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File:SIS System Graph.svg

Original file ‎(SVG file, nominally 1,136 × 853 pixels, file size: 165 KB)

Captions

Captions

Yellow=Susceptible, Maroon=Infected

Summary

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Description
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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Creative Commons CC-Zero 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.

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current06:03, 1 April 2020Thumbnail for version as of 06:03, 1 April 20201,136 × 853 (165 KB)GregoryKaiser (talk | contribs)Uploaded a work by https://commons.wikimedia.org/wiki/User:Bye~commonswiki from https://commons.wikimedia.org/wiki/File:Sissys.png with UploadWizard

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