Original title: Deterministické a stochastické epidemické modely
Translated title: Deterministic and Stochastic Epidemic Models
Authors: Staněk, Jakub ; Štěpán, Josef (advisor) ; Hlubinka, Daniel (referee) ; Dohnal, Gejza (referee)
Document type: Doctoral theses
Year: 2009
Language: eng
Abstract: 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.

Institution: Charles University Faculties (theses) (web)
Document availability information: Available in the Charles University Digital Repository.
Original record: http://hdl.handle.net/20.500.11956/23402

Permalink: http://www.nusl.cz/ntk/nusl-278217


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Universities and colleges > Public universities > Charles University > Charles University Faculties (theses)
Academic theses (ETDs) > Doctoral theses