add further work

chapters/conclusions/conclusions.tex

@@ -5,14 +5,88 @@
 % Part:     conclusions
 % Description:
 %         summary of the content in this chapter
-% Version:  01.01.2012
+% Version:  01.09.2024
 % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \chapter{Conclusions  5}
 \label{chap:conclusions}
 
+The states with the highest transmission rate
+values are Thuringia, Saxony Anhalt and Mecklenburg West-Pomerania. It is also,
+visible that all six of the eastern states have a higher transmission rate than
+Germany. These results may be explainable with the ratio of vaccinated individuals\footnote{\url{https://impfdashboard.de/}}.
+The eastern state have a comparably low complete vaccination ratio, accept for
+Berlin. While Berlin has a moderate vaccination ratio, it is also a hub of
+mobility, which means that contact between individuals happens much more often.
+This is also a reason for Hamburg being a state with an above national standard
+rate of transmission. Bremen has the highest ratio of vaccinated individuals,
+this might be a reason for the it having the lowest transmission of all states.\\
+
+% -------------------------------------------------------------------
+
 \section{Further Work}
 \label{sec:furtherWork}
+Our findings demonstrate that with our methods enable the quantification of the
+course of the COVID-19 pandemic in Germany using the data provided by the
+Robert Koch Institute. Additionally, we present the limitations of our work.
+The SIR model is subject to numerous limitations. For instance, it does not
+account for individuals, who may be immune due to the vaccination status or
+those who are not infectious due to quarantine. In this section, we explore
+epidemiological models that illustrate these dynamics observed in real-world
+pandemics and recommend further investigation for Germany. First, we examine
+extensions of the SIR models, then we focus on agent-based models (ABMs).
 
 % -------------------------------------------------------------------
 
-% insert further sections if necessary
+\subsection{Further Compartmental Models}
+As our results demonstrate, the SIR model is capable of approximating the
+dynamics of real-world pandemics. However, the model is not without
+limitations. As previously stated, the SIR model assumes that recovered
+individuals remain immune and does not account for the reduction of exposure of
+susceptible individuals through the introduction of non-pharmaceutical
+mitigation policies, such as social distancing policies. These shortcomings can
+be addressed by incorporating additional compartments and transmission rates
+into the model. For example, the SEIRD model incorporates an \emph{Exposed}
+group and subdivides the \emph{Removed} group into \emph{Dead} and
+\emph{Recovered} compartments. Furthermore, this adds four additional rates to
+the model: the contact rate, representing the average number of contacts
+between infectious and susceptible people with a high probability of infection;
+the manifestation index, indicating the proportion of individuals exposed to
+the disease who will become infectious; the incubation rate, measuring the time
+required for exposed individuals to become infectious; and the infection
+fatality rate, quantifying the fraction of individuals who succumb to the
+disease. As Doerre and Doblhammer~\cite{Doerre2022} show for Germany using a
+numerical approximation method, for an SIERD model that they specialize to be
+age- and gender-specific, that it shows the impact of non-pharmaceutical
+mitigation policies. In their work, Cooke and van den Driessche~\cite{Cooke1996}
+propose the SEIRS model with two delays. This is model is capable of
+approximating diseases, that have an immune period, after which the recovered
+individual becomes susceptible again. These are just a few examples of
+the numerous modifications of the basic SIR model that can be used to
+approximate and consequently quantify an pandemic.
+
+% -------------------------------------------------------------------
+
+\subsection{Agent based models}
+
+While compartmental models, such as the SIR model, look at the population as a
+divided group, with each group representing a specific characterization that
+all inhabitants of that group share, an \emph{Agent-Based Model} (ABM) sets its
+focus on the individual. Each individual, or agent, has specific attributes
+that determine its behavior and interactions with other agents during the
+simulation. As Gilbert~\cite{Gilbert2010} states, ABMs simulate the behavior of
+large groups, with each individual following simple rules. Kerr
+\etal~\cite{Kerr2021} put forth a simulation tool, \emph{Covasim}, which they
+base on an ABM. The ABM employs local data, including demographic data, disease
+incidence data from the region, and contact data for household, schools and
+workplaces, to define its simulation for a specific region. In their work,
+Maziarz and Zach~\cite{Maziarz2020} address the criticism levied against ABMs
+for simplifying the dynamics and lacking the empirical support for the
+assumptions it they make. The authors utilize an ABM and the data specific to
+Australia to demonstrate the efficacy of ABMs in portraying the dynamics of the
+COVID-19 pandemic. They further state that ABMs can serve as serve as a tool
+for assessing the impact of non-pharmaceutical mitigation policies. This
+illustrates that ABMs play a distinct role in analyzing the COVID-19 pandemic.
+As the data situation has evolved, it is imperative to investigate the
+potential of utilizing ABMs as a tool to assess the pandemic's course.
+
+% -------------------------------------------------------------------

thesis.bbl

@@ -1,4 +1,5 @@
-\begin{thebibliography}{RHW86}
+\newcommand{\etalchar}[1]{$^{#1}$}
+\begin{thebibliography}{KSM{\etalchar{+}}21}
 
 % this bibliography is generated by alphadin.bst [8.2] from 2005-12-21
 
@@ -22,6 +23,25 @@
 \newblock DOI 10.1186/s13662--022--03733--5. --
 \newblock ISSN 2731--4235
 
+\bibitem[CD96]{Cooke1996}
+\textsc{Cooke}, K.~L. ; \textsc{Driessche}, P. van~d.:
+\newblock Analysis of an SEIRS epidemic model with two delays.
+\newblock {In: }\emph{Journal of Mathematical Biology} 35 (1996), Dezember, Nr.
+  2, S. 240--260.
+\newblock \url{http://dx.doi.org/10.1007/s002850050051}. --
+\newblock DOI 10.1007/s002850050051. --
+\newblock ISSN 1432--1416
+
+\bibitem[DD22]{Doerre2022}
+\textsc{Doerre}, Achim ; \textsc{Doblhammer}, Gabriele:
+\newblock The influence of gender on COVID-19 infections and mortality in
+  Germany: Insights from age- and gender-specific modeling of contact rates,
+  infections, and deaths in the early phase of the pandemic.
+\newblock {In: }\emph{PLOS ONE} 17 (2022), Mai, Nr. 5, S. e0268119.
+\newblock \url{http://dx.doi.org/10.1371/journal.pone.0268119}. --
+\newblock DOI 10.1371/journal.pone.0268119. --
+\newblock ISSN 1932--6203
+
 \bibitem[Dem21]{Demtroeder2021}
 \textsc{Demtröder}, Wolfgang:
 \newblock \emph{Lehrbuch}. Bd.~1: {\emph{Experimentalphysik 1}}.
@@ -43,6 +63,14 @@
 \newblock MIT Press, 2016. --
 \newblock \url{http://www.deeplearningbook.org}
 
+\bibitem[Gil10]{Gilbert2010}
+\textsc{Gilbert}, G.~N.:
+\newblock \emph{Agent-based models}.
+\newblock 3. pr.
+\newblock Los Angeles [u.a.] : Sage Publ., 2010 (Quantitative applications in
+  the social sciences 153). --
+\newblock ISBN 978--1--4129--4964--4
+
 \bibitem[HSW89]{Hornik1989}
 \textsc{Hornik}, Kurt ; \textsc{Stinchcombe}, Maxwell  ; \textsc{White},
   Halbert:
@@ -62,6 +90,25 @@
 \newblock DOI 10.1098/rspa.1927.0118. --
 \newblock ISSN 2053--9150
 
+\bibitem[KSM{\etalchar{+}}21]{Kerr2021}
+\textsc{Kerr}, Cliff~C. ; \textsc{Stuart}, Robyn~M. ; \textsc{Mistry}, Dina ;
+  \textsc{Abeysuriya}, Romesh~G. ; \textsc{Rosenfeld}, Katherine ;
+  \textsc{Hart}, Gregory~R. ; \textsc{Núñez}, Rafael~C. ; \textsc{Cohen},
+  Jamie~A. ; \textsc{Selvaraj}, Prashanth ; \textsc{Hagedorn}, Brittany ;
+  \textsc{George}, Lauren ; \textsc{Jastrzębski}, Michał ; \textsc{Izzo},
+  Amanda~S. ; \textsc{Fowler}, Greer ; \textsc{Palmer}, Anna ;
+  \textsc{Delport}, Dominic ; \textsc{Scott}, Nick ; \textsc{Kelly}, Sherrie~L.
+  ; \textsc{Bennette}, Caroline~S. ; \textsc{Wagner}, Bradley~G. ;
+  \textsc{Chang}, Stewart~T. ; \textsc{Oron}, Assaf~P. ; \textsc{Wenger},
+  Edward~A. ; \textsc{Panovska-Griffiths}, Jasmina ; \textsc{Famulare}, Michael
+   ; \textsc{Klein}, Daniel~J.:
+\newblock Covasim: An agent-based model of COVID-19 dynamics and interventions.
+\newblock {In: }\emph{PLOS Computational Biology} 17 (2021), Juli, Nr. 7, S.
+  e1009149.
+\newblock \url{http://dx.doi.org/10.1371/journal.pcbi.1009149}. --
+\newblock DOI 10.1371/journal.pcbi.1009149. --
+\newblock ISSN 1553--7358
+
 \bibitem[LLF97]{Lagaris1997}
 \textsc{Lagaris}, I.~E. ; \textsc{Likas}, A.  ; \textsc{Fotiadis}, D.~I.:
 \newblock Artificial Neural Networks for Solving Ordinary and Partial
@@ -96,6 +143,16 @@
 \newblock \url{http://dx.doi.org/10.48550/ARXIV.2311.09944}. --
 \newblock DOI 10.48550/ARXIV.2311.09944
 
+\bibitem[MZ20]{Maziarz2020}
+\textsc{Maziarz}, Mariusz ; \textsc{Zach}, Martin:
+\newblock Agent‐based modelling for SARS‐CoV‐2 epidemic prediction and
+  intervention assessment: A methodological appraisal.
+\newblock {In: }\emph{Journal of Evaluation in Clinical Practice} 26 (2020),
+  August, Nr. 5, S. 1352--1360.
+\newblock \url{http://dx.doi.org/10.1111/jep.13459}. --
+\newblock DOI 10.1111/jep.13459. --
+\newblock ISSN 1365--2753
+
 \bibitem[OKF21]{Olumoyin2021}
 \textsc{Olumoyin}, K.~D. ; \textsc{Khaliq}, A. Q.~M.  ; \textsc{Furati}, K.~M.:
 \newblock Data-Driven Deep-Learning Algorithm for Asymptomatic COVID-19 Model

thesis.bib

@@ -294,4 +294,76 @@
   publisher = {MDPI AG},
 }
 
+@Article{Kerr2021,
+  author    = {Kerr, Cliff C. and Stuart, Robyn M. and Mistry, Dina and Abeysuriya, Romesh G. and Rosenfeld, Katherine and Hart, Gregory R. and Núñez, Rafael C. and Cohen, Jamie A. and Selvaraj, Prashanth and Hagedorn, Brittany and George, Lauren and Jastrzębski, Michał and Izzo, Amanda S. and Fowler, Greer and Palmer, Anna and Delport, Dominic and Scott, Nick and Kelly, Sherrie L. and Bennette, Caroline S. and Wagner, Bradley G. and Chang, Stewart T. and Oron, Assaf P. and Wenger, Edward A. and Panovska-Griffiths, Jasmina and Famulare, Michael and Klein, Daniel J.},
+  journal   = {PLOS Computational Biology},
+  title     = {Covasim: An agent-based model of COVID-19 dynamics and interventions},
+  year      = {2021},
+  issn      = {1553-7358},
+  month     = jul,
+  number    = {7},
+  pages     = {e1009149},
+  volume    = {17},
+  doi       = {10.1371/journal.pcbi.1009149},
+  editor    = {Marz, Manja},
+  publisher = {Public Library of Science (PLoS)},
+}
+
+@Article{Doerre2022,
+  author    = {Doerre, Achim and Doblhammer, Gabriele},
+  journal   = {PLOS ONE},
+  title     = {The influence of gender on COVID-19 infections and mortality in Germany: Insights from age- and gender-specific modeling of contact rates, infections, and deaths in the early phase of the pandemic},
+  year      = {2022},
+  issn      = {1932-6203},
+  month     = may,
+  number    = {5},
+  pages     = {e0268119},
+  volume    = {17},
+  doi       = {10.1371/journal.pone.0268119},
+  editor    = {Cheong, Siew Ann},
+  publisher = {Public Library of Science (PLoS)},
+}
+
+@Article{Cooke1996,
+  author    = {Cooke, K. L. and van den Driessche, P.},
+  journal   = {Journal of Mathematical Biology},
+  title     = {Analysis of an SEIRS epidemic model with two delays},
+  year      = {1996},
+  issn      = {1432-1416},
+  month     = dec,
+  number    = {2},
+  pages     = {240--260},
+  volume    = {35},
+  doi       = {10.1007/s002850050051},
+  publisher = {Springer Science and Business Media LLC},
+}
+
+@Book{Gilbert2010,
+  author    = {Gilbert, G. Nigel},
+  publisher = {Sage Publ.},
+  title     = {Agent-based models},
+  year      = {2010},
+  address   = {Los Angeles [u.a.]},
+  edition   = {3. pr.},
+  isbn      = {978-1-4129-4964-4},
+  number    = {153},
+  series    = {Quantitative applications in the social sciences},
+  pagetotal = {98},
+  ppn_gvk   = {1615580204},
+}
+
+@Article{Maziarz2020,
+  author    = {Maziarz, Mariusz and Zach, Martin},
+  journal   = {Journal of Evaluation in Clinical Practice},
+  title     = {Agent‐based modelling for SARS‐CoV‐2 epidemic prediction and intervention assessment: A methodological appraisal},
+  year      = {2020},
+  issn      = {1365-2753},
+  month     = aug,
+  number    = {5},
+  pages     = {1352--1360},
+  volume    = {26},
+  doi       = {10.1111/jep.13459},
+  publisher = {Wiley},
+}
+
 @Comment{jabref-meta: databaseType:bibtex;}