|
|
@@ -10,10 +10,17 @@
|
|
|
\chapter{Theoretical Background}
|
|
|
\label{chap:background}
|
|
|
|
|
|
-This chapter introduces the theoretical knowledge that forms the foundation of the work presented in this thesis. In sections~\ref{sec:domain} and~\ref{sec:differentialEq}, we talk about
|
|
|
-differential equations and the underlying theory. In these sections both the explanations and the approach are strongly based on the book on analysis by Rudin~\cite{Rudin2007}
|
|
|
-and the book about ordinary differential equations by Tenenbaum and Pollard~\cite{Tenenbaum1985}. Subsequently, we employ this knowledge to examine various pandemic models in section~\ref{sec:pandemicModel}.
|
|
|
-Finally, we address the topic of neural networks with a focus on the multilayer perceptron in section~\ref{sec:mlp} and physics informed neural networks in section~\ref{sec:pinn}.
|
|
|
+This chapter introduces the theoretical knowledge that forms the foundation of
|
|
|
+the work presented in this thesis. In sections~\ref{sec:domain}
|
|
|
+and~\ref{sec:differentialEq}, we talk about differential equations and the
|
|
|
+underlying theory. In these sections both the explanations and the approach are
|
|
|
+strongly based on the book on analysis by Rudin~\cite{Rudin2007} and the book
|
|
|
+about ordinary differential equations by Tenenbaum and
|
|
|
+Pollard~\cite{Tenenbaum1985}. Subsequently, we employ this knowledge to examine
|
|
|
+various pandemic models in section~\ref{sec:epidemModel}.
|
|
|
+Finally, we address the topic of neural networks with a focus on the multilayer
|
|
|
+perceptron in section~\ref{sec:mlp} and physics informed neural networks in
|
|
|
+section~\ref{sec:pinn}.
|
|
|
|
|
|
% -------------------------------------------------------------------
|
|
|
|
|
|
@@ -78,10 +85,15 @@ by that body. Based on these findings, we can rewrite the equation~\ref{eq:newto
|
|
|
|
|
|
% -------------------------------------------------------------------
|
|
|
|
|
|
-\section{Pandemic Models}
|
|
|
-\label{sec:pandemicModel}
|
|
|
-- modelation in a mathematical sense
|
|
|
-- what do pandemic models have to do?
|
|
|
+\section{Epidemiological Models}
|
|
|
+\label{sec:epidemModel}
|
|
|
+
|
|
|
+After a pandemic like \emph{COVID-19}, which has resulted in a significant number of fatalities, the question remains: How should we fight a pandemic correctly. Also, it is necessary to study whether the employed countermeasures efficacious in
|
|
|
+combating the pandemic. In the light of the unfavorable public responce to measures such as lockdowns, it is imperative to investigate that their efficacy remains commensurate with the costs incurred to those affected. In the event that
|
|
|
+alternative and novel technologies were in use, such as the mRNA vaccines in the context of COVID-19, it is needful to test the effect and find the optimal variant. In order to conduct the aforementioned investigations we to develop a
|
|
|
+method to quantize the pandemic and its course of progression. The real world is a highly complex system, which presents a significant challenge attempting to describe it fully in a model. The model must therefor 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) 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.
|
|
|
|
|
|
% -------------------------------------------------------------------
|
|
|
|
FlipediFlop