MATLAB: How to add a constraint to lsqcurvefit for estimated parameters

lsqcurvefit ode45

Hello I am using lsqcurvefit to estimate parameters a and b. The code is working but I would like the estimated value of a>b. How can I add this constraint? I used options=(x0(2)<x0(1)); but it is not working. Any ideas? Thanks
This is the code:
function modelfit
X_Data=[1,2,3,4,5,6,7,8,9,10,11];
Y_Data=[33,106,95,62,147,133,150,131,150,185,144];
INI=[1000,200,33];
T0=1;
TF=11;
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%Estimate parameters
xdata=X_Data;
ydata=Y_Data;
x0(1)=0.01;      %a
x0(2)=0.1;      %b
LB=[0 0];
UB=[1 1];
options=(x0(2)<x0(1));
x=lsqcurvefit(@Model,x0,xdata,ydata,LB,UB,options)
a=x(1)
b=x(2)
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

figure(1);
hold on
plot(T0+t,P,'r');
plot(X_Data,Y_Data,'b*');
axis([T0 TF 0 200]);
hold off
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  function [ydot]=modelfit(t,y)
  S=y(1);
  I=y(2);
  R=y(3);
  ydot(1) = -a*y(1)-y(2);
  ydot(2) =a*y(1)-y(2)-b*y(2);
  ydot(3) = b*y(2);
  ydot=ydot';
  end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function N=Model(x0,xdata)
%set up parameters
a=x0(1);
b=x0(2);
[t y] = ode45(@modelfit,[0:1:TF-T0],INI);
S=y(:,1);
I=y(:,2);
R=y(:,3);
P=R;
for i=1:length(xdata)
  ind=find(xdata(i)-T0==t);
  S=y(ind,1);
  I=y(ind,2);
  R=y(ind,3);
  N(i)=R;
end   
end  
end

Best Answer

You CAN do this directly with lsqcurvefit, IF you reparameterize the model in to form of the parameters [a,a+b].
Then all you need to do is set a lower bound for b of zero.
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