aim of this thesis is to find out whether computer games cause inclination to aggressive behaviour. The theoretical part is focused on scanning electrical brain activity. It contains description of electroencephalography, evoked potentials and brain waves. It also elaborates various psychological theories of aggression and connects them to relation with physiologist creation of aggressive behaviour. The empirical part is focused on a research project. It describes an experiment which examines reactions to positive, neutral and negative visual stimuli before and after playing computer games by spectral analysis. 42 people, chosen by quota selection, participated in the research. 29 probands got into the final analysis and outcomes. The data were processed by Matlab program and its toolbox EEGlab. The outcomes of spectral analysis and comparison of individual research groups show that violent computer games influence aggression.
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