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Time Delay ODE/PDE Models - Applications in Biomedical Science and Engineering (Hardcover)
Loot Price: R3,388
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Time Delay ODE/PDE Models - Applications in Biomedical Science and Engineering (Hardcover)
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Time delayed (lagged) variables are an inherent feature of
biological/physiological systems. For example, infection from a
disease may at first be asymptomatic, and only after a delay is the
infection apparent so that treatment can begin.Thus, to adequately
describe physiological systems, time delays are frequently required
and must be included in the equations of mathematical models. The
intent of this book is to present a methodology for the formulation
and computer implementation of mathematical models based on time
delay ordinary differential equations (DODEs) and partial
differential equations (DPDEs). The DODE/DPDE methodology is
presented through a series of example applications, particularly in
biomedical science and engineering (BMSE). The computer-based
implementation of the example models is explained 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 DPDE
analysis is based on the method of lines (MOL), an established
general algorithm for PDEs, implemented with finite differences.
The example applications can first be executed to confirm the
reported solutions, then extended by variation of the parameters
and the equation terms, and even the forumulation and use of
alternative DODE/DPDE models. * Introduces time delay ordinary and
partial differential equations (DODE/DPDEs) and their numerical
computer-based integration (solution) * Illustrates the computer
implementation of DODE/DPDE models with coding (programming) in R,
a quality, open-source scientific programming system readily
available from the Internet * Applies DODE/DPDE models to
biological/physiological systems through a series of examples *
Provides the R routines for all of the illustrative applications
through a download link * Facilitates the use of the models with
reasonable time and effort on modest computers
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