ODE/PDE Analysis of Antibiotic/Antimicrobial Resistance

Programming in R

William E. Schiesser

• Publisher: Academic Press
• Year: 2020
• ISBN:
  9780128242506
• Topic: Biological Sciences
• Subtopic: Biotechnology
• Index: Biological Sciences

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

1: Introductory ODE model

Abstract

Antibiotic resistance occurs when germs like bacteria and fungi develop the ability to defeat the drugs designed to kill them. That means the germs are not killed and continue to grow.

In this chapter, a system of four ordinary differential equations (ODEs) to model antibiological resistance is developed. The dependent variables of the ODEs are listed next.

$s(t)$

population of bacteria susceptible to antibiotics

$r(t)$

population of bacteria resistant to antibiotics

$p(t)$

number of plasmids

$c(t)$

concentration of dissolved antibiotics in the host medium

The numerical integration of the ODEs gives $s(t)$

, $r(t)$

, $p(t)$

, $c(t)$

as a function of time, t.

Keywords

Antibiotic resistance (ABR); Antimicrobial resistance (AMR); Mathematical model; Ordinary differential equation (ODE); Numerical integration; R programming

Introduction

General background statements concerning antibiotic/antimicrobial resistance follow [2].

From CDC:

Antibiotic resistance happens when germs like bacteria and fungi develop the ability to defeat the drugs designed to kill them. That means the germs are not killed and continue to grow.

Antibiotic res...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Preface
• 1: Introductory ODE model
• 2: Analysis of the ODE model equations
• 3: ODE analysis of antibiotic/antimicrobial resistance
• 4: Introductory PDE model
• 5: Parameter analysis of the PDE model
• 6: Parameter time variation
• A1: Functions dss004, dss044
• Index