Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period.

In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can also be used for determining the time evolution of the associated number of deaths: for the epidemics in Spain, Germany, Italy and the UK, the parameters defining these formulae were computed using data up to 1 May 2020, a period of lockdown for these countries; then, the predictions of the formulae were compared with the data for the following 122 days, namely until 1 September. These comparisons, in addition to demonstrating the remarkable predictive capacity of our simple formulae, also show that for a rather long time the easing of the lockdown measures did not affect the number of deaths. The importance of these results regarding predictions of the number of Covid-19 deaths during the post-lockdown period is discussed

Covid-19: predictive mathematical formulae for the number of deaths during lockdown and possible scenarios for the post-lockdown period.

In a recent article, we introduced two novel mathematical expressions and a deep learning algorithm for characterizing the dynamics of the number of reported infected cases with SARS-CoV-2. Here, we show that such formulae can also be used for determining the time evolution of the associated number of deaths: for the epidemics in Spain, Germany, Italy and the UK, the parameters defining these formulae were computed using data up to 1 May 2020, a period of lockdown for these countries; then, the predictions of the formulae were compared with the data for the following 122 days, namely until 1 September. These comparisons, in addition to demonstrating the remarkable predictive capacity of our simple formulae, also show that for a rather long time the easing of the lockdown measures did not affect the number of deaths. The importance of these results regarding predictions of the number of Covid-19 deaths during the post-lockdown period is discussed

A Novel Metal-Based Imaging Probe for Targeted Dual-Modality SPECT/MR Imaging of Angiogenesis

Superparamagnetic iron oxide nanoparticles with well-integrated multimodality imaging properties have generated increasing research interest in the past decade, especially when it comes to the targeted imaging of tumors. Bevacizumab (BCZM) on the other hand is a well-known and widely applied monoclonal antibody recognizing VEGF-A, which is overexpressed in angiogenesis. The aim of this proof-of-concept study was to develop a dual-modality nanoplatform for in vivo targeted single photon computed emission tomography (SPECT) and magnetic resonance imaging (MRI) of tumor vascularization. Iron oxide nanoparticles (IONPs) have been coated with dimercaptosuccinic acid (DMSA), for consequent functionalization with the monoclonal antibody BCZM radiolabeled with 99mTc, via well-developed surface engineering. The IONPs were characterized based on their size distribution, hydrodynamic diameter and magnetic properties. In vitro cytotoxicity studies showed that our nanoconstruct does not cause toxic effects in normal and cancer cells. Fe3O4-DMSA-SMCC-BCZM-99mTc were successfully prepared at high radiochemical purity (>92%) and their stability in human serum and in PBS were demonstrated. In vitro cell binding studies showed the ability of the Fe3O4-DMSA-SMCC-BCZM-99mTc to bind to the VEGF-165 isoform overexpressed on M-165 tumor cells. The ex vivo biodistribution studies in M165 tumor-bearing SCID mice showed high uptake in liver, spleen, kidney and lungs. The Fe3O4-DMSA-SMCC-BCZM-99mTc demonstrated quick tumor accumulation starting at 8.9 ± 1.88%ID/g at 2 h p.i., slightly increasing at 4 h p.i. (16.21 ± 2.56%ID/g) and then decreasing at 24 h p.i. (6.01 ± 1.69%ID/g). The tumor-to-blood ratio reached a maximum at 24 h p.i. (~7), which is also the case for the tumor-to-muscle ratio (~18). Initial pilot imaging studies on an experimental gamma-camera and a clinical MR camera prove our hypothesis and demonstrate the potential of Fe3O4-DMSA-SMCC-BCZM-99mTc for targeted dual-modality imaging. Our findings indicate that Fe3O4-DMSA-SMCC-BCZM-99mTc IONPs could serve as an important diagnostic tool for biomedical imaging as well as a promising candidate for future theranostic applications in cancer

SARS-CoV-2: The Second Wave in Europe.

Although the SARS-CoV-2 virus has already undergone several mutations, the impact of these mutations on its infectivity and virulence remains controversial. In this viewpoint, we present arguments suggesting that SARS-CoV-2 mutants responsible for the second wave have less virulence but much higher infectivity. This suggestion is based on the results of the forecasting and mechanistic models developed by our study group. In particular, in May 2020, the analysis of our mechanistic model predicted that the easing of lockdown measures will lead to a dramatic second wave of the COVID-19 outbreak. However, after the lockdown was lifted in many European countries, the resulting number of reported infected cases and especially the number of deaths remained low for approximately two months. This raised the false hope that a substantial second wave will be avoided and that the COVID-19 epidemic in these European countries was nearing an end. Unfortunately, since the first week of August 2020, the number of reported infected cases increased dramatically. Furthermore, this was accompanied by an increasingly large number of deaths. The rate of reported infected cases in the second wave was much higher than that in the first wave, whereas the rate of deaths was lower. This trend is consistent with higher infectivity and lower virulence. Even if the mutated form of SARS-CoV-2 is less virulent, the very high number of reported infected cases implies that a large number of people will perish.ASF acknowledges support from EPSRC, UK, in the form of a Senior Fellowship. The authors are grateful to their co-authors of the papers referred here, as well as to Dr E Gkrania-Klotsas for useful discussions

Simple Formulae, Deep Learning and Elaborate Modelling for the COVID-19 Pandemic

Predictive modelling of infectious diseases is very important in planning public health policies, particularly during outbreaks. This work reviews the forecasting and mechanistic models published earlier. It is emphasized that researchers’ forecasting models exhibit, for large t, algebraic behavior, as opposed to the exponential behavior of the classical logistic-type models used usually in epidemics. Remarkably, a newly introduced mechanistic model also exhibits, for large t, algebraic behavior in contrast to the usual Susceptible-Exposed-Infectious-Removed (SEIR) models, which exhibit exponential behavior. The unexpected success of researchers’ simple forecasting models provides a strong support for the validity of this novel mechanistic model. It is also shown that the mathematical tools used for the analysis of the first wave may also be useful for the analysis of subsequent waves of the COVID-19 pandemic

Chebyshev Interpolation Using Almost Equally Spaced Points and Applications in Emission Tomography

Peer reviewed: TruePublication status: PublishedSince their introduction, Chebyshev polynomials of the first kind have been extensively investigated, especially in the context of approximation and interpolation. Although standard interpolation methods usually employ equally spaced points, this is not the case in Chebyshev interpolation. Instead of equally spaced points along a line, Chebyshev interpolation involves the roots of Chebyshev polynomials, known as Chebyshev nodes, corresponding to equally spaced points along the unit semicircle. By reviewing prior research on the applications of Chebyshev interpolation, it becomes apparent that this interpolation is rather impractical for medical imaging. Especially in clinical positron emission tomography (PET) and in single-photon emission computerized tomography (SPECT), the so-called sinogram is always calculated at equally spaced points, since the detectors are almost always uniformly distributed. We have been able to overcome this difficulty as follows. Suppose that the function to be interpolated has compact support and is known at q equally spaced points in −1,1. We extend the domain to −a,a, a&gt;1, and select a sufficiently large value of a, such that exactlyq Chebyshev nodes are included in −1,1, which are almost equally spaced. This construction provides a generalization of the concept of standard Chebyshev interpolation to almost equally spaced points. Our preliminary results indicate that our modification of the Chebyshev method provides comparable, or, in several cases including Runge’s phenomenon, superior interpolation over the standard Chebyshev interpolation. In terms of the L∞ norm of the interpolation error, a decrease of up to 75% was observed. Furthermore, our approach opens the way for using Chebyshev polynomials in the solution of the inverse problems arising in PET and SPECT image reconstruction.</jats:p

Discrete Shearlets as a Sparsifying Transform in Low-Rank Plus Sparse Decomposition for Undersampled (k, t)-Space MR Data.

The discrete shearlet transformation accurately represents the discontinuities and edges occurring in magnetic resonance imaging, providing an excellent option of a sparsifying transform. In the present paper, we examine the use of discrete shearlets over other sparsifying transforms in a low-rank plus sparse decomposition problem, denoted by L+S. The proposed algorithm is evaluated on simulated dynamic contrast enhanced (DCE) and small bowel data. For the small bowel, eight subjects were scanned; the sequence was run first on breath-holding and subsequently on free-breathing, without changing the anatomical position of the subject. The reconstruction performance of the proposed algorithm was evaluated against k-t FOCUSS. L+S decomposition, using discrete shearlets as sparsifying transforms, successfully separated the low-rank (background and periodic motion) from the sparse component (enhancement or bowel motility) for both DCE and small bowel data. Motion estimated from low-rank of DCE data is closer to ground truth deformations than motion estimated from L and S. Motility metrics derived from the S component of free-breathing data were not significantly different from the ones from breath-holding data up to four-fold undersampling, indicating that bowel (rapid/random) motility is isolated in S. Our work strongly supports the use of discrete shearlets as a sparsifying transform in a L+S decomposition for undersampled MR data

Chebyshev Interpolation Using Almost Equally Spaced Points and Applications in Emission Tomography

Since their introduction, Chebyshev polynomials of the first kind have been extensively investigated, especially in the context of approximation and interpolation. Although standard interpolation methods usually employ equally spaced points, this is not the case in Chebyshev interpolation. Instead of equally spaced points along a line, Chebyshev interpolation involves the roots of Chebyshev polynomials, known as Chebyshev nodes, corresponding to equally spaced points along the unit semicircle. By reviewing prior research on the applications of Chebyshev interpolation, it becomes apparent that this interpolation is rather impractical for medical imaging. Especially in clinical positron emission tomography (PET) and in single-photon emission computerized tomography (SPECT), the so-called sinogram is always calculated at equally spaced points, since the detectors are almost always uniformly distributed. We have been able to overcome this difficulty as follows. Suppose that the function to be interpolated has compact support and is known at q equally spaced points in −1,1. We extend the domain to −a,a, a>1, and select a sufficiently large value of a, such that exactlyq Chebyshev nodes are included in −1,1, which are almost equally spaced. This construction provides a generalization of the concept of standard Chebyshev interpolation to almost equally spaced points. Our preliminary results indicate that our modification of the Chebyshev method provides comparable, or, in several cases including Runge’s phenomenon, superior interpolation over the standard Chebyshev interpolation. In terms of the L∞ norm of the interpolation error, a decrease of up to 75% was observed. Furthermore, our approach opens the way for using Chebyshev polynomials in the solution of the inverse problems arising in PET and SPECT image reconstruction