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Parameter optimization in COVID-19 epidemiological models
 Martínek, Josef ; Kučera, Václav (advisor) ; Kopfová, Jana (referee)
This work is concerned with modelling of the spread of infectious diseases with em- phasis on the current COVID-19 pandemic. Our goal is to estimate unknown parameters in epidemiological models from real data on the spread of the disease in the Czech Repub- lic. To model the evolution of the epidemic, we consider compartmental models, which lead to a system of ordinary differential equations. We then formulate a non-linear least squares problem for the optimization of the model parameters to fit the model outcome to the observed data. We numerically optimize by the Levenberg-Marquardt method, which requires the Jacobian of the vector of residuals. This is obtained by deriving and solving the sensitivity equations corresponding to the considered model. We test the method on noisy artificial data and on a well documented English boarding school in- fluenza epidemic. Finally, we apply the method to Czech COVID-19 data and discuss the results. One of the conclusions of this work is the introduction of the concept of effective population size, to overcome the unrealistic assumption of complete homogeneity of the population. Thus the population size is not apriori given, but is an unknown parameter to be optimized. This leads to much better agreement of the models and real data. This appears to be a new concept. 1
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2 KOPFOVÁ, Jiřina
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