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I'm trying to create an SIR model of disease. These are the starting parameters, and i'd lake to be able to manipulate b and k. Thanks!

system = {y'[t] == -b y[t] i[t], i'[t] == b y[t] i[t] - k i[t], 
i[0] == 1.27*10^-6, r'[t] == k i[t], r[0] == 0, y[0] == 1}
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1 Answer 1

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system = {
   y'[t] == -b y[t] i[t], i'[t] == b y[t] i[t] - k i[t], r'[t] == k i[t],
   i[0] == 1.27*10^-6, r[0] == 0, y[0] == 1
 };

parfun = ParametricNDSolveValue[system, {y, i, r}, {t, 0, 60}, {b, k}];

Manipulate[
 Plot[
   Evaluate@Through[parfun[b, k][t]], {t, 0, 60},
   PlotLegends -> {"y[t]", "i[t]", "r[t]"}
 ],
 {{b, 3}, 0, 10}, {{k, 2}, 0, 10}
]

Mathematica graphics

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