%% Normalized Reduced Model
function xdot=glucfunnorm(t,x);
%   Glucose-Dependent Insulin Secretion reduced and normalized model
%   example call:  ode45('glucfunnorm',[0 4],[6/9.8;.3]);
global Vm Km Vs Ks Vmax2 K2 Vmax1 K1 L ko Io Go KI Ki tau n m

Vmx=tau*Vm/Km;
Vsx=tau*Vs/KI;
Ksx=tau*Ks/Km;
Vmax2x=tau*Vmax2/Km;
K2x=K2/Km;
Vmax1x=tau*Vmax1/Km;
K1x=K1/Km;
Lx=tau*L/Km;
kox=tau*ko;
Gox=Go/Km;
Kix=Ki/KI;
Gis=x(1,1);
Jis=x(2,1);
Gx=Gox;
Rm=(Vmx*Gis)/(1+Gis);
Rs=(Vsx*(Rm^4+Lx^4))/(Ksx^4+Rm^4+Lx^4);
I=Rs/kox;
Jinf=1/(I+1);
R1=(K1x*Vmax1x*(Gx-Gis)*I^n)/((K1x+Gx)*(K1x+Gis)*(Kix^n+I^n));
R2=(K2x*Vmax2x*(Gx*Jis^m-Gis))/((K2x+Gx)*(K2x+Gis));
xdot(1,1)=R1+R2-Rm;
xdot(2,1)=Jinf-Jis;