{"title":"Modeling of COVID-19 propagation with compartment models.","authors":"Günter Bärwolff","doi":"10.1007/s00591-021-00312-9","DOIUrl":"10.1007/s00591-021-00312-9","url":null,"abstract":"<p><p>The current pandemic is a great challenge for several research areas. In addition to virology research, mathematical models and simulations can be a valuable contribution to the understanding of the dynamics of the pandemic and can give recommendations to both physicians and politicians. In this paper we give an overview about mathematical models to describe the pandemic by differential equations. As a matter of principle the historic origin of the epidemic growth models will be remembered. Moreover we discuss models for the actual pandemic of 2020/2021. This will be done based on actual data of people infected with COVID-19 from the European Centre for Disease Prevention and Control (ECDC), input parameters of mathematical models will be determined and applied. These parameters will be estimated for the UK, Italy, Spain, and Germany and used in a <i>SIR</i>-type model. As a basis for the model's calibration, the initial exponential growth phase of the COVID-19 pandemic in the named countries is used. Strategies for the commencing and ending of social and economic shutdown measures are discussed. To respect heterogeneity of the people density in the different federal states of Germany diffusion effects are considered.</p>","PeriodicalId":40032,"journal":{"name":"Mathematische Semesterberichte","volume":"68 2","pages":"181-219"},"PeriodicalIF":0.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8564799/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"39725883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Neue Erkenntnisse über die Abstammung Georg Cantors","authors":"G. Singer","doi":"10.1007/s00591-020-00289-x","DOIUrl":"https://doi.org/10.1007/s00591-020-00289-x","url":null,"abstract":"","PeriodicalId":40032,"journal":{"name":"Mathematische Semesterberichte","volume":"67 1","pages":"135 - 159"},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00591-020-00289-x","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41913448","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Statistical independence in mathematics–the key to a Gaussian law","authors":"G. Leobacher, J. Prochno","doi":"10.1007/s00591-020-00287-z","DOIUrl":"https://doi.org/10.1007/s00591-020-00287-z","url":null,"abstract":"","PeriodicalId":40032,"journal":{"name":"Mathematische Semesterberichte","volume":"68 1","pages":"69 - 104"},"PeriodicalIF":0.0,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00591-020-00287-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46150767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Fabio Toscano: The Secret Formula – How a Mathematical Duel Inflamed Renaissance Italy and Uncovered the Cubic Equation","authors":"J. Hilgert","doi":"10.1007/s00591-020-00283-3","DOIUrl":"https://doi.org/10.1007/s00591-020-00283-3","url":null,"abstract":"","PeriodicalId":40032,"journal":{"name":"Mathematische Semesterberichte","volume":"67 1","pages":"307 - 309"},"PeriodicalIF":0.0,"publicationDate":"2020-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00591-020-00283-3","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48849452","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Four rational squares in arithmetic progressions and a family of elliptic curves with positive Mordell-Weil rank","authors":"H. Knaf, Erich Selder, K. Spindler","doi":"10.1007/s00591-020-00279-z","DOIUrl":"https://doi.org/10.1007/s00591-020-00279-z","url":null,"abstract":"","PeriodicalId":40032,"journal":{"name":"Mathematische Semesterberichte","volume":"80 1","pages":"213 - 236"},"PeriodicalIF":0.0,"publicationDate":"2020-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s00591-020-00279-z","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"51878038","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"David M. Bressoud: Calculus Reordered – A History of the Big Ideas","authors":"J. Hilgert","doi":"10.1007/s00591-020-00280-6","DOIUrl":"https://doi.org/10.1007/s00591-020-00280-6","url":null,"abstract":"","PeriodicalId":40032,"journal":{"name":"Mathematische Semesterberichte","volume":"3 3","pages":"297 - 299"},"PeriodicalIF":0.0,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141202178","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"David M. Bressoud: Calculus Reordered – A History of the Big Ideas","authors":"J. Hilgert","doi":"10.1007/s00591-020-00280-6","DOIUrl":"https://doi.org/10.1007/s00591-020-00280-6","url":null,"abstract":"","PeriodicalId":40032,"journal":{"name":"Mathematische Semesterberichte","volume":"3 6","pages":"297 - 299"},"PeriodicalIF":0.0,"publicationDate":"2020-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141202301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}