12.Operations04.Differential equation modeling - sporedata/researchdesigneR GitHub Wiki

1. Use cases: in which situations should I use this method?

  1. 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

  2. Modeling of circadian rhythms - see Circadian Rhythm of Blood Pressure of Dipper and Non-dipper Patients With Essential Hypertension: A Mathematical Modeling Approach

  3. 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

2. Input: what kind of data does the method require?

  • Time-dependent variable, either continuous or discrete.

3. Algorithm: how does the method work?

Model mechanics

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.

Reporting guidelines

Data science packages

Suggested companion methods

Learning materials

  1. Books
    • Solving Differential Equations in R [1].
    • Differential Equation Analysis in Biomedical Science and Engineering: Ordinary Differential Equation Applications with R [2]
    • Differential Equation Analysis in Biomedical Science and Engineering: Partial Differential Equation Applications with R [3].
  2. Articles combining theory and scripts
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4. Output: how do I interpret this method's results?

Mock conclusions or most frequent format for conclusions reached at the end of a typical analysis.

Tables, plots, and their interpretation

5. SporeData-specific

Templates

Data science functions

References

[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.

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