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OverviewThe reproduction and spread of a virus during an epidemic proceeds when the virus attaches to a host cell and viral genetic material (VGM) (protein, DNA, RNA) enters the cell, then replicates, and perhaps mutates, in the cell. The movement of the VGM across the host cell outer membrane and within the host cell is a spatiotemporal dynamic process that is modeled in this book as a system of ordinary and partial differential equations (ODE/PDEs). The movement of the virus proteins through the cell membrane is modeled as a diffusion process expressed by the diffusion PDE (Fick’s second law). Within the cell, the time variation of the VGM is modeled as ODEs. The evolution of the dependent variables is computed by the numerical integration of the ODE/PDEs starting from zero initial conditions (ICs). The departure of the dependent variables from zero is in response to the virus protein concentration at the outer membrane surface (the point at which the virus binds to the host cell). The numerical integration of the ODE/PDEs is performed with 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 ODE/PDE dependent variables are displayed graphically with basic R plotting utilities. The R 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 ODE/PDE model, such as changes in the parameters and the form of the model equations. Full Product DetailsAuthor: William E. SchiesserPublisher: Springer Nature Switzerland AG Imprint: Springer Nature Switzerland AG Edition: 1st ed. 2022 Weight: 0.285kg ISBN: 9783030688677ISBN 10: 3030688674 Pages: 170 Publication Date: 03 December 2022 Audience: Professional and scholarly , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Manufactured on demand  We will order this item for you from a manufactured on demand supplier. Table of Contents1. Virus Protein ODE/PDE Models2. Implementation of the ODE/PDE Models3. Host Cell Proteins with Cross Diffusion4. Postulated Vaccine and Therapeutic 5. Detailed ODE/PDE Model AnalysisReviewsAuthor InformationWilliam E. Schiesser is Emeritus McCann Professor of Computational Biomedical Engineering, Biomolecular and Chemical Engineering, and Professor of Mathematics at Lehigh University. Tab Content 6Author Website:Countries AvailableAll regions |
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