% Created by Nick Fidalgo, Chris Gatesman, Phillip Less, Brett Peters, Samantha Sandwick, and Alex Shetler
% Re-dimensionalized results for 2,3,4
% Hill function parameters
K_m = .0003502;
K_5 = 55.33;
om = 1;

% Parameters
sig = 5;
gam = 483;
phi = .35;
xi = 1.8741*10^-4;
nu = 1;
mu = 15.75;

% Initial Conditions
B_0 = 1;
D_0 = 0;
E_0 = 1;
F_0 = 1;

B_D = 174;
E_D = 45;


tspan = linspace(0,21);
S0 = [B_0;(D_0/B_0);E_0];
S1 = [B_0;(D_0/B_0);E_0;F_0];


% A(t) parameters and dosages
P = [0 .3 .6 1.2 2.4 3.6 4.8;0 11.29 14.29 22.44 69.44 76.54 110.66;0 .82 .57 .58 .2 .3 .17];
[m,n] = size(P);

% Model Version 2
figure('Name', 'Model 2')
for i = 1:n
    % B(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    [t,H] = ode45(@(t,s) hill_M2(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a),tspan,S0);
    A = A_0*exp(-a*t);
    plot(t, B_D*H(:,1),'Linewidth',1.3)
    hold on
end
title('B(t): Healthy Hepatocytes', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg', '0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
ylabel('Healthy Cells (Billions)')

figure('Name', 'Model 2')
for i = 1:n
    % D(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    [t,H] = ode45(@(t,s) hill_M2(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a),tspan,S0);
    A = A_0*exp(-a*t);
    plot(t,B_D*H(:,2),'Linewidth',1.3)
    hold on
end
title('D(t): Damaged Hepatocytes', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg','FontSize',12,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
ylabel('Damaged Cells (Billions)')

figure('Name', 'Model 2')
for i = 1:n
    %E(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    [t,H] = ode45(@(t,s) hill_M2(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a),tspan,S0);
    A = A_0*exp(-a*t);
    plot(t,E_D*H(:,3),'Linewidth',1.3)
    hold on
end
title('E(t): Molecules of ALT in the Serum', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize',15,'Interpreter','Latex')
ylabel('ALT Molecules (IU)')

% Model version 3
% To recreate omega varation results:
% Uncomment fixed A_0 and a, comment out dose specific A_0, a, and p.
% Change n to be equal to 3
% Uncomment new om and the appropriate legend
figure('Name', 'Model 3')
for i = 1:n
    % B(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    %A_0 = 76.54;
    %a = .3;
    [t,H] = ode45(@(t,s) hill_m3(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a,nu),tspan,S0);
    A = A_0*exp(-a*t);
    plot(t,B_D*H(:,1),'-','Linewidth',1.3)
    hold on
end
title('B(t): Healthy Hepatocytes', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg', '0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
%legend('ω = 0.5','ω = 1.0','ω = 1.5', 'FontSize', 12)
ylabel('Healthy Cells (Billions)')

figure('Name', 'Model 3')
for i = 1:n
    % D(t)
    p = P(:,i);
    dose = p(1);
    %dose = 3.6;
    A_0 = p(2);
    %A_0 = 76.54;
    a = p(3);
    %a = .3;
    [t,H] = ode45(@(t,s) hill_m3(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a,nu),tspan,S0);
    A = A_0*exp(-a*t);
    plot(t,B_D*H(:,2),'-','Linewidth',1.3)
    hold on
end
title('D(t): Damaged Hepatocytes', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg','FontSize',12,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
%legend('ω = 0.5','ω = 1.0','ω = 1.5', 'FontSize', 12)
ylabel('Damaged Cells (Billions)')

figure('Name', 'Model 3')
for i = 1:n
    %E(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    %A_0 = 76.54;
    %a = .3;
    [t,H] = ode45(@(t,s) hill_m3(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a,nu),tspan,S0);
    A = A_0*exp(-a*t);
    plot(t,E_D*H(:,3),'-','Linewidth',1.3)
    hold on
end
title('E(t): Molecules of ALT in the Serum', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize',15,'Interpreter','Latex')
%legend('ω = 0.5','ω = 1.0','ω = 1.5', 'FontSize', 12)
ylabel('ALT Molecules (IU)')

% Model Version 4
figure('Name', 'Model 4')
for i = 1:n
    % B(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    [t,H] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan,S1);
    A = A_0*exp(-a*t);
    plot(t,B_D*H(:,1),'Linewidth',1.3)
    hold on
end
title('B(t): Healthy Hepatocytes', 'FontSize', 18, 'Interpreter','Latex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
ylabel('Healthy Cells (Billions)')

figure('Name', 'Model 4')
for i = 1:n
    % D(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    [t,H] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan,S1);
    A = A_0*exp(-a*t);
    plot(t,B_D*H(:,2),'Linewidth',1.3)
    hold on
end
title('D(t): Damaged Hepatocytes', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15)
ylabel('Damaged Cells (Billions)')

figure('Name', 'Model 4')
for i = 1:n
    %F(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    [t,H] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan,S1);
    A = A_0*exp(-a*t);
    plot(t,H(:,3),'Linewidth',1.3)
    hold on
end
title('F(t): Delay', 'FontSize', 18,'Interpreter','Laex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize',15,'Interpreter','Latex')
ylabel('ALT Moleclues (IU)')

figure('Name', 'Model 4')
for i = 1:n
    %E(t)
    p = P(:,i);
    dose = p(1);
    A_0 = p(2);
    a = p(3);
    [t,H] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan,S1);
    A = A_0*exp(-a*t);
    plot(t,E_D*H(:,4),'Linewidth',1.3)
    hold on
end
title('E(t): Molecules of ALT in the Serum', 'FontSize', 18,'Interpreter','Latex')
legend('0 mg/kg','0.3 mg/kg','0.6 mg/kg','1.2 mg/kg','2.4 mg/kg','3.6 mg/kg','4.8 mg/kg', 'FontSize', 12,'Interpreter','Latex')
xlabel('Days', 'FontSize',15,'Interpreter','Latex')
ylabel('ALT Molecules (IU)')