File:Graph_SIR_model_without_vital_dynamics.svg
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Summary
DescriptionGraph SIR model without vital dynamics.svg |
English: Basic SIR system:
dS/dt = -βIS/N dI/dt = βIS/N-γI dR/dt = γI Initial Conditions: S(0)=3000000, I(0)=1, R(0)=0 Parameters: β=0.001, γ=0.07, N=3400000, t∈[0,60], step size=0.5 Yellow → Susceptible, Maroon → Infectious, Teal → Recovered |
Date | |
Source | File:Sirsys-p9.png |
Author | Bye~commonswiki |
Clear[IC, a, b, h, i, m, n, f, NN, β, γ];
IC = {3000000, 1, 0}; m = Length[IC];
a = 0; b = 60; h = 0.5;
NN = 1;
n = (b - a)/h;
β = 0.001; γ = 0.1;
f[1, t_, S_, I_, R_] := -((β I S)/NN);
f[2, t_, S_, I_, R_] := (β I S)/NN - γ I;
f[3, t_, S_, I_, R_] := γ I;
Clear[t, k1, k2, k3, k4, w];
t[i_] := a + i*h;
For[i = 1, i <= m, i++, w[i, 0] = IC[[i]]];
k1[i_, j_] := h*(f @@ Flatten[{i, t[j - 1], Table[w[k, j - 1], {k, 1, m}]}]);
k2[i_, j_] := h*(f @@ Flatten[{i, t[j - 1] + h/2, Table[w[k, j - 1] + k1[k, j]/2, {k, 1, m}]}]);
k3[i_, j_] := h*(f @@ Flatten[{i, t[j - 1] + h/2, Table[w[k, j - 1] + k2[k, j]/2, {k, 1, m}]}]);
k4[i_, j_] := h*(f @@ Flatten[{i, t[j - 1] + h, Table[w[k, j - 1] + k3[k, j], {k, 1, m}]}]);
w[i_, j_] := w[i, j] = w[i, j - 1] + (k1[i, j] + 2*k2[i, j] + 2*k3[i, j] + k4[i, j])/6
t1 = Table[Table[{t[j], w[i, j]}, {j, 0, n}], {i, 1, m}](*//TableForm*);
DkYellow = RGBColor[.808, .808, .192];
Teal = RGBColor[0, .5, .5];
Maroon = RGBColor[.5, 0, 0];
ListPlot[t1, PlotMarkers -> {Automatic, Scaled[0.01]}, PlotStyle -> {DkYellow, Maroon, Teal}, AspectRatio -> 420/560]
Licensing
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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31 March 2020
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 23:46, 31 March 2020 | 964 × 723 (206 KB) | GregoryKaiser | Uploaded a work by https://commons.wikimedia.org/wiki/User:Bye~commonswiki from https://en.wikipedia.org/w/index.php?title=File:Sirsys-p9.png&gettingStartedReturn=true with UploadWizard |
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Width | 771pt |
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Height | 578pt |