ODE/PDE Analysis of Antibiotic/Antimicrobial Resistance (eBook)

Mathematical models for antibiotic/antimicrobial resistance based on ordinary and partial differential equations (ODE/PDEs) are presented in this book, starting with a basic ODE model in Chapter 1, and concluding with a detailed PDE model in Chapters 4 and 5 that gives the spatiotemporal distribution of four dependent variable components: (1) susceptible bacteria population density, (2) resistant bacteria population density, (3) plasmid number, and (4) antibiotic concentration.

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 antibiotic/antimicrobial models, such as changes in the ODE/PDE parameters (constants) and the form of the model equations.

• Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models
• Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to the mathematical model and algorithms
• Authored by a leading researcher and educator in PDE models

Dr. William E. Schiesser is Emeritus McCann Professor of Chemical and Biomolecular Engineering and Professor of Mathematics at Lehigh University, Bethlehem, PA, USA. He holds a PhD from Princeton University and a ScD (hon) from the University of Mons, Belgium. His research is directed toward numerical methods and associated software for ordinary, differential-algebraic and partial differential equations (ODE/DAE/PDEs), and the development of mathematical models based on ODE/DAE/PDEs. He is the author or coauthor of more than 16 books, and his ODE/DAE/PDE computer routines have been accessed by some 5,000 colleges and universities, corporations and government agencies.

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ODE/PDE Analysis of Antibiotic/Antimicrobial Resistance: Programming in R presents mathematical models for antibiotic/antimicrobial resistance based on ordinary and partial differential equations (ODE/PDEs). Sections cover the basic ODE model, the detailed PDE model that gives the spatiotemporal distribution of four dependent variable components, including susceptible bacteria population density, resistant bacteria population density, plasmid number, and antibiotic concentration. 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. As such, formal mathematics is minimized and no theorems and proofs are required. The PDE analysis is based on the method of lines (MOL), an established general algorithm for PDEs that is implemented with finite differences. 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. Routines can then be applied to variations and extensions of the antibiotic/antimicrobial models, such as changes in the ODE/PDE parameters (constants) and the form of the model equations. Includes PDE routines based on the method of lines (MOL) for computer-based implementation of PDE models Offers transportable computer source codes for readers in R, with line-by-line code descriptions as it relates to mathematical model and algorithms Authored by a leading researcher and educator in PDE models