Thesis/thesis.bbl

\begin{thebibliography}{10}

\bibitem{WHO}
{World Health Organization}.
\newblock Coronavirus disease (covid-19).
\newblock \url{https://www.who.int/health-topics/coronavirus#tab=tab_1}.
\newblock {Accessed: 2024-09-06}.

\bibitem{RKI}
{Robert Koch Institute}.
\newblock Covid-19-strategiepapiere und nationaler pandemieplan.
\newblock
  \url{https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ZS/Pandemieplan_Strategien.html}.
\newblock {Accessed: 2024-09-06}.

\bibitem{RKIa}
{Robert Koch Institute}.
\newblock Sars-cov-2: Virologische basisdaten sowie virusvarianten im zeitraum
  von 2020 - 2022.
\newblock
  \url{https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Virologische_Basisdaten.html?nn=13490888#doc14716546bodyText10}.
\newblock {Accessed: 2024-09-05}.

\bibitem{SRD}
{Statista Research Department}.
\newblock Anzahl infektionen und todesfälle in zusammenhang mit dem
  coronavirus (covid-19) in deutschland seit februar 2020.
\newblock
  https://de.statista.com/statistik/daten/studie/1102667/umfrage/erkrankungs-und-todesfaelle-aufgrund-des-coronavirus-in-deutschland/.
\newblock {Accessed: 2024-09-06}.

\bibitem{1927}
William~Ogilvy Kermack and A.~G. McKendrick.
\newblock A contribution to the mathematical theory of epidemics.
\newblock {\em Proceedings of the Royal Society of London. Series A, Containing
  Papers of a Mathematical and Physical Character}, 115(772):700--721, August
  1927.

\bibitem{Liu2012}
Xinzhi Liu and Peter Stechlinski.
\newblock Infectious disease models with time-varying parameters and general
  nonlinear incidence rate.
\newblock {\em Applied Mathematical Modelling}, 36(5):1974--1994, May 2012.

\bibitem{Setianto2023}
Setianto Setianto and Darmawan Hidayat.
\newblock Modeling the time-dependent transmission rate using gaussian pulses
  for analyzing the covid-19 outbreaks in the world.
\newblock {\em Scientific Reports}, 13(1), March 2023.

\bibitem{Shaier2021}
Sagi Shaier, Maziar Raissi, and Padmanabhan Seshaiyer.
\newblock Data-driven approaches for predicting spread of infectious diseases
  through dinns: Disease informed neural networks.
\newblock {\em Letters in Biomathematics}, 9(1):71--105, 2023.

\bibitem{Millevoi2023}
Caterina Millevoi, Damiano Pasetto, and Massimiliano Ferronato.
\newblock A physics-informed neural network approach for compartmental
  epidemiological models.
\newblock 20(9):e1012387, September 2023.

\bibitem{Smirnova2017}
Alexandra Smirnova, Linda deCamp, and Gerardo Chowell.
\newblock Forecasting epidemics through nonparametric estimation of
  time-dependent transmission rates using the seir model.
\newblock {\em Bulletin of Mathematical Biology}, 81(11):4343--4365, May 2017.

\bibitem{Berkhahn2022}
Sarah Berkhahn and Matthias Ehrhardt.
\newblock A physics-informed neural network to model covid-19 infection and
  hospitalization scenarios.
\newblock {\em Advances in Continuous and Discrete Models}, 2022(1), October
  2022.

\bibitem{Olumoyin2021}
K.~D. Olumoyin, A.~Q.~M. Khaliq, and K.~M. Furati.
\newblock Data-driven deep-learning algorithm for asymptomatic covid-19 model
  with varying mitigation measures and transmission rate.
\newblock {\em Epidemiologia}, 2(4):471--489, September 2021.

\bibitem{Rudin2007}
Walter Rudin.
\newblock {\em Analysis}.
\newblock Oldenbourg Wissenschaftsverlag GmbH, 2007.

\bibitem{Tenenbaum1985}
Morris Tenenbaum and Harry Pollard.
\newblock {\em Ordinary Differential Equations}.
\newblock Harper and Row, Publishers, Inc., 1985.

\bibitem{Demtroeder2021}
Wolfgang Demtröder.
\newblock {\em Experimentalphysik 1}, volume~1 of {\em Lehrbuch}.
\newblock Springer Spektrum, Berlin, 9. auflage edition, 2021.
\newblock Auf dem Umschlag: Mit über 2,5 h Lösungsvideos zu ausgewählten
  Aufgaben.

\bibitem{Kirchhoff1845}
Studiosus Kirchhoff.
\newblock Ueber den durchgang eines elektrischen stromes durch eine ebene,
  insbesondere durch eine kreisförmige.
\newblock {\em Annalen der Physik}, 140(4):497--514, January 1845.

\bibitem{Oksendal2000}
Bernt Oksendal.
\newblock {\em Stochastic Differential Equations}.
\newblock Universitext Ser. Springer Berlin / Heidelberg, Berlin, Heidelberg,
  5th ed. edition, 2000.
\newblock Description based on publisher supplied metadata and other sources.

\bibitem{Jaschke2023}
Philipp Jaschke, Sekou Keita, Ehsan Vallizadeh, and Simon Kühne.
\newblock Satisfaction with pandemic management and compliance with public
  health measures: Evidence from a german household survey on the covid-19
  crisis.
\newblock {\em PLOS ONE}, 18(2):e0281893, February 2023.

\bibitem{EdelsteinKeshet2005}
Leah Edelstein-Keshet.
\newblock {\em Mathematical Models in Biology}.
\newblock Society for Industrial and Applied Mathematics, 2005.

\bibitem{Anderson1991}
Robert~M. Anderson, Roy Malcolm;~May.
\newblock {\em Infectious diseases of humans : dynamics and control}.
\newblock Oxford University Press, 1991.

\bibitem{Rumelhart1986}
David~E. Rumelhart, Geoffrey~E. Hinton, and Ronald~J. Williams.
\newblock Learning representations by back-propagating errors.
\newblock {\em Nature}, 323(6088):533--536, October 1986.

\bibitem{Goodfellow-et-al-2016}
Ian Goodfellow, Yoshua Bengio, and Aaron Courville.
\newblock {\em Deep Learning}.
\newblock MIT Press, 2016.
\newblock \url{http://www.deeplearningbook.org}.

\bibitem{Rosenblatt1958}
F.~Rosenblatt.
\newblock The perceptron: A probabilistic model for information storage and
  organization in the brain.
\newblock {\em Psychological Review}, 65(6):386--408, 1958.

\bibitem{Minsky1972}
Marvin Minsky and Seymour~A. Papert.
\newblock {\em Perceptrons}.
\newblock The MIT Press, Cambridge/Mass. [u.a.], 2. print. with corr edition,
  1972.
\newblock Literaturangaben.

\bibitem{Hornik1989}
Kurt Hornik, Maxwell Stinchcombe, and Halbert White.
\newblock Multilayer feedforward networks are universal approximators.
\newblock {\em Neural Networks}, 2(5):359--366, January 1989.

\bibitem{Lagaris1998}
Isaac Lagaris, Aristidis Likas, and Dimitrios Fotiadis.
\newblock Artificial neural networks for solving ordinary and partial
  differential equations.
\newblock {\em IEEE Transactions on Neural Networks}, 9:987--1000, 09 1998.

\bibitem{Raissi2019}
M.~Raissi, P.~Perdikaris, and G.E. Karniadakis.
\newblock Physics-informed neural networks: A deep learning framework for
  solving forward and inverse problems involving nonlinear partial differential
  equations.
\newblock {\em Journal of Computational Physics}, 378:686--707, February 2019.

\bibitem{Moseley}
Ben Moseley.
\newblock So, what is a physics-informed neural network?
\newblock
  \url{https://benmoseley.blog/my-research/so-what-is-a-physics-informed-neural-network/}.
\newblock {Accessed: 2024-09-08}.

\bibitem{GHDead}
{Robert Koch Institute}.
\newblock Github covid-19-todesfälle in deutschland.
\newblock
  \url{https://github.com/robert-koch-institut/COVID-19-Todesfaelle_in_Deutschland}.
\newblock {Accessed: 2024-09-05}.

\bibitem{GHInf}
{Robert Koch Institute}.
\newblock Github sars-cov-2 infektionen in deutschland.
\newblock
  \url{https://github.com/robert-koch-institut/SARS-CoV-2-Infektionen_in_Deutschland}.
\newblock {Accessed: 2024-09-05}.

\bibitem{GFSO}
{German Federal Statistical Office}.
\newblock Gemeindeverzeichnis-informationssystem gv-isys.
\newblock
  \url{https://www.destatis.de/DE/Themen/Laender-Regionen/Regionales/Gemeindeverzeichnis/_inhalt.html}.
\newblock {Accessed: 2024-09-05}.

\bibitem{Fukushima1969}
Kunihiko Fukushima.
\newblock Visual feature extraction by a multilayered network of analog
  threshold elements.
\newblock {\em IEEE Transactions on Systems Science and Cybernetics},
  5(4):322--333, 1969.

\bibitem{Paszke2019}
Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory
  Chanan, Trevor Killeen, Zeming Lin, Natalia Gimelshein, Luca Antiga, Alban
  Desmaison, Andreas K\"{o}pf, Edward Yang, Zach DeVito, Martin Raison, Alykhan
  Tejani, Sasank Chilamkurthy, Benoit Steiner, Lu~Fang, Junjie Bai, and Soumith
  Chintala.
\newblock {\em PyTorch: an imperative style, high-performance deep learning
  library}.
\newblock Curran Associates Inc., Red Hook, NY, USA, 2019.

\bibitem{FMH}
{German Federal Ministry of Health}.
\newblock Übersicht zum impfstatus - covid-19-impfung in deutschland bis zum
  8. april 2023.
\newblock \url{https://impfdashboard.de/}.
\newblock {Accessed: 2024-09-08}.

\bibitem{COVInfo}
{German Federal Centre for Health Education}.
\newblock Ansteckung, Übertragung und krankheitsverlauf.
\newblock
  \url{https://www.infektionsschutz.de/coronavirus/fragen-und-antworten/ansteckung-uebertragung-und-krankheitsverlauf/}.
\newblock {Accessed: 2024-09-05}.

\bibitem{COVIDChronik}
{German Federal Ministry of Health}.
\newblock Coronavirus-pandemie: Was geschah wann?
\newblock
  \url{https://www.bundesgesundheitsministerium.de/coronavirus/chronik-coronavirus.html}.
\newblock {Accessed: 2024-09-05}.

\bibitem{Desson2022}
Zachary Desson, Lukas Kauer, Thomas Otten, Jan~Willem Peters, and Francesco
  Paolucci.
\newblock Finding the way forward: Covid-19 vaccination progress in germany,
  austria and switzerland.
\newblock {\em Health Policy and Technology}, 11(2):100584, June 2022.

\bibitem{Korolev2021}
Ivan Korolev.
\newblock Identification and estimation of the seird epidemic model for
  covid-19.
\newblock {\em Journal of Econometrics}, 220(1):63--85, January 2021.

\bibitem{Doerre2022}
Achim Doerre and Gabriele Doblhammer.
\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 {\em PLOS ONE}, 17(5):e0268119, May 2022.

\bibitem{Cooke1996}
K.~L. Cooke and P.~van~den Driessche.
\newblock Analysis of an seirs epidemic model with two delays.
\newblock {\em Journal of Mathematical Biology}, 35(2):240--260, December 1996.

\bibitem{Gilbert2010}
G.~Nigel Gilbert.
\newblock {\em Agent-based models}.
\newblock Number 153 in Quantitative applications in the social sciences. Sage
  Publ., Los Angeles [u.a.], 3. pr. edition, 2010.

\bibitem{Bodine2020}
Erin~N. Bodine, Robert~M. Panoff, Eberhard~O. Voit, and Anton~E. Weisstein.
\newblock Agent-based modeling and simulation in mathematics and biology
  education.
\newblock {\em Bulletin of Mathematical Biology}, 82(8), July 2020.

\bibitem{Kerr2021}
Cliff~C. Kerr, Robyn~M. Stuart, Dina Mistry, Romesh~G. Abeysuriya, Katherine
  Rosenfeld, Gregory~R. Hart, Rafael~C. Núñez, Jamie~A. Cohen, Prashanth
  Selvaraj, Brittany Hagedorn, Lauren George, Michał Jastrzębski, Amanda~S.
  Izzo, Greer Fowler, Anna Palmer, Dominic Delport, Nick Scott, Sherrie~L.
  Kelly, Caroline~S. Bennette, Bradley~G. Wagner, Stewart~T. Chang, Assaf~P.
  Oron, Edward~A. Wenger, Jasmina Panovska-Griffiths, Michael Famulare, and
  Daniel~J. Klein.
\newblock Covasim: An agent-based model of covid-19 dynamics and interventions.
\newblock {\em PLOS Computational Biology}, 17(7):e1009149, July 2021.

\bibitem{Maziarz2020}
Mariusz Maziarz and Martin Zach.
\newblock Agent‐based modelling for sars‐cov‐2 epidemic prediction and
  intervention assessment: A methodological appraisal.
\newblock {\em Journal of Evaluation in Clinical Practice}, 26(5):1352--1360,
  August 2020.

\end{thebibliography}