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Epidemiological modeling of Covid-19
Schubert, Richard ; Kašpar, Jakub (referee) ; Mézl, Martin (advisor)
This thesis deals with the continuous epidemiological deterministic compartmental models and the COVID-19 pandemic modeling distinctive features. The effect of different probability distributions of individuals stay in compartments is studied numerically in relation to basic reproductive number and the final size of the epidemic, respectively. New model for a retrospective analysis of the first half of 2020 northern Italy epidemiological data is proposed. The model parameters estimation is performed using minimisation of weighted sum of squared residuals and the search through parameter space with BFGS algorithm implementation.
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Spatial-temporal epidemiologic models of Covid-19
Schubert, Richard ; Ředina, Richard (referee) ; Mézl, Martin (advisor)
This work aims to establish a fundamental framework for studying spatially diffusive models that describe the dynamics of infectious disease spread with constant parameters in a homogeneous domain. Initially, compartmental models and their extension to spatial domains are examined, followed by the theory of metapopulation models, where the degree of coupling between populations and the overall reproductive number R0 is discussed. Furthermore, the relationship between R0 and the shape of the spatial distribution of infected individuals in a simple diffusive SIR model is modeled. The influence of Neumann boundary conditions versus Dirichlet boundary conditions on R0 is demonstrated. In the second part of the work, selected findings and conclusions of studies that applied models in the spatiotemporal domain to analyze and predict the COVID-19 pandemic are summarized. In the third part of the work, a model with diffusive and metapopulation elements is fitted to epidemiological data from Lombardy in 2020, and the suitability of this approach is discussed.
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Spatial-temporal epidemiologic models of Covid-19
Schubert, Richard ; Ředina, Richard (referee) ; Mézl, Martin (advisor)
This work aims to establish a fundamental framework for studying spatially diffusive models that describe the dynamics of infectious disease spread with constant parameters in a homogeneous domain. Initially, compartmental models and their extension to spatial domains are examined, followed by the theory of metapopulation models, where the degree of coupling between populations and the overall reproductive number R0 is discussed. Furthermore, the relationship between R0 and the shape of the spatial distribution of infected individuals in a simple diffusive SIR model is modeled. The influence of Neumann boundary conditions versus Dirichlet boundary conditions on R0 is demonstrated. In the second part of the work, selected findings and conclusions of studies that applied models in the spatiotemporal domain to analyze and predict the COVID-19 pandemic are summarized. In the third part of the work, a model with diffusive and metapopulation elements is fitted to epidemiological data from Lombardy in 2020, and the suitability of this approach is discussed.
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Epidemiological modeling of Covid-19
Schubert, Richard ; Kašpar, Jakub (referee) ; Mézl, Martin (advisor)
This thesis deals with the continuous epidemiological deterministic compartmental models and the COVID-19 pandemic modeling distinctive features. The effect of different probability distributions of individuals stay in compartments is studied numerically in relation to basic reproductive number and the final size of the epidemic, respectively. New model for a retrospective analysis of the first half of 2020 northern Italy epidemiological data is proposed. The model parameters estimation is performed using minimisation of weighted sum of squared residuals and the search through parameter space with BFGS algorithm implementation.
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