Numerically solving non-linear algebraic equations

Questions
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1

Hello, I can not solve the system. Can any one help me with that? Thanks.

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equilibrium.nb (8.83 KB)
equilibrium.pdf (47.2 KB)

2

What kind of solution would you expect from NSolve?

3

Hello Daniel Lichtblau ,Thank you for your reply.I expect all solutions of the systems.In my system,
S, e, I1, I2 and R are unknowns except the others.I can not see the results since the running of the code does not finish by NSolve and Solve.Thanks.

4

What I mean, as noted in comments to the MSE x-post, is that it is impossible to return a numeric solution because several parameters are symbolic.

5

Please ignore NSolve. Solve does not give any solution,too.

6

I wonder if there are no solutions because of the following:

eq = Expand[{f1[S, e, I1, I2, R] == 0,
    f2[S, e, I1, I2, R] == 0,
    f3[S, e, I1, I2, R] == 0,
    f4[S, e, I1, I2, R] == 0,
    f5[S, e, I1, I2, R] == 0}];

Solve[eq[[{1, 2}]], {I1, I2}]
(* {} *)

If there are no solutions for I1 and I2 using just the first two equations, then adding additional equations can’t help. Of course, the fact that in the first two equations are both functions of I1+I2 might negate that conclusion.

7

Hello, Jim Baldwin;
Thank you for your reply. I guess the idea in your mind is the substitution method.
By the way, the followings give result:

Solve[eq[[{1, 3}]], {I1, I2}]
Solve[eq[[{1, 4}]], {I1, I2}]
Solve[eq[[{1, 5}]], {I1, I2}]
Solve[eq[[{2, 3}]], {I1, I2}]
Solve[eq[[{2, 4}]], {I1, I2}]
Solve[eq[[{2, 5}]], {I1, I2}]