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% Author:   Phillip Rothenbeck
% Title:    Your Thesis
% File:     conclusions/conclusions.tex
% Part:     conclusions
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%         summary of the content in this chapter
% Version:  01.09.2024
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\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.\\

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\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).

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\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.

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\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.

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