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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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Optimalization in allocation drivers at bus service
Sokol, Petr ; Štěpán, Josef (referee) ; Bartušek, Bohumír (advisor)
The thesis is focused on suggesting an algorithm for planning of optimal assignment drivers and vehicles to scheme of expeditions. When we make the assignment, we aspire to minimize the total transportation costs. By the same mail we push for well-balanced assignment, with respect to utilization of drivers and vehicles . The structure of the planning problem there is describing by making out of a wide linear model, whose parts are algebraic formulations of restrictions, which one must in traffic abide. In this model we can see binary and real variables that mean we draw up a model of mixed integer programming. We can say, that the integer programming is in general more complicated, then integer programming. We used optimization software named GAMS for solution this problem. The software uses Branch and Bound algorithm for the integer number problems. We draw up a program in GAMS, which is able to set an optimal pian for assignment drivers and vehicles to expeditions. A part of this work is couple of exemplary tasks, with their solution.
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Macroeconomic Modeling of the Economy of CR during the Accession to the EU
Švarcová, Radka ; Hušek, Roman (advisor) ; Štěpán, Josef (referee) ; Nováček, Jan (referee)
Práce zkoumá možnosti analýzy mechanismů působících během vstupu ČR do EU pomocí 2 ekonometrických modelů. První model je makroekonomický, vychází z Romerova IS-MP modelu. Je specifikovaný a odhadnutý jako GARCH model za použití časových řad pozorování, na jeho základě jsou stanoveny předpovědi. Výsledky ukazují velkou propojenost ekonomiky ČR s ekonomikou EU v období před vstupem do EU. Druhý model je mikroekonomický, tzv. "model obecné rovnováhy" (GE model). Jeho parametry jsou kalibrovány na základě dat z jednoho období. Model lze využít k simulacím změn souvisejících se vstupem ČR do EU.
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