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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
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_]:=-((βIS)/NN);
f[2,t_,S_,I_,R_]:=(βIS)/NN-γI;
f[3,t_,S_,I_,R_]:=γI;
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

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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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