Computational Modeling Of The Covid-19 Disease: Numerical Ode Analysis With R Programming


Book Description

The book is intended for readers who are interested in learning about the use of computer-based modelling of the COVID-19 disease. It provides a basic introduction to a five-ordinary differential equation (ODE) model by providing a complete statement of the model, including a detailed discussion of the ODEs, initial conditions and parameters, followed by a line-by-line explanation of a set of R routines (R is a quality, scientific programming system readily available from the Internet). The reader can access and execute these routines without having to first study numerical algorithms and computer coding (programming) and can perform numerical experimentation with the model on modest computers.







Covid-19 Unmasked: The News, The Science, And Common Sense


Book Description

How can we keep up with the deluge of information about COVID-19 and tell which parts are most important and trustworthy?We read: 'Scientists recommend', 'Experts warn', 'A new model predicts'. How do scientific experts come up with their recommendations? What do their predictions really mean for us, for our friends, and our families?How can we make rational decisions? And how can we have sensible conversations about the pandemic when we disagree?These are the questions that this book is trying to address.It is written in the form of dialogues. Alice, a student of epidemiology, explains the science to three of her fellow students who have a lot of questions for her. The students have the same concerns that we all share to varying degrees: What the pandemic is doing to our health, our economy, and our cherished freedoms. In their conversations, they discover how the science relates to these questions.The book focuses on epidemiology, the science of how infections spread and how the spread can be mitigated. The science of how many infections can be prevented by certain kinds of actions. This is what we need to understand if we want to act wisely, as individuals and as a society.The author's goal is to help the reader think about the COVID-19 pandemic like an epidemiologist. About the various preventive measures, what they are trying to accomplish, what the obstacles are. About what is likely to be most effective in the long run at moderate economic and personal cost. About the likely consequences of personal decisions. About how to best protect oneself and others while allowing all of us to lead lives that are as close as possible to normal.While some chapters present slightly more advanced material than others, no scientific background is needed to follow the conversations. The technical concepts are explained in small steps and the occasional calculations in the book require only high-school mathematics.Related Link(s)




Numerical Modeling of COVID-19 Neurological Effects


Book Description

Covid-19 is primarily a respiratory disease which results in impaired oxygenation of blood. The O2-deficient blood then moves through the body, and for the study in this book, the focus is on the blood flowing to the brain. The dynamics of blood flow along the brain capillaries and tissue is modeled as systems of ordinary and partial differential equations (ODE/PDEs). The ODE/PDE methodology is presented through a series of examples, 1. A basic one PDE model for O2 concentration in the brain capillary blood. 2. A two PDE model for O2 concentration in the brain capillary blood and in the brain tissue, with O2 transport across the blood brain barrier (BBB). 3. The two model extended to three PDEs to include the brain functional neuron cell density. Cognitive impairment could result from reduced neuron cell density in time and space (in the brain) that follows from lowered O2 concentration (hypoxia). The computer-based implementation of the example models is presented through routines coded (programmed) in R, a quality, open-source scientific computing system that is readily available from the Internet. Formal mathematics is minimized, e.g., no theorems and proofs. Rather, the presentation is through detailed examples that the reader/researcher/analyst can execute on modest computers. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs, implemented with finite differences. The routines are available from a download link so that the example models can be executed without having to first study numerical methods and computer coding. The routines can then be applied to variations and extensions of the blood/brain hypoxia models, such as changes in the ODE/PDE parameters (constants) and form of the model equations.




Mathematical Epidemiology


Book Description

Based on lecture notes of two summer schools with a mixed audience from mathematical sciences, epidemiology and public health, this volume offers a comprehensive introduction to basic ideas and techniques in modeling infectious diseases, for the comparison of strategies to plan for an anticipated epidemic or pandemic, and to deal with a disease outbreak in real time. It covers detailed case studies for diseases including pandemic influenza, West Nile virus, and childhood diseases. Models for other diseases including Severe Acute Respiratory Syndrome, fox rabies, and sexually transmitted infections are included as applications. Its chapters are coherent and complementary independent units. In order to accustom students to look at the current literature and to experience different perspectives, no attempt has been made to achieve united writing style or unified notation. Notes on some mathematical background (calculus, matrix algebra, differential equations, and probability) have been prepared and may be downloaded at the web site of the Centre for Disease Modeling (www.cdm.yorku.ca).




Mathematical Models in Epidemiology


Book Description

The book is a comprehensive, self-contained introduction to the mathematical modeling and analysis of disease transmission models. It includes (i) an introduction to the main concepts of compartmental models including models with heterogeneous mixing of individuals and models for vector-transmitted diseases, (ii) a detailed analysis of models for important specific diseases, including tuberculosis, HIV/AIDS, influenza, Ebola virus disease, malaria, dengue fever and the Zika virus, (iii) an introduction to more advanced mathematical topics, including age structure, spatial structure, and mobility, and (iv) some challenges and opportunities for the future. There are exercises of varying degrees of difficulty, and projects leading to new research directions. For the benefit of public health professionals whose contact with mathematics may not be recent, there is an appendix covering the necessary mathematical background. There are indications which sections require a strong mathematical background so that the book can be useful for both mathematical modelers and public health professionals.




Computational Mathematics


Book Description

This textbook is a comprehensive introduction to computational mathematics and scientific computing suitable for undergraduate and postgraduate courses. It presents both practical and theoretical aspects of the subject, as well as advantages and pitfalls of classical numerical methods alongside with computer code and experiments in Python. Each chapter closes with modern applications in physics, engineering, and computer science. Features: No previous experience in Python is required. Includes simplified computer code for fast-paced learning and transferable skills development. Includes practical problems ideal for project assignments and distance learning. Presents both intuitive and rigorous faces of modern scientific computing. Provides an introduction to neural networks and machine learning.




The Covid-19 Epidemic In China


Book Description

This book contains an in-depth quantitative analysis of the development of the COVID-19 epidemic in China from its very beginning in December 2019 to early April 2020 when it was brought under control. It begins with adjustments of the official cumulative data on newly confirmed cases and deaths, removing any inconsistencies and smoothing the surges not attributable directly to the COVID-19 virus itself. It discusses the measures undertaken by the Chinese Government to control the epidemic. It examines the extent of the infection, the case mortality, and the costs to the Chinese economy in both Hubei, the province in which the first confirmed case was discovered, and the rest of the Mainland outside of Hubei. There is also an international comparison of the Chinese experience with those of other countries.




Adaptive Method of Lines


Book Description

The general Method of Lines (MOL) procedure provides a flexible format for the solution of all the major classes of partial differential equations (PDEs) and is particularly well suited to evolutionary, nonlinear wave PDEs. Despite its utility, however, there are relatively few texts that explore it at a more advanced level and reflect the method's




Basics and Trends in Sensitivity Analysis: Theory and Practice in R


Book Description

This book provides an overview of global sensitivity analysis methods and algorithms, including their theoretical basis and mathematical properties. The authors use a practical point of view and real case studies as well as numerous examples, and applications of the different approaches are illustrated throughout using R code to explain their usage and usefulness in practice. Basics and Trends in Sensitivity Analysis: Theory and Practice in R covers a lot of material, including theoretical aspects of Sobol’ indices as well as sampling-based formulas, spectral methods, and metamodel-based approaches for estimation purposes; screening techniques devoted to identifying influential and noninfluential inputs; variance-based measures when model inputs are statistically dependent (and several other approaches that go beyond variance-based sensitivity measures); and a case study in R related to a COVID-19 epidemic model where the full workflow of sensitivity analysis combining several techniques is presented. This book is intended for engineers, researchers, and undergraduate students who use complex numerical models and have an interest in sensitivity analysis techniques and is appropriate for anyone with a solid mathematical background in basic statistical and probability theories who develops and uses numerical models in all scientific and engineering domains.