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# Epidemiology equilibria solved, but what happened??

var('beta gamma S I R N')

dS = - beta * S * I / N dI = beta * S * I / N - gamma * I dR = gamma * I

solve([dS == 0, dI == 0, dR == 0], [S, I, R]) [[S == r7, I == 0, R == r8]]

Why am i getting different values for S and R which correlate to how many times I run the code? At first I thought that it was because I did an interpolate above, but when I went and modified the code a bit at the beginning I was still left with increasing equilibria values.

the next run will be [[S == r9, I == 0, R == r10]] Does anyone know why this is happening??

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## 1 Answer

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The solution [[S == r7, I == 0, R == r8]] should be read as follows: the set of solutions is an infinite two-parameter space, which can be parametrized by two anonymous parameters r7 and r8 that Sage created for the purpose of describing the solution set. Each time you solve a new equation whose set of solutions is huge, Sage will create new parameters (symbolic variables) to serve as a parameters to describe the solutions set.

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Asked: 2016-11-20 09:59:00 +0200

Seen: 114 times

Last updated: Nov 20 '16