Mathematical And Computational Modelling Of Covid 19 Transmission

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Mathematical and Computational Modelling of Covid-19 Transmission

Author : Mandeep Mittal
Publisher : CRC Press
ISBN 13 : 1003807127
Total Pages : 337 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Mathematical and Computational Modelling of Covid-19 Transmission by : Mandeep Mittal

Download or read book Mathematical and Computational Modelling of Covid-19 Transmission written by Mandeep Mittal and published by CRC Press. This book was released on 2023-12-07 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infectious diseases are leading threats and are of highest risk to the human population globally. Over the last two years, we saw the transmission of Covid-19. Millions of people died or were forced to live with a disability. Mathematical models are effective tools that enable analysis of relevant information, simulate the related process and evaluate beneficial results. They can help to make rational decisions to lead toward a healthy society. Formulation of mathematical models for a pollution-free environment is also very important for society. To determine the system which can be modelled, we need to formulate the basic context of the model underlying some necessary assumptions. This describes our beliefs in terms of the mathematical language of how the world functions. This book addresses issues during the Covid phase and post-Covid phase. It analyzes transmission, impact of coinfections, and vaccination as a control or to decrease the intensity of infection. It also talks about the violence and unemployment problems occurring during the post-Covid period. This book will help societal stakeholders to resume normality slowly and steadily.

Computational Epidemiology

Author : Ellen Kuhl
Publisher : Springer Nature
ISBN 13 : 3030828905
Total Pages : 312 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Computational Epidemiology by : Ellen Kuhl

Download or read book Computational Epidemiology written by Ellen Kuhl and published by Springer Nature. This book was released on 2021-09-22 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This innovative textbook brings together modern concepts in mathematical epidemiology, computational modeling, physics-based simulation, data science, and machine learning to understand one of the most significant problems of our current time, the outbreak dynamics and outbreak control of COVID-19. It teaches the relevant tools to model and simulate nonlinear dynamic systems in view of a global pandemic that is acutely relevant to human health. If you are a student, educator, basic scientist, or medical researcher in the natural or social sciences, or someone passionate about big data and human health: This book is for you! It serves as a textbook for undergraduates and graduate students, and a monograph for researchers and scientists. It can be used in the mathematical life sciences suitable for courses in applied mathematics, biomedical engineering, biostatistics, computer science, data science, epidemiology, health sciences, machine learning, mathematical biology, numerical methods, and probabilistic programming. This book is a personal reflection on the role of data-driven modeling during the COVID-19 pandemic, motivated by the curiosity to understand it.

Computational Modeling and Data Analysis in COVID-19 Research

Author : Chhabi Rani Panigrahi
Publisher : CRC Press
ISBN 13 : 1000384977
Total Pages : 271 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Computational Modeling and Data Analysis in COVID-19 Research by : Chhabi Rani Panigrahi

Download or read book Computational Modeling and Data Analysis in COVID-19 Research written by Chhabi Rani Panigrahi and published by CRC Press. This book was released on 2021-05-09 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book covers recent research on the COVID-19 pandemic. It includes the analysis, implementation, usage, and proposed ideas and models with architecture to handle the COVID-19 outbreak. Using advanced technologies such as artificial intelligence (AI) and machine learning (ML), techniques for data analysis, this book will be helpful to mitigate exposure and ensure public health. We know prevention is better than cure, so by using several ML techniques, researchers can try to predict the disease in its early stage and develop more effective medications and treatments. Computational technologies in areas like AI, ML, Internet of Things (IoT), and drone technologies underlie a range of applications that can be developed and utilized for this purpose. Because in most cases there is no one solution to stop the spreading of pandemic diseases, and the integration of several tools and tactics are needed. Many successful applications of AI, ML, IoT, and drone technologies already exist, including systems that analyze past data to predict and conclude some useful information for controlling the spread of COVID-19 infections using minimum resources. The AI and ML approach can be helpful to design different models to give a predictive solution for mitigating infection and preventing larger outbreaks. This book: Examines the use of artificial intelligence (AI), machine learning (ML), Internet of Things (IoT), and drone technologies as a helpful predictive solution for controlling infection of COVID-19 Covers recent research related to the COVID-19 pandemic and includes the analysis, implementation, usage, and proposed ideas and models with architecture to handle a pandemic outbreak Examines the performance, implementation, architecture, and techniques of different analytical and statistical models related to COVID-19 Includes different case studies on COVID-19 Dr. Chhabi Rani Panigrahi is Assistant Professor in the Department of Computer Science at Rama Devi Women’s University, Bhubaneswar, India. Dr. Bibudhendu Pati is Associate Professor and Head of the Department of Computer Science at Rama Devi Women’s University, Bhubaneswar, India. Dr. Mamata Rath is Assistant Professor in the School of Management (Information Technology) at Birla Global University, Bhubaneswar, India. Prof. Rajkumar Buyya is a Redmond Barry Distinguished Professor and Director of the Cloud Computing and Distributed Systems (CLOUDS) Laboratory at the University of Melbourne, Australia.

Mathematical Analysis for Transmission of COVID-19

Author : Nita H. Shah
Publisher : Springer Nature
ISBN 13 : 9813362642
Total Pages : 366 pages
Book Rating : 4.8/5 (133 download)

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Book Synopsis Mathematical Analysis for Transmission of COVID-19 by : Nita H. Shah

Download or read book Mathematical Analysis for Transmission of COVID-19 written by Nita H. Shah and published by Springer Nature. This book was released on 2021-04-01 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes various mathematical models that can be used to better understand the spread of novel Coronavirus Disease 2019 (COVID-19) and help to fight against various challenges that have been developed due to COVID-19. The book presents a statistical analysis of the data related to the COVID-19 outbreak, especially the infection speed, death and fatality rates in major countries and some states of India like Gujarat, Maharashtra, Madhya Pradesh and Delhi. Each chapter with distinctive mathematical model also has numerical results to support the efficacy of these models. Each model described in this book provides its unique prediction policy to reduce the spread of COVID-19. This book is beneficial for practitioners, educators, researchers and policymakers handling the crisis of COVID-19 pandemic.

Computational Modelling and Imaging for SARS-CoV-2 and COVID-19

Author : S. Prabha
Publisher : CRC Press
ISBN 13 : 1000439372
Total Pages : 144 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Computational Modelling and Imaging for SARS-CoV-2 and COVID-19 by : S. Prabha

Download or read book Computational Modelling and Imaging for SARS-CoV-2 and COVID-19 written by S. Prabha and published by CRC Press. This book was released on 2021-09-02 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to present new computational techniques and methodologies for the analysis of the clinical, epidemiological and public health aspects of SARS-CoV-2 and COVID-19 pandemic. The book presents the use of soft computing techniques such as machine learning algorithms for analysis of the epidemiological aspects of the SARS-CoV-2. This book clearly explains novel computational image processing algorithms for the detection of COVID-19 lesions in lung CT and X-ray images. It explores various computational methods for computerized analysis of the SARS-CoV-2 infection including severity assessment. The book provides a detailed description of the algorithms which can potentially aid in mass screening of SARS-CoV-2 infected cases. Finally the book also explains the conventional epidemiological models and machine learning techniques for the prediction of the course of the COVID-19 epidemic. It also provides real life examples through case studies. The book is intended for biomedical engineers, mathematicians, postgraduate students; researchers; medical scientists working on identifying and tracking infectious diseases.

Exploring Susceptible-Infectious-Recovered (SIR) Model for COVID-19 Investigation

Author : Rahul Saxena
Publisher : Springer Nature
ISBN 13 : 9811941750
Total Pages : 63 pages
Book Rating : 4.8/5 (119 download)

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Book Synopsis Exploring Susceptible-Infectious-Recovered (SIR) Model for COVID-19 Investigation by : Rahul Saxena

Download or read book Exploring Susceptible-Infectious-Recovered (SIR) Model for COVID-19 Investigation written by Rahul Saxena and published by Springer Nature. This book was released on 2022-09-02 with total page 63 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book focuses on mathematical modelling of COVID-19 pandemic using the Susceptible, Infectious, and Recovered (SIR) model. The predictive modelling of the disease, with the exact facts and figures, provides a ground to reason about growing trends and its future trajectory. The book emphasizes on how the pandemic actually spreads out, lockdown impact analysis, and future course of actions based on mathematical calculations. Moreover, since COVID-19 spread outburst has been twice, the intensity studies and comparative analysis of the two waves of COVID-19 are another interesting feature of the book content. The book is a knowledge base for various researchers and academicians to dive into the detailing of the COVID spread (mathematical) model and understand how it could be explored to draw outcomes. To represent the factual information and analytical results effectively, graphical and diagrammatic representations have been appended at appropriate places. To keep the explanation simple and yet concrete, mathematical concepts have also been introduced; to carry out analysis to generate results for understanding the viral dynamics.

Assessing COVID-19 and Other Pandemics and Epidemics using Computational Modelling and Data Analysis

Author : Subhendu Kumar Pani
Publisher : Springer Nature
ISBN 13 : 3030797538
Total Pages : 416 pages
Book Rating : 4.0/5 (37 download)

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Book Synopsis Assessing COVID-19 and Other Pandemics and Epidemics using Computational Modelling and Data Analysis by : Subhendu Kumar Pani

Download or read book Assessing COVID-19 and Other Pandemics and Epidemics using Computational Modelling and Data Analysis written by Subhendu Kumar Pani and published by Springer Nature. This book was released on 2021-12-13 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book comprehensively covers the topic of COVID-19 and other pandemics and epidemics data analytics using computational modelling. Biomedical and Health Informatics is an emerging field of research at the intersection of information science, computer science, and health care. The new era of pandemics and epidemics bring tremendous opportunities and challenges due to the plentiful and easily available medical data allowing for further analysis. The aim of pandemics and epidemics research is to ensure high-quality, efficient healthcare, better treatment and quality of life by efficiently analyzing the abundant medical, and healthcare data including patient’s data, electronic health records (EHRs) and lifestyle. In the past, it was a common requirement to have domain experts for developing models for biomedical or healthcare. However, recent advances in representation learning algorithms allow us to automatically learn the pattern and representation of the given data for the development of such models. Medical Image Mining, a novel research area (due to its large amount of medical images) are increasingly generated and stored digitally. These images are mainly in the form of: computed tomography (CT), X-ray, nuclear medicine imaging (PET, SPECT), magnetic resonance imaging (MRI) and ultrasound. Patients’ biomedical images can be digitized using data mining techniques and may help in answering several important and critical questions related to health care. Image mining in medicine can help to uncover new relationships between data and reveal new and useful information that can be helpful for scientists and biomedical practitioners. Assessing COVID-19 and Other Pandemics and Epidemics using Computational Modelling and Data Analysis will play a vital role in improving human life in response to pandemics and epidemics. The state-of-the-art approaches for data mining-based medical and health related applications will be of great value to researchers and practitioners working in biomedical, health informatics, and artificial intelligence..

Mathematical Modeling and Intelligent Control for Combating Pandemics

Author : Zakia Hammouch
Publisher : Springer Nature
ISBN 13 : 3031331834
Total Pages : 278 pages
Book Rating : 4.0/5 (313 download)

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Book Synopsis Mathematical Modeling and Intelligent Control for Combating Pandemics by : Zakia Hammouch

Download or read book Mathematical Modeling and Intelligent Control for Combating Pandemics written by Zakia Hammouch and published by Springer Nature. This book was released on 2023-09-11 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in this carefully curated volume, present cutting-edge research in applied mathematical modeling for combating COVID-19 and other potential pandemics. Mathematical modeling and intelligent control have emerged as powerful computational models and have shown significant success in combating any pandemic. These models can be used to understand how COVID-19 or other pandemics can spread, analyze data on the incidence of infectious diseases, and predict possible future scenarios concerning pandemics. This book also discusses new models, practical solutions, and technological advances related to detecting and analyzing COVID-19 and other pandemics based on intelligent control systems that assist decision-makers, managers, professionals, and researchers. Much of the book focuses on preparing the scientific community for the next pandemic, particularly the application of mathematical modeling and intelligent control for combating the Monkeypox virus and Langya Henipavirus.

COVID-19 Epidemiology and Virus Dynamics

Author : Till D. Frank
Publisher : Springer Nature
ISBN 13 : 3030971783
Total Pages : 367 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis COVID-19 Epidemiology and Virus Dynamics by : Till D. Frank

Download or read book COVID-19 Epidemiology and Virus Dynamics written by Till D. Frank and published by Springer Nature. This book was released on 2022-03-30 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses the COVID-19 pandemic from a quantitative perspective based on mathematical models and methods largely used in nonlinear physics. It aims to study COVID-19 epidemics in countries and SARS-CoV-2 infections in individuals from the nonlinear physics perspective and to model explicitly COVID-19 data observed in countries and virus load data observed in COVID-19 patients. The first part of this book provides a short technical introduction into amplitude spaces given by eigenvalues, eigenvectors, and amplitudes.In the second part of the book, mathematical models of epidemiology are introduced such as the SIR and SEIR models and applied to describe COVID-19 epidemics in various countries around the world. In the third part of the book, virus dynamics models are considered and applied to infections in COVID-19 patients. This book is written for researchers, modellers, and graduate students in physics and medicine, epidemiology and virology, biology, applied mathematics, and computer sciences. This book identifies the relevant mechanisms behind past COVID-19 outbreaks and in doing so can help efforts to stop future COVID-19 outbreaks and other epidemic outbreaks. Likewise, this book points out the physics underlying SARS-CoV-2 infections in patients and in doing so supports a physics perspective to address human immune reactions to SARS-CoV-2 infections and similar virus infections.

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

Author : William E Schiesser
Publisher : World Scientific
ISBN 13 : 9811222894
Total Pages : 109 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Computational Modeling Of The Covid-19 Disease: Numerical Ode Analysis With R Programming by : William E Schiesser

Download or read book Computational Modeling Of The Covid-19 Disease: Numerical Ode Analysis With R Programming written by William E Schiesser and published by World Scientific. This book was released on 2020-06-16 with total page 109 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Mathematical Modelling, Simulations, and AI for Emergent Pandemic Diseases

Author : Esteban A. Hernandez-Vargas
Publisher : Elsevier
ISBN 13 : 0323950647
Total Pages : 350 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Mathematical Modelling, Simulations, and AI for Emergent Pandemic Diseases by : Esteban A. Hernandez-Vargas

Download or read book Mathematical Modelling, Simulations, and AI for Emergent Pandemic Diseases written by Esteban A. Hernandez-Vargas and published by Elsevier. This book was released on 2023-03 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Modeling, Simulations, and Artificial Intelligence for Emergent Pandemic Diseases: Lessons Learned from COVID-19 includes new research, models and simulations developed during the COVID-19 pandemic into how mathematical methods and practice can impact future response. Chapters go beyond forecasting COVID-19, bringing different scale angles and mathematical techniques (e.g., ordinary differential and difference equations, agent-based models, artificial intelligence, and complex networks) which could have potential use in modeling other emergent pandemic diseases. A major part of the book focuses on preparing the scientific community for the next pandemic, particularly the application of mathematical modeling in ecology, economics and epidemiology. Readers will benefit from learning how to apply advanced mathematical modeling to a variety of topics of practical interest, including optimal allocations of masks and vaccines but also more theoretical problems such as the evolution of viral variants. Provides a comprehensive overview of the state-of-the-art in mathematical modeling and computational simulations for emerging pandemics Presents modeling techniques that go beyond COVID-19, and that can be applied to tailoring interventions to attenuate high death tolls Includes illustrations, tables and dialog boxes to explain highly specialized concepts and insights with complex algorithms, along with links to programming code

Mathematical Analysis of Infectious Diseases

Author : Praveen Agarwal
Publisher : Academic Press
ISBN 13 : 0323904580
Total Pages : 346 pages
Book Rating : 4.3/5 (239 download)

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Book Synopsis Mathematical Analysis of Infectious Diseases by : Praveen Agarwal

Download or read book Mathematical Analysis of Infectious Diseases written by Praveen Agarwal and published by Academic Press. This book was released on 2022-06-01 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Mathematical Analysis of Infectious Diseases updates on the mathematical and epidemiological analysis of infectious diseases. Epidemic mathematical modeling and analysis is important, not only to understand disease progression, but also to provide predictions about the evolution of disease. One of the main focuses of the book is the transmission dynamics of the infectious diseases like COVID-19 and the intervention strategies. It also discusses optimal control strategies like vaccination and plasma transfusion and their potential effectiveness on infections using compartmental and mathematical models in epidemiology like SI, SIR, SICA, and SEIR. The book also covers topics like: biodynamic hypothesis and its application for the mathematical modeling of biological growth and the analysis of infectious diseases, mathematical modeling and analysis of diagnosis rate effects and prediction of viruses, data-driven graphical analysis of epidemic trends, dynamic simulation and scenario analysis of the spread of diseases, and the systematic review of the mathematical modeling of infectious disease like coronaviruses. Offers analytical and numerical techniques for virus models Discusses mathematical modeling and its applications in treating infectious diseases or analyzing their spreading rates Covers the application of differential equations for analyzing disease problems Examines probability distribution and bio-mathematical applications

Mathematical Modeling in the Age of the Pandemic

Author : William P. Fox
Publisher : CRC Press
ISBN 13 : 1000395022
Total Pages : 174 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis Mathematical Modeling in the Age of the Pandemic by : William P. Fox

Download or read book Mathematical Modeling in the Age of the Pandemic written by William P. Fox and published by CRC Press. This book was released on 2021-06-09 with total page 174 pages. Available in PDF, EPUB and Kindle. Book excerpt: One cannot watch or read about the news these days without hearing about the models for COVID-19 or the testing that must occur to approve vaccines or treatments for the disease. The purpose of Mathematical Modeling in the Age of a Pandemic is to shed some light on the meaning and interpretations of many of the types of models that are or might be used in the presentation of analysis. Understanding the concepts presented is essential in the entire modeling process of a pandemic. From the virus itself and its infectious rates and deaths rates to explain the process for testing a vaccine or eventually a cure, the author builds, presents, and shows model testing. This book is an attempt, based on available data, to add some validity to the models developed and used, showing how close to reality the models are to predicting "results" from previous pandemics such as the Spanish flu in 1918 and more recently the Hong Kong flu. Then the author applies those same models to Italy, New York City, and the United States as a whole. Modeling is a process. It is essential to understand that there are many assumptions that go into the modeling of each type of model. The assumptions influence the interpretation of the results. Regardless of the modeling approach the results generally indicate approximately the same results. This book reveals how these interesting results are obtained.

Modeling and Simulation of Infectious Diseases

Author : Tarek I. Zohdi
Publisher : Springer Nature
ISBN 13 : 3031180534
Total Pages : 123 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Modeling and Simulation of Infectious Diseases by : Tarek I. Zohdi

Download or read book Modeling and Simulation of Infectious Diseases written by Tarek I. Zohdi and published by Springer Nature. This book was released on 2023-02-09 with total page 123 pages. Available in PDF, EPUB and Kindle. Book excerpt: The COVID-19 pandemic that started in 2019-2020 has led to a gigantic increase in modeling and simulation of infectious diseases. There are numerous topics associated with this epoch-changing event, such as (a) disease propagation, (b) transmission, (c) decontamination, and (d) vaccines. This is an evolving field. The targeted objective of this book is to expose researchers to key topics in this area, in a very concise manner. The topics selected for discussion have evolved with the progression of the pandemic. Beyond the introductory chapter on basic mathematics, optimization, and machine learning, the book covers four themes in modeling and simulation infectious diseases, specifically: Part 1: Macroscale disease propagation, Part 2: Microscale disease transmission and ventilation system design, Part 3: Ultraviolet viral decontamination, and Part 4: Vaccine design and immune response. It is important to emphasize that the rapid speed at which the simulations operate makes the presented computational tools easily deployable as digital twins, i.e., digital replicas of complex systems that can be inexpensively and safely optimized in a virtual setting and then used in the physical world afterward, thus reducing the costs of experiments and also accelerating development of new technologies.

Mathematical Modelling and Nonstandard Schemes for the Corona Virus Pandemic

Author : Sarah Marie Treibert
Publisher : Springer Nature
ISBN 13 : 3658359323
Total Pages : 260 pages
Book Rating : 4.6/5 (583 download)

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Book Synopsis Mathematical Modelling and Nonstandard Schemes for the Corona Virus Pandemic by : Sarah Marie Treibert

Download or read book Mathematical Modelling and Nonstandard Schemes for the Corona Virus Pandemic written by Sarah Marie Treibert and published by Springer Nature. This book was released on 2021-12-11 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the prediction of possible future scenarios concerning the COVID-19 pandemic. Based on the well-known SIR model by Kermack and McKendrick a compartment model is established. This model comprises its own assumptions, transition rates and transmission dynamics, as well as a corresponding system of ordinary differential equations. Making use of numerical methods and a nonstandard-finite-difference scheme, two submodels are implemented in Matlab in order to make parameter estimations and compare different scenarios with each other.

Mathematical modelling of the pandemic of 2019 novel coronavirus (COVID-19): Patterns, Dynamics, Prediction, and Control

Author : Hui-Jia Li
Publisher : Frontiers Media SA
ISBN 13 : 2889713865
Total Pages : 308 pages
Book Rating : 4.8/5 (897 download)

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Book Synopsis Mathematical modelling of the pandemic of 2019 novel coronavirus (COVID-19): Patterns, Dynamics, Prediction, and Control by : Hui-Jia Li

Download or read book Mathematical modelling of the pandemic of 2019 novel coronavirus (COVID-19): Patterns, Dynamics, Prediction, and Control written by Hui-Jia Li and published by Frontiers Media SA. This book was released on 2021-09-27 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Numerical Modeling of COVID-19 Neurological Effects

Author : William Schiesser
Publisher : CRC Press
ISBN 13 : 1000509982
Total Pages : 165 pages
Book Rating : 4.0/5 (5 download)

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Book Synopsis Numerical Modeling of COVID-19 Neurological Effects by : William Schiesser

Download or read book Numerical Modeling of COVID-19 Neurological Effects written by William Schiesser and published by CRC Press. This book was released on 2021-12-27 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.