Curve fitting SIR model (ODEs)

Fitting SIR model, ODEs

Fits the evolution in differential equations.

2024.Nov.25 06:49:10

File to upload

Such as dataSIR.xlsx (data table)

Data table

0	0.9669	0.0101	0
0.122	0.9526	0.0123	0.002
0.245	0.9519	0.0136	0.0047
0.367	1.0015	0.0164	0.0075
0.49	1.0087	0.0195	0.0104
0.612	0.9979	0.0244	0.0145
0.735	0.9277	0.028	0.0196
0.857	0.8891	0.0341	0.0245
0.98	1.0053	0.0385	0.0319
1.102	0.9074	0.0456	0.0426
1.224	0.8674	0.0536	0.0498
1.347	0.8717	0.0637	0.0593
1.469	0.8708	0.0703	0.0715
1.592	0.8433	0.0849	0.0862
1.714	0.8188	0.0884	0.101
1.837	0.797	0.1008	0.114
1.959	0.7715	0.1146	0.1421
2.082	0.7054	0.1192	0.1643
2.204	0.7025	0.1285	0.1794
2.327	0.677	0.1359	0.2115
2.449	0.6203	0.1504	0.2415
2.571	0.5959	0.1486	0.2616
2.694	0.5738	0.16	0.2943
2.816	0.5349	0.1602	0.3134
2.939	0.503	0.1545	0.3671
3.061	0.4629	0.1547	0.3807
3.184	0.4295	0.1514	0.4106
3.306	0.4177	0.1417	0.4369
3.429	0.3808	0.1473	0.455
3.551	0.385	0.1424	0.4694
3.673	0.3578	0.1277	0.5152
3.796	0.3346	0.1221	0.5271
3.918	0.3118	0.1196	0.5822
4.041	0.321	0.1131	0.5497
4.163	0.309	0.1017	0.6336
4.286	0.2932	0.0975	0.5949
4.408	0.2902	0.0894	0.6096
4.531	0.2729	0.0802	0.6155
4.653	0.2609	0.0761	0.6572
4.776	0.2571	0.07	0.6187
4.898	0.2555	0.062	0.6615
5.02	0.2233	0.0565	0.6811
5.143	0.2449	0.0495	0.6987
5.265	0.2257	0.0471	0.7523
5.388	0.2384	0.045	0.7601
5.51	0.2247	0.039	0.739
5.633	0.219	0.0349	0.7261
5.755	0.2229	0.0328	0.7466
5.878	0.2199	0.0282	0.7765
6	0.2276	0.0258	0.7389

Data (matrix or 'csv').

Rate initial guesses

Initial guesses for the rate constants (β, γ).

Computation mode

Verify Optimize Opt. bounded

Mode ("bounded": ≮ 0), and termination tolerance.

Method

RK45 RK23 DOP853 Radau BDF LSODA

Method of integration.

Show values

Show graph coordinates.

Seeks the rate constants for the evolution by integrating its ODEs, from the initial values at t = 0 . It is: S' = −β S I; I' = β S I −γ I; R' = γ I. Integration is by Python 'scipy' module solver solve_ivp.

Files involved: P-curfitSIR.php (this one), CurfitSIR.php, curfitSIR.py.

Draws plots of the integrated functions vs. time.

Computation structure — A PHP file (this page: 'P-curfitSIR.php') calls (via 'action=...') an intermediate PHP file ('CurfitSIR.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: FittingSIRmodel

• (Wikipedia) PHP (from Personal Home Page)

• Python module 'scipy' solver scipy.integrate.solve_ivp.

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

• 1936-08-18: Kovács, László György (†2013-07-28, 76 yrs.)

http://web.ist.utl.pt/~mcasquilho/randomkinet/curfitSIR/P-curfitSIR.php
Created: 2024-08-18 — Last modified: 2024-08-24