% Understanding the behaviour of systems pharmacology
% models: mathematical analysis of differential equations
% Suruchi Bakshi, Elizabeth C. de Lange, Piet H. van der Graaf, Meindert
% Danhof, and Lambertus A. Peletier


% Run the pool model with PF with various constant concentrations of the
% drug
% Generates figure 4 in the manuscript

function y=snoeck()
global D;

 
t=linspace(0,100,100000);
kr=0.091;kel=2.2;ks=26;Smax=66;SC50=22;
R0=ks/kel;ka=0.2;
R0=ks/kel;P0=ks/kr;
D=0;
[t1,x1]=ode23s(@feedback,[0 10000],[P0 R0]);
D=3;
[t2,x2]=ode23s(@feedback,[0 10000],[P0 R0]);
D=0.03;
[t3,x3]=ode23s(@feedback,[0 10000],[P0 R0]);
D=0.1;
[t4,x4]=ode23s(@feedback,[0 10000],[P0 R0]);
D=0.3;
[t5,x5]=ode23s(@feedback,[0 10000],[P0 R0]);

p_mesh = 0:1:400;
r_mesh = 0:1:70;
p_null = ks/kr.*ones(71,1);
r_null = kr.*p_mesh./kel;

figure(1); set(gca,'Fontsize',16); hold on; plot(t2,x2(:,2)/R0,'r',t2,x2(:,1)/P0,'b',t,1+0*t,'k--','LineWidth',2); xlabel('Time (h)'); ylabel('\it{R/R_0} & \it{P/P_0}'); axis([0 35 0 6]);% For dose = 3.
figure(2); set(gca,'Fontsize',16); hold all; plot(p_null./P0,r_mesh./R0,':k'); plot(p_mesh./P0,r_null./R0,'--k'); plot(x2(:,1)./P0,x2(:,2)./R0,'r','Linewidth',2); ylabel('\it{R/R_{0}}'); xlabel('\it{P/P_{0}}');
figure(2); legend('\it{\Gamma_P}','\it{\Gamma_R}','Orbit')

function xdot = feedback(t,x)
global D;
kr=0.091;kel=2.2;ks=26;Smax=66;SC50=22;R0=ks/kel;ka=0.2;
s=D*exp(-ka*t);
Emax=0;
xdot(1)= ks - kr*(1+Smax*s/(SC50+s))*x(1); % Lactotroph PRL
xdot(2)= kr*(1+Smax*s/(SC50+s))*x(1)- kel*x(2); % Plasma PRL
xdot = xdot';