Analysis of the Spread of COVID-19 and Effectiveness of Containment Strategies: Case study of Germany

The following slides presents an analysis of the spread of COVID-19 inGermany, and the effects of different containment strategies.Details of the mathematical model and how the parameters of themodel are estimated from the available data on the spread ofCOVID-19 is explained in:https://people.tuebingen.mpg.de/vbokharaie/Estimating_Covid19_contact_rates.pdfThe following few slide provides enough information to make thepresented figures understandable

A Mathematical Model to Predict the Spread of COVID-19 in a Population and Evaluate the Effectiveness of Containment Strategies

The available data on the spread of COVID-19 in China has been used to estimate the parameters of epidemiological models in a population stratified based on age distribution. The models can then be adapted and used for other countries or populations with different age distributions. The resulting models can be used to calculate the trajectory of the spread of the disease in various age groups in different countries. More importantly, it can be used to predict the effects of different containment strategies on the spread of COVID-19

Electricity Exchange: Demand Side Unit performance monitoring

Demand Side Response management encourages elec- tricity demand reduction during peak hours. One avenue for achieving this is through Demand Side Units (DSUs). These are large electricity consumers who can afford to reduce their demand on the electricity grid when required. Issues with DSUs revolve around verification that the correct demand reduction takes place, with limited monitoring capabilities from the electrical grid operator Eir- Grid. This issue is studied here with the current methods thoroughly analysed and new methods proposed. In this report six different forecasting methods are presented, and their accuracy is compared using two different error metrics. Due to inherent stochasticity in demand it is found that there is no one fore- casting method which is unequivocally best, but the ‘Keep it simple’ weekly and the temperature dependent models are identified as the most promising models to pursue. Initial investigations suggest that a ‘proxy day’ mechanism may be preferable to the current method of verifying that the correct demand reduction takes place

Uncertain Positive Systems: with applications in epidemiology

Although in recent years much attention has been paid to positive systems in general, there are still many areas that are left untouched. One of these areas, is the stability analysis of positive systems under any form of uncertainty. In this book, we study three broad classes of positive systems subject to different forms of uncertainty: nonlinear, switched and time-delay positive systems. Our focus is on positive systems which are monotone. Naturally, monotonicity methods play a key role in obtaining our results. As an application of our theoretical work on positive systems, we study a class of epidemiological systems with time-varying parameters. Most of the work done so far in epidemiology has been focused on models with time-independent parameters. Based on some of the recent results in this area, we describe the epidemiological model as a switched system and present some results on stability properties of the disease-free state of the epidemiological model

MiTfAT: A Python-based Analysis Tool for Molecular fMRI Experiments

Functional Magnetic Resonance Imaging, fMRI, is a technique used in neuroscience to measurebrain activity based on any signal that can be measured in an MRI scanner. Normally, fMRI isused to detect changes associated with blood flow, but it can also be used to detect changes inconcentrations of molecules with different magnetic properties that might be directly injectedinto the brain of a subject.Regardless of the signal that is measured in fMRI recordings, from a computational pointof view, fMRI recordings will result in a number of time-series. And then those time-seriesshould be analyzed to find the answers to various questions of interest. The length of thetime-series depends on the number of time-steps in which we have measured the signals, andtheir number depends on how-many voxels we have measured (a voxel is a 3-dimensional pixelor the unit of volume in which each fMRI signal is measured). The size of each of these voxelsdepends on the magnetic flux density of the MRI scanner, measured in Tesla (T). The higherthe magnetic flux density, the smaller the voxels can be, and the higher is the spatial resolutionof the measurements. Hence, we end up with one time-series for each of the voxels arrangedin a 3-dimensional structure. One characteristic of the fMRI measurements is that while theycan have a high spatial resolution, and while they allow us to measure brain activity not onlyin the cortex but also in deeper regions of the brain, their temporal resolution is not normallyhigh. And that can provide challenges for researchers who need to analyze the fMRI data

A Robust Stability Condition for Subhomogeneous Cooperative Time-delay Systems

In this manuscript, we present conditions for delay-independent stability of subhomogeneous cooperative time-delay systems. We consider the case where the time-delay system has a unique equilibrium at the origin and the case where it has a unique equilibrium in the interior of the positive orthant and prove global delay-independent stability results in both cases

An LMI Approach to Automatic Loop-Shaping of QFT Controllers

Quantitative Feedback Theory (QFT) is one of the most effective methods of robust controller design. In QFT design, we can consider the phase information of the perturbed plant so it is less conservative than H$\infty$ and µ-synthesis methods. In this paper, we want to overcome the major drawback of QFT method, i.e., lack of an automated technique for loop-shaping. Clearly such an automatic process must involve some sort of optimization, and while recent results on convex optimization have found fruitful applications in other areas of control theory we have tried to use LMI theory for automating the loop-shaping step of QFT design