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Direct SIR model, ODEs
Computes the evolution in differential equations (no fitting).
2024.Nov.25 06:29:04
ti, tf Time range.
Rate constants Rate constants (β, γ).
Initial values IVP: initial.
Method        Method of integration.
Points N. of points in plot (from No. 0)
Show values Show graph coordinates.

Computes the evolution by integrating its ODEs, from given initial values. It is:  S' = −β S I; I' = β S I −γ I; R' = γ I.

ODEs

Integration is by Python 'scipy' module solver solve_ivp.

Files involved: P-directSIR.php (this one), DirectSIR.php, directSIR.py.

Draws plots of the integrated functions vs. time.

Computation structure — A PHP file (this page: 'P-directSIR.php') calls (via 'action=...') an intermediate PHP file ('DirectSIR.php'), which (through $_POST) sends the problem data as command line arguments to a Python script. This last does the computing, and makes 'system' call(s) to 'gnuplot', for the final (temporary) webpage.

Keywords: PHP, command line arguments, Python script, gnuplot.

References: Plate: DirectSIRmodel

• (Wikipedia) PHP (from Personal Home Page)

• Python module 'scipy' solver scipy.integrate.solve_ivp, accessed 02-Oct-2023.

• MOSAIC, Use of Basic Elements II – Ordinary Differential Equation System.

• Wolfram Research, Inc., Arnoud Buzing, The SIR Model for Spread of Disease, tf = 100, (β, γ) = (0.5 0.0714).

• D'Arienzo, M. and A. Coniglio, 2020, "Assessment of the SARS-CoV-2 basic reproduction number, R0, based on the early phase of COVID-19 outbreak in Italy", Biosafety and Health, 2:2, 57–59. DOI: https://doi.org/10.1016/j.bsheal.2020.03.004.

• 1881-08-01: Toeplitz, Otto (†1940-02-15, 58 yrs.).

 
 
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Created: 2024-08-01 — Last modified: 2024-08-26