Benjamin Wacker

Bio: Benjamin Wacker is an academic researcher from Max Planck Society. The author has contributed to research in topics: Finite element method & Nonlinear system. The author has an hindex of 5, co-authored 19 publications receiving 54 citations. Previous affiliations of Benjamin Wacker include University of Göttingen & University of Lübeck.

Time-continuous and time-discrete SIR models revisited: theory and applications

Abstract: Since Kermack and McKendrick have introduced their famous epidemiological SIR model in 1927, mathematical epidemiology has grown as an interdisciplinary research discipline including knowledge from biology, computer science, or mathematics. Due to current threatening epidemics such as COVID-19, this interest is continuously rising. As our main goal, we establish an implicit time-discrete SIR (susceptible people–infectious people–recovered people) model. For this purpose, we first introduce its continuous variant with time-varying transmission and recovery rates and, as our first contribution, discuss thoroughly its properties. With respect to these results, we develop different possible time-discrete SIR models, we derive our implicit time-discrete SIR model in contrast to many other works which mainly investigate explicit time-discrete schemes and, as our main contribution, show unique solvability and further desirable properties compared to its continuous version. We thoroughly show that many of the desired properties of the time-continuous case are still valid in the time-discrete implicit case. Especially, we prove an upper error bound for our time-discrete implicit numerical scheme. Finally, we apply our proposed time-discrete SIR model to currently available data regarding the spread of COVID-19 in Germany and Iran.

A Novel Similarity Measure for Image Sequences

Abstract: Quantification of image similarity is a common problem in image processing. For pairs of two images, a variety of options is available and well-understood. However, some applications such as dynamic imaging or serial sectioning involve the analysis of image sequences and thus require a simultaneous and unbiased comparison of many images.

An age- and sex-structured SIR model: Theory and an explicit-implicit numerical solution algorithm.

Abstract: Since age and sex play an important role in transmission of diseases, we propose a SIR (susceptible-infectious-recovered) model for short-term predictions where the population is divided into subgroups based on both factors without taking into account vital dynamics. After stating our model and its underlining assumptions, we analyze its qualitative behavior thoroughly. We prove global existence and uniqueness, non-negativity, boundedness and certain monotonicity properties of the solution. Furthermore, we develop an explicit-implicit numerical solution algorithm and show that all properties of the continuous solution transfer to its time-discrete version. Finally, we provide one numerical example to illustrate our theoretical findings.

Clinical characteristics and intrauterine vertical transmission potential of COVID-19 infection in nine pregnant women: a retrospective review of medical records

Abstract: Summary Background Previous studies on the pneumonia outbreak caused by the 2019 novel coronavirus disease (COVID-19) were based on information from the general population. Limited data are available for pregnant women with COVID-19 pneumonia. This study aimed to evaluate the clinical characteristics of COVID-19 in pregnancy and the intrauterine vertical transmission potential of COVID-19 infection. Methods Clinical records, laboratory results, and chest CT scans were retrospectively reviewed for nine pregnant women with laboratory-confirmed COVID-19 pneumonia (ie, with maternal throat swab samples that were positive for severe acute respiratory syndrome coronavirus 2 [SARS-CoV-2]) who were admitted to Zhongnan Hospital of Wuhan University, Wuhan, China, from Jan 20 to Jan 31, 2020. Evidence of intrauterine vertical transmission was assessed by testing for the presence of SARS-CoV-2 in amniotic fluid, cord blood, and neonatal throat swab samples. Breastmilk samples were also collected and tested from patients after the first lactation. Findings All nine patients had a caesarean section in their third trimester. Seven patients presented with a fever. Other symptoms, including cough (in four of nine patients), myalgia (in three), sore throat (in two), and malaise (in two), were also observed. Fetal distress was monitored in two cases. Five of nine patients had lymphopenia ( Interpretation The clinical characteristics of COVID-19 pneumonia in pregnant women were similar to those reported for non-pregnant adult patients who developed COVID-19 pneumonia. Findings from this small group of cases suggest that there is currently no evidence for intrauterine infection caused by vertical transmission in women who develop COVID-19 pneumonia in late pregnancy. Funding Hubei Science and Technology Plan, Wuhan University Medical Development Plan.