Virus Host Cell Genetic Material Transport
Computational ODE/PDE Modeling with R
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Beschreibung
The focus of this book is a detailed discussion of the modeling of virus host cell interactions by exploring a variety of differential equation-based models frequently used in mathematical biology. The book provides numerical schemes, implemented in R, for Mathematical models of viral genetic material spread. The numerical schemes are implemented in R, an open source software that is freely available on the internet.
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.The 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.
Provides a detailed discussion on the reproduction and spread of a virus during an epidemic Presents research findings through detailed examples, rather than formal mathematics, so that the reader can execute themselves on modest computers Routines are programmed in R, a quality open-source computing system that is readily available as a download from the internet
Autor*in
William E. Schiesser
Themen in »Virus Host Cell Genetic Material Transport«
virus protein ODE/PDE model R routines ODE/MOL routine Host Cell Proteins Postulated vaccine Postulated therapeutic DNA RNA mutate virus replication single protein model numerical integration cellular membrane genetic material