12.Operations04.Differential equation modeling - sporedata/researchdesigneR GitHub Wiki
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Ordinary and partial differential equations are used to describe time-dependent phenomena with time modeled as a continuous variable, such as epidemics - see Analytical features of the SIR model and their applications to COVID-19
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Modeling of circadian rhythms - see Circadian Rhythm of Blood Pressure of Dipper and Non-dipper Patients With Essential Hypertension: A Mathematical Modeling Approach
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When time is modeled as a discrete unit, then one can use difference equations. - see Impaired Pulmonary V˙O2 Kinetics in Cystic Fibrosis Depend on Exercise Intensity
- Time-dependent variable, either continuous or discrete.
Ordinary differential equations deal involve models with a single variable, while partial differential equations (linear, separable, and exact) can be used to model multivariable and nonlinear phenomena. Solving a differential equation simply means to turn them into a simpler equation without the differential portion, so that the model becomes easier to manipulate, graph, and use for predictions.
- Julia package can be embedded in markdown files.
- Books
- Articles combining theory and scripts
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[1] Soetaert K, Cash J, Mazzia F. Solving Differential Equations in R. Springer Science & Business Media; 2012 Jun 6.
[2] Schiesser WE. Schiesser WE. Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R. John Wiley & Sons; 2014 Feb 24.
[3] Schiesser WE. Schiesser WE.Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R. John Wiley & Sons; 2014 Feb 24.