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Re: SIR epidemic Model

  • To: mathgroup at smc.vnet.net
  • Subject: [mg36277] Re: SIR epidemic Model
  • From: "Kevin J. McCann" <kjm at KevinMcCann.com>
  • Date: Thu, 29 Aug 2002 01:38:04 -0400 (EDT)
  • References: <aki0v3$i76$1@smc.vnet.net>
  • Reply-to: kjm at KevinMcCann.com
  • Sender: owner-wri-mathgroup at wolfram.com

Majid,

I separately sent you a nb that addresses the numerical curve fit of an 
NDSolve result. I have had this and have used the technique for a long 
time; the example, however, did not originate with me. Apologies to the 
original author - lost in the mists of mind and time.

Kevin

Abdelmajid Khelil wrote:

> 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


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