Fakultät für Mathematik und Naturwissenschaften

Mathematische Modelle für die COVID19-Pandemie

  1. M. Martcheva, An Introduction to Mathematical Epidemiology, Springer, New York, 2015.
  2. H.W. Hethcote, The mathematics of infectious diseases, SIAM Rev. 42(4) (2000),599-653.
  3. F. Brauer, Compartmental models in epidemiology, In: Mathematical epidemiology. Berlin: Springer, 2008, pp. 19-79.
  4. J. Bracher, D. Wolffram, J. Deuschel, K. Görgen, J.L. Ketterer, A. Ullrich, S. Abbott, M.V. Barbarossa, et al., Short-term forecasting of COVID-19 in Germany and Poland during the second wave – a preregistered study, preprint (2020).
  5. M.V. Barbarossa, N. Bogya, A. Dénes, G. Röst, H.V. Varma, Zs. Vizi, Fleeing lockdown and its impact on the size of epidemic outbreaks in the source and target regions - a COVID-19 lesson, preprint on Research Square (2020).
  6. M.V. Barbarossa, J. Fuhrmann, Germany's next shutdown - possible scenarios and outcomes, Influenza and Other Respiratory Viruses (2020).
  7. M.V. Barbarossa, J. Fuhrmann, J. Meinke, S. Krieg, H.V. Varma, N. Castelletti, Th. Lippert, Modeling the spread of COVID-19 in Germany: Early assessment and possible scenarios, PLoS ONE 15(9) (2020), e0238559.
  8. J. Fuhrmann, M.V. Barbarossa, The significance of case detection ratios for predictions on the outcome of an epidemic - a message from mathematical modelers, Arch. Public Health 78 (2020), 63.
  9. M.V. Barbarossa, J. Fuhrmann, J. Heidecke, H.V. Varma, N. Castelletti, J. Meinke, S. Krieg, Th. Lippert, A first study on the impact of current and future control measures on the spread of COVID-19 in Germany, medRxiv (2020).
  10. M.V. Barbarossa, M. Polner, G. Röst, Stability switches induced by immune system boosting in an SIRS model with discrete and distributed delays, SIAM Journal of Applied Mathematics 77(3) (2017), 903-925.

Die Verlässlichkeit von COVID-19 Schnelltests

  1. Robert-Koch Institut, Infografik: Corona-Schnelltest-Ergebnisse verstehen, 25. Februar 2021.
  2. Wikipedia, Satz von Bayes.
  3. C.F. Manski, Bounding the accuracy of diagnostic tests, with application to COVID-19 antibody tests, Epidemiology 32(2) (2020), 162-167.
  4. N. Augenblick, J. Kolstad, Z. Obermeyer, A. Wang, Pooled testing efficiency increases with test frequency, Proceedings of the National Academy of Sciences, 119(2) (2022).
  5. G. Ziegler, How many people are infected? A case study on SARS-CoV-2 prevalence in Austria, arXiv preprint arXiv:2012.12020, (2020).
  6. G. Ziegler, Binary Classification Tests, Imperfect Standards, and Ambiguous Information, arXiv preprint arXiv:2012.11215, (2020).

Robuste Inzidenzzahlen

  1. M. Català, D. Pino, M. Marchena, et al., Robust estimation of diagnostic rate and real incidence of COVID-19 for European policymakers, PLOS ONE, January 7, 2021.
  2. Robert Koch-Institut, COVID-19-Dashboard.
  3. Bundeseinheitliche Notbremse-Regelungen
  4. A. Kergaßner, C. Burkhardt, D. Lippold, et al., Memory-based meso-scale modeling of COVID-19, Comput. Mech. 66 (2020), 1069-1079.
  5. F. Zhou, T. Yu, R. Du, G. Fan, Y. Liu, et al., Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study, Lancet 395 (2020), 1054-1062.
  6. European Centre for Disease Prevention and Control, Rapid Risk Assessment: Coronavirus disease 2019 (COVID-19) in the EU/EEA and the UK – tenth update, 11th June, 2020.
  7. D. Moriña, A. Fernández-Fontelo, A. Cabaña, A. Arratia, G. Ávalos, P. Puig, Cumulated burden of COVID-19 in Spain from a Bayesian perspective, European Journal of Public Health, 31(4) (2021), 917-920.
  8. L. Böttcher, M.R. D'Orsogna, T. Chou, A statistical model of COVID-19 testing in populations: effects of sampling bias and testing errors, Philosophical Transactions of the Royal Society A, 380(2214) (2022), 20210121.
  9. V. Vasiliauskaite, N. Antulov-Fantulin, D. Helbing, On some fundamental challenges in monitoring epidemics, Philosophical Transactions of the Royal Society A, 380(2214) (2022), 20210117.
  10. Q. Zhang, Data science approaches to infectious disease surveillance, Philosophical Transactions of the Royal Society A, 380(2214) (2022), 20210115.

Optimale Steuerung der COVID19-Pandemie

  1. M. Kantner, Th. Koprucki, Beyond just “flattening the curve”: Optimal control of epidemics with purely non-pharmaceutical interventions, In: A. Micheletti, A. Araújo, N. Budko, A. Carpio and M. Ehrhardt (eds.), Mathematical models of the spread and consequences of the SARS-CoV-2 pandemics. Effects on health, society, industry, economics and technology, Special Issue of Journal of Mathematics in Industry, Springer, July 2021.
  2. F.L. Lewis, D. Vrabie, V.L. Syrmos, Optimal control, Wiley, New York, 2012.
  3. S. Lenhart, J.T. Workman, Optimal control applied to biological models, Boca Raton: Chapman & Hall/CRC Press, 2007.
  4. S.L. Chang, N. Harding, C. Zachreson, O.M. Cliff, M. Prokopenko, Modelling transmission and control of the COVID-19 pandemic in Australia, 2020. arXiv:2003.10218.
  5. J. Jia, J. Ding, S. Liu S, et al., Modeling the control of COVID-19: impact of policy interventions and meteorological factors. Electron. J. Differ. Equ. 23 (2020), 1.
  6. A.J. Kucharski, T.W. Russell, C. Diamond, et al., Early dynamics of transmission and control of COVID-19: a mathematical modelling study, Lancet Infect. Dis. 20(5) (2020), 553-558.
  7. M.V. Barbarossa, J. Fuhrmann, J. Heidecke, et al., A first study on the impact of current and future control measures on the spread of COVID-19 in Germany, medRxiv 2020.
  8. C. Tsay, F. Lejarza, M.A. Stadtherr, M. Baldea, Modeling, state estimation, and optimal control for the US COVID-19 outbreak, Sci. Rep. 10 (2020), 10711.
  9. K. Wickwire, Mathematical models for the control of pests and infectious diseases: a survey, Theor. Popul. Biol. 11(2) (1977), 182-238.
  10. O. Sharomi, T. Malik, Optimal control in epidemiology, Ann. Oper. Res. 251(1–2) (2015), 55-71.
  11. H. Behncke, Optimal control of deterministic epidemics, Optim. Control Appl. Methods 21(6) (2000), 269-285.
  12. C. Nowzari, V.M. Preciado, G.J. Pappas, Analysis and control of epidemics: a survey of spreading processes on complex networks, IEEE Control. Syst. Mag. 36(1) (2016), 26-46.
  13. R. Morton, K.H. Wickwire, On the optimal control of a deterministic epidemic, Adv. Appl. Probab. 6(4) (1974), 622-635.
  14. A. Abakuks, Optimal immunisation policies for epidemics, Adv. Appl. Probab. 6(3) (1974), 494–511.
  15. G. Zaman, Y.H. Kang, I.H. Jung, Stability analysis and optimal vaccination of an SIR epidemic model, Biosystems 93(3) (2008), 240-249.
  16. G. Zaman, Y.H. Kang, I.H. Jung, Optimal treatment of an SIR epidemic model with time delay, Biosystems 98 (2009), 43-50.
  17. T. Kar, A. Batabyal, Stability analysis and optimal control of an SIR epidemic model with vaccination, Biosystems 104(2) (2011), 127-135.
  18. A.D. Liddo, Optimal control and treatment of infectious diseases. The case of huge treatment costs, Mathematics 4(2) (2016), 21.
  19. H. Gaff, E. Schaefer, Optimal control applied to vaccination and treatment strategies for various epidemiological models, Math. Biosci. Eng. 6 (2009), 469-492.
  20. E. Hansen, T. Day, Optimal control of epidemics with limited resources, J. Math. Biol. 62(3) (2011), 423-451.
  21. D. Iacoviello, N. Stasio, Optimal control for SIRC epidemic outbreak, Comput. Methods Programs Biomed. 110(3) (2013), 333-342.
  22. L. Bolzoni, E. Bonacini, C. Soresina, M. Groppi, Time-optimal control strategies in SIR epidemic models, Math. Biosci. 292 (2017), 86-96.
  23. L. Bolzoni, E. Bonacini, R. Della Marca, M. Groppi, Optimal control of epidemic size and duration with limited resources, Math. Biosci. 315 (2019), 108232.
  24. M. Barro, A. Guiro, D. Ouedraogo, Optimal control of a SIR epidemic model with general incidence function and a time delays, CUBO 20(2) (2018), 53-66.
  25. R. Djidjou-Demasse, Y. Michalakis, M. Choisy, M.T. Sofonea, S. Alizon, Optimal COVID-19 epidemic control until vaccine deployment, medRxiv 2020.
  26. T.A. Perkins, G. España, Optimal control of the COVID-19 pandemic with non-pharmaceutical interventions, medRxiv 2020.
  27. T. Kruse, P. Strack, Optimal control of an epidemic through social distancing, SSRN Electron. J. (2020), 3581295.
  28. D.I. Ketcheson, Optimal control of an sir epidemic through finite-time non-pharmaceutical intervention, 2020, arXiv:2004.08848.
  29. F.E. Alvarez, D. Argente, F. Lippi, A simple planning problem for COVID-19 lockdown, Cambridge, MA. 2020. Tech. rep., NBER Working Paper No. 26981.
  30. J.F. Bonnans, J. Gianatti, Optimal control techniques based on infection age for the study of the COVID-19 epidemic, 2020, HAL-02558980v2.
  31. J. Köhler, L. Schwenkel, A. Koch, J. Berberich, P. Pauli, F. Allgöwer, Robust and optimal predictive control of the COVID-19 outbreak, 2020, arXiv:2005.03580.
  32. L. Miclo, D. Spiro, J. Weibull, Optimal epidemic suppression under an ICU constraint, 2020, arXiv:2005.01327.
  33. A. Charpentier, R. Elie, M. Laurière, V.C. Tran, COVID-19 pandemic control: balancing detection policy and lockdown intervention under ICU sustainability, 2020, arXiv:2005.06526.

Mathematische Modellierung von Impfprogrammen

  1. U. Heininger, Risiken von Infektionskrankheiten und der Nutzen von Impfungen, Bundesgesundheitsbl. Gesundheitsforsch. – Gesundheitsschutz 47 (2004), 1129-1135.
  2. J. Lopez Bernal, N. Andrews N, C. Gower, C. Robertson, J. Stowe E. Tessier, et al., Effectiveness of the Pfizer-BioNTech and Oxford-AstraZeneca vaccines on covid-19 related symptoms, hospital admissions, and mortality in older adults in England: test negative case-control study, BMJ 373 (2021), n1088
  3. Nature Milestones in Vaccines, Springer Nature, 2020.
  4. F.P. Polack, S.J. Thomas, N. Kitchin, J. Absalon, A. Gurtman, S. Lockhart, et al., Safety and efficacy of the BNT162b2 mRNA Covid-19 Vaccine, The New England Journal of Medicine 383 (2020), 2603-2615.
  5. H. Schroten, H. Brunner, Prävention durch Impfung – Kosten-Effektivität am Beispiel der Pneumokokken – Konjugat – Impfung, In: A. Gerber, K. Lauterbach, Gesundheitsökonomie und Pädiatrie (2006), 174-183, Schattauer Verlag.
  6. J.L. Schultze, A.C. Aschenbrenner, COVID-19 and the human innate immune system, Cell 184 (2021), 1671-1602.
  7. S. Treibert, H. Brunner, M. Ehrhardt, Compartment models for vaccine effectiveness and non-specific effects for Tuberculosis, Mathematical Biosciences and Engineering 16 (2019), 7250-4298.
  8. M. van Wijhe, S.A. McDonald, H.E. de Melker, M.J. Postma, J. Wallinga, Effect of vaccination programmes on mortality burden among children and young adults in the Netherlands during the 20th century: a historical analysis, The Lancet Infectious Diseases 16 (2016), 592-598.
  9. M. van Wijhe, A.D. Tulen, H. Korthals Altes, S.A. McDonald, H.E. de Melker, M.J. Postma, J. Wallinga, Quantifying the impact of mass vaccination programmes on notified cases in the Netherlands, Epidemiology and Infection 146 (2018), 716-722.
  10. L. Calzetta, B.L. Ritondo, A. Coppola, M.G. Matera, N. Di Daniele, P. Rogliani, Factors influencing the efficacy of COVID-19 vaccines: A Quantitative Synthesis of Phase III Trials, Vaccines 9: 341 (2021).
  11. T.H. Luong, Mathematical modeling of vaccinations: Modified SIR model, vaccination effects, and herd immunity, University Honors Theses 695 (2019).
  12. R. Mikolajczyk, R. Krumkamp, R. Bornemann, A. Ahmad, M. Schwehm, H. Duerr, Influenza-insights from mathematical modelling, Deutsches Ärzteblatt International 106 (2009) 777–782.
  13. S. Moore, E.M. Hill, M.J. Tildesley, L. Dyson, M.J. Keeling, Vaccination and non-pharmaceutical interventions for COVID-19: a mathematical modelling study, The Lancet Infectious Diseases 1473-3099(21)00143-2 (2021).
  14. M. Thießen, Immunisierte Gesellschaft: Impfen in Deutschland im 19. und 20. Jahrhundert, Bundeszentrale für politische Bildung, Schriftenreihe Band 10721, Bonn, 2021.

Mathematik ermöglicht Kulturveranstaltungen

  1. Hygienerahmenkonzept Juni für Kultureinrichtungen im Land Berlin, (Seite 21) Stand 7.6.2021

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