In this seminar we consider a topic that somehow marked the years 2020 and 2021. Namely, we talk about the COVID-19 coronavirus epidemic and how its spread could be predicted with the help of various numerical models. More precisely, we get to know three different models. First, we describe the SIR model, which is one of the most basic models for predicting the spread of infectious diseases. It tells us how the epidemic would spread if nothing would be done about it. It describes the transitions of people between three conditions - susceptible, infected and cured. In the following, we present the extended SIR model, where we take into account that certain measures are taken at certain moments to curb the spread of the COVID-19 virus. We show how this affects the very course of the spread of the epidemic. The third model, to which we devote most words, is the $\Theta$-SEIHRD model, which describes the transition of people between 9 different conditions, taking into account various measures to curb the spread of the virus. Here we show that additional conditions bring more equations and parameters that need to be determined, which turns out to be a difficult problem as the results are highly dependent on the accuracy of the chosen parameters.
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