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SIR epidemic Model

• To: mathgroup at smc.vnet.net
• Subject: [mg36240] SIR epidemic Model
• From: "Abdelmajid Khelil" <khelil at informatik.uni-stuttgart.de>
• Date: Wed, 28 Aug 2002 04:15:59 -0400 (EDT)
• Reply-to: <khelil at informatik.uni-stuttgart.de>
• Sender: owner-wri-mathgroup at wolfram.com

Hi everybody,

I solved the epidemic SIR ODE System
(<http://library.wolfram.com/webMathematica/MSP/Explore/Biology/Epidemic>
) numerically using NDSolve:

approxsolutions=NDSolve[{

s´[t]==-a s[t] i[t],
i´[t]==a s[t] i[t] - b i[t],
r´[t]==b i[t],

s[0]==700, i[0]==1, r[0]==0}, {i[t], s[t], r[t]}, {t,0,20}];

and this for fixed values of a and b.

Now I want to fit the solution for variable a and b to a list of given
points (fitting using the least squares method and the mathematica fonction
findminimum). My questions are
1- Is it possible to solve the ODE (with mathematica) for not fixed values
of a and b (so to get a parametric solution that depends on a and b)?
2- Is it possible in mathematica to use the fonction findminimum with the
(not explicit) solutions of the ODE, if not are there some other
alternatives?

In advance, thank you very much

Majid

• Follow-Ups:
  • Re: SIR epidemic Model
    • From: Daniel Lichtblau <danl@wolfram.com>