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Modeling COVID Pandemics: Strengths and Weaknesses of Epidemic Models
Šmíd, Martin
We generally discuss modeling the present COVID pandemics. We argue that useful models have to be simple in the first case, yet their uncertainty has to be handled properly. In order to study circumstances of the upcoming wave of infection,\nwe construct a simple stochastic model and present predictions it gives. We conclude that the autumn wave is most likely unavoidable and suggest concentrating to mitigation.
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Numerical solution of a stochastic model of a ball-type vibration absorber
Fischer, Cyril ; Náprstek, Jiří
The mathematical model of a ball-type vibration absorber represents a non-linear differential system which includes non-holonomic constraints. When a random ambient excitation is taken into account, the system has to be treated as a stochastic deferential equation. Depending on the level of simplifcation, an analytical solution is not practicable and numerical solution procedures have to be applied. The contribution presents a simple stochastic analysis of a particular resonance effect which can negatively influence efficiency of the absorber.
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Population viability analysis of endangered species in Czech Republic
Šťastná, Andrea ; Helman, Karel (advisor) ; Bašta, Milan (referee)
Diploma thesis analyzes the viability of the selected species populations in the Czech Republic. The thesis is divided into two main parts. The first part contains a stochastic model simulating possible scenarios of the Eurasian lynx population size in the Czech Republic. For this model program Vortex was used. The second part is focused on Time series analysis of the Grey Partridge and the Common Kingfisher population, where data was obtained from the Czech Society for Ornithology. This analysis aims on identification of factors that may affect the viability of the two bird species.
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Solving optimization problems using Monte Carlo method
Švehla, Pavel ; Jablonský, Josef (advisor) ; Dlouhý, Martin (referee)
The goal of the text is to communicate basic principles of Monte Carlo method and its application in solving linear programming problems with uncertain parameters. Monte Carlo method is widely used in various areas of science. However, the document focuses mainly on usage in economic applications. Nature of the second part is purely practical. It clearly describes finding solution of stochastic model using Crystal Ball software and its embedded solver -- OptQuest. Ambition of this work is also to be a brief Czech version of Crystal Ball user guide.
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