SIS_System_Graph.svg
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Summary
Description SIS System Graph.svg |
English:
Basic SIS system: dS/dt = -βIS/N + γI, dI/dt = βIS/N - γI
Initial Conditions: S(0) = 499, I(0) = 1 Parameters: β=0.001, γ=0.1, N=1, t∈[0,60], step size=0.5 |
Date | |
Source | File:Sissys.png |
Author | https://commons.wikimedia.org/wiki/User:Bye~commonswiki |
Graph generated from Mathematica
Clear[IC, a, b, h, i, m, n, f, NN, β, γ]; IC = {499, 1}; 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_] := -((β I S)/NN) + γ I; f[2, t_, S_, I_] := (β I S)/NN - 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]; Maroon = RGBColor[.5, 0, 0]; ListPlot[t1, PlotMarkers -> {Automatic, Scaled[0.01]}, PlotStyle -> {DkYellow, Maroon}, AspectRatio -> 420/560]
Licensing
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