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**Latest update: April 2nd, 2020**
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[[_TOC_]]
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The basic reproduction number ($`R_0`$) is a good measure for the long-term evolution of an epidemic that can be derived from such models.
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However, it assumes constant conditions over the whole period analysed.
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We opted for a shifting time window in each of which the reproduction number ($`R_t`$) is determined (time-window of **1 week** and shifting time of **1 day**).
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We developed an automatized algorithm for the fast analysis of the current $`R_t`$.
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Importantly, each time window is not analysed independently but includes the history of the epidemic by starting from the saved state of the simulation at the beginning of each time window.
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This analysis was developed for the sake of providing a daily updated evaluation of the reproduction number suitable to support political decisions on non-pharmaceutical interventions in the course of the CoV-outbreak and applied to German data.
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# Time-varying reproduction number for Germany
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Data for Germany were fitted to the cumulative number of reported cases in a sliding time window with a size of one week. The transmission rate $`R_1`$ was varied to fit to the data. Parameter sets were randomly sampled within the specified ranges (see figure 2) and, upon refitting, this induced a variability of reported $`R_t`$ values. The box plot shows the 25 and 75 percentiles as well as the min and the max values. Outliers were removed. Both used parameters sets (literature-based and derived from Italy-fit) are compared.
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![Germany_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Germany_iter_104.png)
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# Evolution of reproduction number for federal states of Germany
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Same analysis as previous section was performed for all federal state in Germany separately.
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![Baden-Württemberg_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Baden-Württemberg_iter_104.png)
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![Bayern_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Bayern_iter_104.png)
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![Berlin_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Berlin_iter_104.png)
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![Brandenburg_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Brandenburg_iter_104.png)
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![Bremen_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Bremen_iter_104.png)
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![Hamburg_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Hamburg_iter_104.png)
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![Hessen_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Hessen_iter_104.png)
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![Mecklenburg-Vorpommern_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Mecklenburg-Vorpommern_iter_104.png)
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![Niedersachsen_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Niedersachsen_iter_104.png)
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![Nordrhein-Westfalen_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Nordrhein-Westfalen_iter_104.png)
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![Rheinland-Pfalz_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Rheinland-Pfalz_iter_104.png)
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![Saarland_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Saarland_iter_104.png)
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![Sachsen_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Sachsen_iter_104.png)
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![Sachsen-Anhalt_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Sachsen-Anhalt_iter_104.png)
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![Schleswig-Holstein_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Schleswig-Holstein_iter_104.png)
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![Thueringen_iter_104](https://gitlab.com/simm/covid19/secir/raw/master/img/dynamic/Thueringen_iter_104.png)
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# Our model
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Based on a classical model of infection epidemics, we developed a mathematical model particularly adapted to the requirements and specificities of the CoV-outbreak (SECIR model).
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## Model structure
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![Model scheme](https://gitlab.com/simm/covid19/secir/raw/master/img/static/SECIR-Schematic.png)*The scheme of the SECIR model, which distinguishes susceptible ($`S`$), healthy individuals without immune memory of CoV, exposed ($`E`$), who already carry the virus but are not yet infectious to others, carriers ($`C`$), who carry the virus and are infectious to others but do not yet show symptoms, infected ($`I`$), who carry the virus with symptoms and are infectious to others, hospitalized ($`H`$), who experience a severe development of the disease, transferred to intensive care unit ($`U`$), dead ($`D`$), and recovered ($`R`$), who acquired immune memory and cannot be infected again.*
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## Parameter values
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![Parameter values](https://gitlab.com/simm/covid19/secir/raw/master/img/static/parameters.png)
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