do corrections

chapters/appendix/appendix.tex

@@ -16,14 +16,14 @@ Additionally, we show visualizations of the underlying dataset.
 
 \subsection{SIR Datasets}
 \label{sec:sir_datasets}
-In this section, we present the datasets utiized for~\Cref{sec:sir}.~\Cref{fig:SIR_state_results_1}
+In this section, we present the datasets utilized for~\Cref{sec:sir}.~\Cref{fig:SIR_state_results_1}
 and ~\Cref{fig:SIR_state_results_2} show the datasets, which we use for finding
 the epidemiological parameters of $\alpha$ and $\beta$.
 
 \begin{figure}[h!]
     \centering
     \includegraphics[width=\textwidth]{state_sir_cluster_1.pdf}
-    \caption{Part 1 of the datasets}
+    \caption{Part 1 of the datasets, used in the experiments in~\Cref{sec:pinn:sir}.}
     \label{fig:SIR_state_results_1}
 \end{figure}
 
@@ -36,7 +36,7 @@ the epidemiological parameters of $\alpha$ and $\beta$.
     \begin{subfigure}{0.35\textwidth}
         \includegraphics[width=\textwidth]{germany_single_sir.pdf}
     \end{subfigure}
-    \caption{Part 1 of the datasets}
+    \caption{Part 2 of the datasets, used in the experiments in~\Cref{sec:pinn:sir}.}
     \label{fig:SIR_state_results_2}
 \end{figure}
 
@@ -55,7 +55,7 @@ right.
     \begin{subfigure}{0.45\textwidth}
         \includegraphics[width=\textwidth]{I_cluster_0.pdf}
     \end{subfigure}
-    \caption{Part 1 of the results}
+    \caption{Part 1 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.}
     \label{fig:I_state_results_1}
 \end{figure}
 
@@ -67,7 +67,7 @@ right.
     \begin{subfigure}{0.45\textwidth}
         \includegraphics[width=\textwidth]{I_cluster_1.pdf}
     \end{subfigure}
-    \caption{Part 2 of the results}
+    \caption{Part 2 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.}
     \label{fig:I_state_results_2}
 \end{figure}
 
@@ -79,7 +79,7 @@ right.
     \begin{subfigure}{0.45\textwidth}
         \includegraphics[width=\textwidth]{I_cluster_2.pdf}
     \end{subfigure}
-    \caption{Part 3 of the results}
+    \caption{Part 3 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.}
     \label{fig:I_state_results_3}
 \end{figure}
 
@@ -91,7 +91,9 @@ right.
     \begin{subfigure}{0.45\textwidth}
         \includegraphics[width=\textwidth]{I_cluster_3.pdf}
     \end{subfigure}
-    \caption{Part 3 of the results}
+    \caption{Part 4 of the results, yielded by the experiments in~\Cref{sec:pinn:rsir}.
+        The graph showing prediction of $I$ for Germany, has a different y-axis scale
+        compared to all other graphs for the predictions of $I$.}
     \label{fig:I_state_results_4}
 \end{figure}
 

chapters/chap01-introduction/chap01-introduction.tex

@@ -58,7 +58,7 @@ model.\\
 The objective of this thesis is to identify the epidemiological parameters
 $\beta$ and $\alpha$, as well as the reproduction number $\Rt$ of COVID-19 over
 the first 1200 days of recorded data in Germany and its federal states. The
-Robert Koch Institute (RKI) has compiled data on both reported cases and
+Robert Koch Institute (RKI)\footnote{\url{https://www.rki.de/EN/Home/homepage_node.html}} has compiled data on both reported cases and
 associated moralities from the beginning of the outbreak in Germany to the
 present. We utilize and preprocess this data according to the required format of
 our approaches. As the raw data lacks information on recovery incidence, we

chapters/chap02/chap02.tex

@@ -154,10 +154,10 @@ challenge attempting to describe it fully in a mathematical model. Therefore,
 the model must reduce the complexity while retaining the essential information.
 Furthermore, it must address the issue of limited data availability. For
 instance, during COVID-19 institutions such as the Robert Koch Institute
-(RKI)\footnote[1]{\url{https://www.rki.de/EN/Home/homepage_node.html}} were only
-able to collect data on infections and mortality cases. Consequently, we require
-a model that employs an abstraction of the real world to illustrate the events
-and relations that are pivotal to understanding the problem.
+(RKI) were only able to collect data on infections and mortality cases.
+Consequently, we require a model that employs an abstraction of the real world
+to illustrate the events and relations that are pivotal to understanding the
+problem.
 
 % -------------------------------------------------------------------
 
@@ -205,7 +205,7 @@ As visualized in the~\Cref{fig:sir_model} the
 individuals may transition between groups based on epidemiological parameters. The
 transmission rate $\beta$ is responsible for individuals becoming infected,
 while the rate of removal or recovery rate $\alpha$ (also referred to as
-$\delta$ or $\nu$, \eg,~\cite{EdelsteinKeshet2005,Millevoi2023}) moves
+$\delta$ or $\nu$, \eg,~\cite{Millevoi2023,EdelsteinKeshet2005}) moves
 individuals from $I$ to $R$.\\
 
 We can describe this problem mathematically using a system of differential

chapters/chap03/chap03.tex

@@ -13,11 +13,11 @@ This chapter provides the methods, that we employ to address the problem that we
 present in~\Cref{chap:introduction}.~\Cref{sec:preprocessing} outlines
 our approaches for preprocessing of the available data and has two
 sections. The first section describes the publicly available data provided by
-the \emph{Robert Koch Institute} (RKI)\footnote{\url{https://www.rki.de/EN/Home/homepage_node.html}}.
-The second section outlines the techniques we use to process this data to fit
-our project's requirements. Subsequently, we give a theoretical overview of the
-PINN's that we employ. These latter sections, establish the foundation for the
-implementations described in~\Cref{sec:sir:setup} and~\Cref{sec:rsir:setup}.
+the \emph{Robert Koch Institute} (RKI). The second section outlines the
+techniques we use to process this data to fit our project's requirements.
+Subsequently, we give a theoretical overview of the PINN's that we employ.
+These latter sections, establish the foundation for the implementations
+described in~\Cref{sec:sir:setup} and~\Cref{sec:rsir:setup}.
 
 % -------------------------------------------------------------------
 
@@ -78,7 +78,7 @@ a weekly basis.\\
 
 The second repository is entitled \emph{SARS-CoV-2 Infektionen in Deutschland}~\cite{GHInf}.
 This dataset contains comprehensive data regarding the infections of each county
-on a daily basis. The counties are encoded using the \emph{Community Identification Number}\footnote{\url{https://www.destatis.de/DE/Themen/Laender-Regionen/Regionales/Gemeindeverzeichnis/_inhalt.html}},
+on a daily basis. The counties are encoded using the \emph{Community Identification Number}~\cite{GFSO},
 wherein the first two digits denote the state, the third digit represents the
 government district, and the last two digits indicate the county. Each data
 point displays the gender, the age group, number death, infection and recovery

chapters/chap04/chap04.tex

@@ -133,7 +133,7 @@ $\nu$ for each state provided by the Robert Koch Institute~\cite{FMH}.\\
         \caption{Mean and standard deviation, the error $e_{\text{SIR}}$ which we
             calculate with~\Cref{eq:error} and the distance
             $\Delta\beta_{\text{Germany}} = \beta_{\text{state}} - \beta_{\text{Germany}}$
-            across the 5 iterations, that we conducted for each German state (Mecklenburg-Western Pomerania=MWP, North Rhine-Westphalia=NRW) and Germany
+            across the 5 iterations, that we conducted for each German state (MWP=Mecklenburg-Western Pomerania, NRW=North Rhine-Westphalia) and Germany
             as the whole country. Furthermore, we include the vaccination percentage
             $\nu$ provided from the RKI~\cite{FMH}.}
         \label{table:state_mean_std}
@@ -169,7 +169,7 @@ $\nu$ for each state provided by the Robert Koch Institute~\cite{FMH}.\\
     \centering
     \includegraphics[width=\textwidth]{mean_std_alpha_beta_res.pdf}
     \caption{Visualization of the mean and standard deviation of the transition
-        rates $\alpha$ and $\beta$ for each state compared to the mean values of
+        rates $\alpha$ and $\beta$ for each state (MWP=Mecklenburg-Western Pomerania) compared to the mean values of
         $\alpha$ and $\beta$ for Germany.}
     \label{fig:alpha_beta_mean_std}
 \end{figure}
@@ -369,7 +369,7 @@ at the beginning.\\
             this table presents the error $e_{\text{I}}$, calculated with~\Cref{eq:error},
             the average number of days with $\Rt > 1$, and
             the average peak values of $\Rt$ for all German states
-            (Mecklenburg-Western Pomerania=MWP, North Rhine-Westphalia=NRW) and
+            (MWP=Mecklenburg-Western Pomerania, NRW=North Rhine-Westphalia) and
             Germany. The average is formed across all
             10 iteration.}
         \label{table:state_error}