Thesis/thesis.bib

@inbook{Eichner2003,
  author    = {Eichner, Martin and Kretzschmar, Mirjam},
  pages     = {81--93},
  publisher = {Springer Berlin Heidelberg},
  title     = {Mathematische Modelle in der Infektionsepidemiologie},
  year      = {2003},
  isbn      = {9783642556128},
  booktitle = {Infektionsepidemiologie},
  doi       = {10.1007/978-3-642-55612-8_8}
}

@article{1927,
  author    = {William Ogilvy Kermack and A. G. McKendrick},
  journal   = {Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character},
  title     = {A contribution to the mathematical theory of epidemics},
  year      = {1927},
  issn      = {2053-9150},
  month     = aug,
  number    = {772},
  pages     = {700--721},
  volume    = {115},
  doi       = {10.1098/rspa.1927.0118},
  publisher = {The Royal Society}
}

@article{Foerster2024,
  author    = {Foerster, Dietrich and Bhatkar, Sayali and Bhanot, Gyan},
  title     = {Parametrization of Worldwide Covid-19 data for multiple variants: How is the SAR-Cov2 virus evolving?},
  year      = {2024},
  month     = apr,
  doi       = {10.1101/2024.04.09.24305557},
  publisher = {Cold Spring Harbor Laboratory}
}

@misc{Shaier2021,
  author    = {Shaier, Sagi and Raissi, Maziar and Seshaiyer, Padmanabhan},
  title     = {Data-driven approaches for predicting spread of infectious diseases through DINNs: Disease Informed Neural Networks},
  year      = {2021},
  copyright = {Creative Commons Attribution 4.0 International},
  doi       = {10.48550/ARXIV.2110.05445},
  keywords  = {Machine Learning (cs.LG), Quantitative Methods (q-bio.QM), FOS: Computer and information sciences, FOS: Computer and information sciences, FOS: Biological sciences, FOS: Biological sciences},
  publisher = {arXiv}
}

@article{Jayatilaka2022,
  author    = {Jayatilaka, R. and Patel, R. and Brar, M. and Tang, Y. and Jisrawi, N.M. and Chishtie, F. and Drozd, J. and Valluri, S.R.},
  journal   = {Materials Today: Proceedings},
  title     = {A mathematical model of COVID-19 transmission},
  year      = {2022},
  issn      = {2214-7853},
  pages     = {101--112},
  volume    = {54},
  doi       = {10.1016/j.matpr.2021.11.480},
  publisher = {Elsevier BV}
}

@book{Zill1997,
  author    = {Dennis G. Zill},
  editor    = {Gary Ostedt},
  publisher = {Brooks/Cole Publishing Company, a division of Internaltional Thomson Publishing Inc.},
  title     = {A First Course In Differential Equations With Modelling Applications},
  year      = {1997},
  edition   = {6}
}

@book{Rudin2007,
  author    = {Walter Rudin},
  publisher = {Oldenbourg Wissenschaftsverlag GmbH},
  title     = {Analysis},
  year      = {2007}
}

@book{Tenenbaum1985,
  author    = {Morris Tenenbaum and Harry Pollard},
  publisher = {Harper and Row, Publishers, Inc.},
  title     = {Ordinary Differential Equations},
  year      = {1985}
}

@Book{EdelsteinKeshet2005,
  author    = {Leah Edelstein-Keshet},
  publisher = {Society for Industrial and Applied Mathematics},
  title     = {Mathematical Models in Biology},
  year      = {2005},
}

@Book{Anderson1991,
  author    = {Anderson, Roy Malcolm; May, Robert M.},
  publisher = {Oxford University Press},
  title     = {Infectious diseases of humans : dynamics and control},
  year      = {1991},
}

@Article{Millevoi2023,
  author    = {Millevoi, Caterina and Pasetto, Damiano and Ferronato, Massimiliano},
  title     = {A Physics-Informed Neural Network approach for compartmental epidemiological models},
  year      = {2023},
  copyright = {Creative Commons Attribution Non Commercial No Derivatives 4.0 International},
  doi       = {10.48550/ARXIV.2311.09944},
  keywords  = {Numerical Analysis (math.NA), FOS: Mathematics, FOS: Mathematics},
}

@Book{Goodfellow-et-al-2016,
  author    = {Ian Goodfellow and Yoshua Bengio and Aaron Courville},
  publisher = {MIT Press},
  title     = {Deep Learning},
  year      = {2016},
  note      = {\url{http://www.deeplearningbook.org}},
}

@Article{Lagaris1997,
  author    = {Lagaris, I. E. and Likas, A. and Fotiadis, D. I.},
  title     = {Artificial Neural Networks for Solving Ordinary and Partial Differential Equations},
  year      = {1997},
  copyright = {Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004},
  doi       = {10.48550/ARXIV.PHYSICS/9705023},
  keywords  = {Computational Physics (physics.comp-ph), Cellular Automata and Lattice Gases (nlin.CG), Quantum Physics (quant-ph), FOS: Physical sciences, FOS: Physical sciences},
}

@Article{Hornik1989,
  author    = {Hornik, Kurt and Stinchcombe, Maxwell and White, Halbert},
  journal   = {Neural Networks},
  title     = {Multilayer feedforward networks are universal approximators},
  year      = {1989},
  issn      = {0893-6080},
  month     = jan,
  number    = {5},
  pages     = {359--366},
  volume    = {2},
  doi       = {10.1016/0893-6080(89)90020-8},
  publisher = {Elsevier BV},
}

@Article{Rosenblatt1958,
  author    = {Rosenblatt, F.},
  journal   = {Psychological Review},
  title     = {The perceptron: A probabilistic model for information storage and organization in the brain.},
  year      = {1958},
  issn      = {0033-295X},
  number    = {6},
  pages     = {386--408},
  volume    = {65},
  doi       = {10.1037/h0042519},
  publisher = {American Psychological Association (APA)},
}

@Book{Minsky1972,
  author    = {Minsky, Marvin and Papert, Seymour A.},
  publisher = {The MIT Press},
  title     = {Perceptrons},
  year      = {1972},
  address   = {Cambridge/Mass. [u.a.]},
  edition   = {2. print. with corr},
  isbn      = {9780262630221},
  note      = {Literaturangaben},
  pagetotal = {258},
  ppn_gvk   = {223298433},
  subtitle  = {An introduction to computational geometry},
}

@Misc{Raissi2017,
  author    = {Raissi, Maziar and Perdikaris, Paris and Karniadakis, George Em},
  title     = {Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations},
  year      = {2017},
  copyright = {arXiv.org perpetual, non-exclusive license},
  doi       = {10.48550/ARXIV.1711.10561},
  keywords  = {Artificial Intelligence (cs.AI), Machine Learning (cs.LG), Numerical Analysis (math.NA), Dynamical Systems (math.DS), Machine Learning (stat.ML), FOS: Computer and information sciences, FOS: Computer and information sciences, FOS: Mathematics, FOS: Mathematics},
  publisher = {arXiv},
}

@Book{Demtroeder2021,
  author    = {Demtröder, Wolfgang},
  publisher = {Springer Spektrum},
  title     = {Experimentalphysik 1},
  year      = {2021},
  address   = {Berlin},
  edition   = {9. Auflage},
  isbn      = {978-3-662-62727-3},
  note      = {Auf dem Umschlag: Mit über 2,5 h Lösungsvideos zu ausgewählten Aufgaben},
  series    = {Lehrbuch},
  volume    = {1},
  pagetotal = {507},
  ppn_gvk   = {176791136X},
  subtitle  = {Wolfgang},
}

@Article{Schroedinger1926,
  author    = {Schrödinger, E.},
  journal   = {Physical Review},
  title     = {An Undulatory Theory of the Mechanics of Atoms and Molecules},
  year      = {1926},
  issn      = {0031-899X},
  month     = dec,
  number    = {6},
  pages     = {1049--1070},
  volume    = {28},
  doi       = {10.1103/physrev.28.1049},
  publisher = {American Physical Society (APS)},
}

@Book{Oksendal2000,
  author    = {Oksendal, Bernt},
  publisher = {Springer Berlin / Heidelberg},
  title     = {Stochastic Differential Equations},
  year      = {2000},
  address   = {Berlin, Heidelberg},
  edition   = {5th ed.},
  isbn      = {3-540-63720-6},
  note      = {Description based on publisher supplied metadata and other sources.},
  series    = {Universitext Ser.},
  pagetotal = {1332},
  ppn_gvk   = {1763063550},
  subtitle  = {An Introduction with Applications},
}

@Article{Matsumoto1984,
  author    = {Matsumoto, T.},
  journal   = {IEEE Transactions on Circuits and Systems},
  title     = {A chaotic attractor from Chua’s circuit},
  year      = {1984},
  issn      = {0098-4094},
  month     = dec,
  number    = {12},
  pages     = {1055--1058},
  volume    = {31},
  doi       = {10.1109/tcs.1984.1085459},
  publisher = {Institute of Electrical and Electronics Engineers (IEEE)},
}

@Article{Rumelhart1986,
  author    = {Rumelhart, David E. and Hinton, Geoffrey E. and Williams, Ronald J.},
  journal   = {Nature},
  title     = {Learning representations by back-propagating errors},
  year      = {1986},
  issn      = {1476-4687},
  month     = oct,
  number    = {6088},
  pages     = {533--536},
  volume    = {323},
  doi       = {10.1038/323533a0},
  publisher = {Springer Science and Business Media LLC},
}

@Article{Smirnova2017,
  author    = {Smirnova, Alexandra and deCamp, Linda and Chowell, Gerardo},
  journal   = {Bulletin of Mathematical Biology},
  title     = {Forecasting Epidemics Through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model},
  year      = {2017},
  issn      = {1522-9602},
  month     = may,
  number    = {11},
  pages     = {4343--4365},
  volume    = {81},
  doi       = {10.1007/s11538-017-0284-3},
  publisher = {Springer Science and Business Media LLC},
}

@Article{Berkhahn2022,
  author    = {Berkhahn, Sarah and Ehrhardt, Matthias},
  journal   = {Advances in Continuous and Discrete Models},
  title     = {A physics-informed neural network to model COVID-19 infection and hospitalization scenarios},
  year      = {2022},
  issn      = {2731-4235},
  month     = oct,
  number    = {1},
  volume    = {2022},
  doi       = {10.1186/s13662-022-03733-5},
  publisher = {Springer Science and Business Media LLC},
}

@Article{Long2021,
  author    = {Long, Jie and Khaliq, A. Q. M. and Furati, K. M.},
  journal   = {International Journal of Computer Mathematics},
  title     = {Identification and prediction of time-varying parameters of COVID-19 model: a data-driven deep learning approach},
  year      = {2021},
  issn      = {1029-0265},
  month     = may,
  pages     = {1--16},
  doi       = {10.1080/00207160.2021.1929942},
  publisher = {Informa UK Limited},
}

@Article{Olumoyin2021,
  author    = {Olumoyin, K. D. and Khaliq, A. Q. M. and Furati, K. M.},
  journal   = {Epidemiologia},
  title     = {Data-Driven Deep-Learning Algorithm for Asymptomatic COVID-19 Model with Varying Mitigation Measures and Transmission Rate},
  year      = {2021},
  issn      = {2673-3986},
  month     = sep,
  number    = {4},
  pages     = {471--489},
  volume    = {2},
  doi       = {10.3390/epidemiologia2040033},
  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},
}

@Article{Setianto2023,
  author    = {Setianto, Setianto and Hidayat, Darmawan},
  journal   = {Scientific Reports},
  title     = {Modeling the time-dependent transmission rate using gaussian pulses for analyzing the COVID-19 outbreaks in the world},
  year      = {2023},
  issn      = {2045-2322},
  month     = mar,
  number    = {1},
  volume    = {13},
  doi       = {10.1038/s41598-023-31714-5},
  publisher = {Springer Science and Business Media LLC},
}

@Article{Liu2012,
  author    = {Liu, Xinzhi and Stechlinski, Peter},
  journal   = {Applied Mathematical Modelling},
  title     = {Infectious disease models with time-varying parameters and general nonlinear incidence rate},
  year      = {2012},
  issn      = {0307-904X},
  month     = may,
  number    = {5},
  pages     = {1974--1994},
  volume    = {36},
  doi       = {10.1016/j.apm.2011.08.019},
  publisher = {Elsevier BV},
}

@Misc{Kingma2014,
  author    = {Kingma, Diederik P. and Ba, Jimmy},
  title     = {Adam: A Method for Stochastic Optimization},
  year      = {2014},
  copyright = {arXiv.org perpetual, non-exclusive license},
  doi       = {10.48550/ARXIV.1412.6980},
  keywords  = {Machine Learning (cs.LG), FOS: Computer and information sciences, FOS: Computer and information sciences},
  publisher = {arXiv},
}

@Misc{Paszke2019,
  author    = {Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Köpf, Andreas and Yang, Edward and DeVito, Zach and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu and Bai, Junjie and Chintala, Soumith},
  title     = {PyTorch: An Imperative Style, High-Performance Deep Learning Library},
  year      = {2019},
  copyright = {arXiv.org perpetual, non-exclusive license},
  doi       = {10.48550/ARXIV.1912.01703},
  keywords  = {Machine Learning (cs.LG), Mathematical Software (cs.MS), Machine Learning (stat.ML), FOS: Computer and information sciences, FOS: Computer and information sciences},
  publisher = {arXiv},
}

@Misc{GHInf,
  author       = {RKI},
  howpublished = {\url{https://github.com/robert-koch-institut/SARS-CoV-2-Infektionen_in_Deutschland}},
  note         = {{Accessed: 2024-09-05}},
  title        = {GitHub SARS-CoV-2 Infektionen in Deutschland},
}

@Misc{GHDead,
  author       = {RKI},
  howpublished = {\url{https://github.com/robert-koch-institut/COVID-19-Todesfaelle_in_Deutschland}},
  note         = {{Accessed: 2024-09-05}},
  title        = {GitHub COVID-19-Todesfälle in Deutschland},
}

@Misc{COVIDChronik,
  author       = {{Federal Ministry of Health}},
  howpublished = {\url{https://www.bundesgesundheitsministerium.de/coronavirus/chronik-coronavirus.html}},
  note         = {{Accessed: 2024-09-05}},
  title        = {Coronavirus-Pandemie: Was geschah wann?},
}

@Misc{COVInfo,
  author       = {{Federal Centre for Health Education}},
  howpublished = {\url{https://www.infektionsschutz.de/coronavirus/fragen-und-antworten/ansteckung-uebertragung-und-krankheitsverlauf/}},
  note         = {{Accessed: 2024-09-05}},
  title        = {Ansteckung, Übertragung und Krankheitsverlauf},
}

@Misc{WHO,
  author       = {WHO},
  howpublished = {\url{https://www.who.int/health-topics/coronavirus#tab=tab_1}},
  note         = {{Accessed: 2024-09-06}},
  title        = {Coronavirus disease (COVID-19)},
}

@Misc{RKI,
  author       = {RKI},
  howpublished = {\url{https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/ZS/Pandemieplan_Strategien.html}},
  note         = {{Accessed: 2024-09-06}},
  title        = {COVID-19-Strategiepapiere und Nationaler Pandemieplan},
}

@Misc{RKIa,
  author       = {RKI},
  howpublished = {\url{https://www.rki.de/DE/Content/InfAZ/N/Neuartiges_Coronavirus/Virologische_Basisdaten.html?nn=13490888#doc14716546bodyText10}},
  note         = {{Accessed: 2024-09-05}},
  title        = {SARS-CoV-2: Virologische Basisdaten sowie Virusvarianten im Zeitraum von 2020 - 2022},
}

@Misc{SRD,
  author       = {{Statista Research Department}},
  howpublished = {https://de.statista.com/statistik/daten/studie/1102667/umfrage/erkrankungs-und-todesfaelle-aufgrund-des-coronavirus-in-deutschland/},
  note         = {{Accessed: 2024-09-06}},
  title        = {Anzahl Infektionen und Todesfälle in Zusammenhang mit dem Coronavirus (COVID-19) in Deutschland seit Februar 2020},
}

@Article{Kirchhoff1845,
  author    = {Kirchhoff, Studiosus},
  journal   = {Annalen der Physik},
  title     = {Ueber den Durchgang eines elektrischen Stromes durch eine Ebene, insbesondere durch eine kreisförmige},
  year      = {1845},
  issn      = {1521-3889},
  month     = jan,
  number    = {4},
  pages     = {497--514},
  volume    = {140},
  doi       = {10.1002/andp.18451400402},
  publisher = {Wiley},
}

@Comment{jabref-meta: databaseType:bibtex;}