MaplePrimes - answers and comments on Question, Data fitting to SIR model

Misprint and maxfun

Markiyan Hirnyk — Wed, 28 Nov 2012 13:02:51 Z

It should be initialvalues instead of intialvalues in the following command:

> params := NonlinearFit(Vcompute, iV, tV, output = parametervalues, initialvalues = [.5, .3]);
Error, (in Statistics:-NonlinearFit) cannot evaluate the solution further right of 0.14196195e-1, maxfun limit exceeded (see ?dsolve,maxfun for details)

I tried to increase maxfun

but it doesn't help

Error, (in Statistics:-NonlinearFit) cannot evaluate the solution further right of .92020862, maxfun limit exceeded (see ?dsolve,maxfun for details)
Data_fit1.mw

A different approach

Preben Alsholm — Wed, 28 Nov 2012 21:10:47 Z

I used a slightly different approach. SSQ is the sum of squares of the differences between the iV values and the i-values from the model. You will see that your initial guess is not very good.

(That may account for the problems NonlinearFit is having, but maybe not quite. NonlinearFit doesn't even return a result (in the time I allotted) when given the parameter values found below as initialvalues (with maxfun=0 in dsolve). Without maxfun=0 NonlinearFit complained that it couldn't go beyond 12.276 and the parameters obtained at that time were beta = 0.028879..., alpha = -.59691..., which are definitely lousy.)
Please also see addendum at bottom!

With everything above N defined as before, you can do as follows:

N := dsolve(sys, numeric, parameters = [beta, alpha], output = listprocedure);
ip:=subs(N,i(t));
SSQ:=proc(beta,alpha) local j;
N(parameters=[beta,alpha]);
add((ip(j)-iV[j])^2,j=1..len)
end proc;
SSQ(.5,.3);
plot3d(SSQ,0..0.2,0..0.5,axes=boxed,labels=[beta,alpha,SSQ]);
plot3d(SSQ,0..0.01,0..0.5,axes=boxed,labels=[beta,alpha,SSQ]);
contourplot(SSQ,0.002..0.008,0.2..0.5,labels=[beta,alpha],contours=50);
res:=Minimize(SSQ,0.002..0.008,0.2..0.5);
res[2];
N(parameters=convert(res[2],list));

odeplot(N,[t,i(t)],1..len,color=blue):
display(%,pp);

Addendum.
Again with everything above N defined as before, you can use the Matrix form referred to in the help page for NonlinearFit as follows, where again I use the default output from dsolve/numeric, i.e. procedurelist.

N1 := dsolve(eval(sys), {i(t), r(t), s(t)}, numeric, parameters = [beta, alpha]);
Vcompute := proc (t1, beta, alpha)
N1('parameters' = [beta, alpha]);
eval(i(t), N1(t1))
end proc;
TI:=Matrix([tV,iV]);
f:=proc(p, v, i) Vcompute(v[i,1],p[1],p[2])-v[i,2] end proc:
NonlinearFit(2,f,TI,initialvalues=);
#Notice that I have changed Vcompute slightly in order to make the implicit subtleties in Joe Riel's Vcompute explicit.
# t is the global t appearing in the output from e.g. N1(0.1). t1 is the formal parameter in the procedure.

DirectSearch package

maple fan — Thu, 13 Dec 2012 05:20:40 Z

who can make this parameter estimation with DirectSearch package?

thank you very much.

Didn´t see that. But i still think

kierstejn — Wed, 28 Nov 2012 18:19:54 Z

Didn´t see that. But i still think my problem is caused by the proc.

Have you got

Markiyan Hirnyk — Wed, 28 Nov 2012 19:19:50 Z

@kierstejn some arguments for it?

Parameter estimation

kierstejn — Fri, 30 Nov 2012 04:30:43 Z

This is really great!!! The first part works well, but there is just one other problem.

When i use the top part(SSQ method) on different data with another set of initial conditions, i cant find the proper parameters that fit my data.

Tried the method on a set of real data from the epidemic "the Great Plague of London" during 1665, but couldn´t figure out the value of beta and alpha. The number of susceptibles is 460.000 and the number infected is 10 at t(0).

London_plague.mw

It is especially the 3d and contour plot that makes no sense to me, no matter what interval i choose.

Is there an easy way to estimate the interval for my parameters, beta and alpha, when plotting my data to an abitrary set of data?? Preferably without using the 3d and contour plot, because it takes years for maple to calculate the plot on my pc??