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