% Created by Nick Fidalgo, Chris Gatesman, Phillip Less, Brett Peters, Samantha Sandwick, and Alex Shetler
% Dimensional solutions for 2,3,4 at fixed A(t) parameters
% Hill function parameters
K_m = .0003502;
K_5 = 55.33;
om = 1;
% Parameters
beta = .004;
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_N = 174;
E_N = 45;



tspan_2 = linspace(0,21);
S0_2 = [B_0;(D_0/B_0);E_0];

t = tspan_2;

tspan_3 = tspan_2;
S0_3 = S0_2;

tspan_4 = linspace(0,21);
S0_4 = [B_0;(D_0/B_0);E_0;F_0];

% A(t) parameters and dosages
A_0 = 46511.17195379639;
a = .2349288;
alpha = a;

figure 
[t_2,H_2] = ode45(@(t,s) hill_M2(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a),tspan_2,S0_2);
[t_3,H_3] = ode45(@(t,s) hill_m3(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a,nu),tspan_3,S0_3);
[t_4,H_4] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan_4,S0_4);
A = A_0*exp(-a*t);


plot(t_2,H_2(:,1),'-.','Linewidth',1.3, 'Color', '#135513')
hold on
plot(t_3,H_3(:,1),':','Linewidth',1.3,'Color', 'blue')
hold on
plot(t_4,H_4(:,1),'--','Linewidth',1.3','Color', 'red', 'Linewidth',1.3')


title('Healthy Hepatocytes', 'FontSize', 18,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
legend('Model 2', 'Model 3', 'Model 4', 'Interpreter','Latex', 'FontSize', 12)
figure

[t_2,H_2] = ode45(@(t,s) hill_M2(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a),tspan_2,S0_2);
[t_3,H_3] = ode45(@(t,s) hill_m3(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a,nu),tspan_3,S0_3);
[t_4,H_4] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan_4,S0_4);

plot(t_2,H_2(:,2),'-.','Linewidth',1.3,'Color', '#135513', 'Linewidth',1.3')
hold on
plot(t_3,H_3(:,2),':', 'Linewidth',1.3', 'Color', 'blue')
hold on
plot(t_4,H_4(:,2),'--', 'Linewidth',1.3', 'Color', 'red')
title('Damaged Hepatocytes', 'FontSize', 18,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
legend('Model 2', 'Model 3', 'Model 4', 'Interpreter','Latex', 'FontSize', 12)
figure

[t_4,H_4] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan_4,S0_4);

plot(t_4,H_4(:,3),'--', 'Linewidth',1.3', 'Color', 'red')
title('ALT in the Liver','Interpreter','Latex')
xlabel('Days', 'FontSize',15,'Interpreter','Latex')
legend('Model 4', 'Interpreter','Latex', 'FontSize', 12)
figure

[t_2,H_2] = ode45(@(t,s) hill_M2(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a),tspan_2,S0_2);
[t_3,H_3] = ode45(@(t,s) hill_m3(t,s,K_m,K_5,om,sig,gam,xi,phi,A_0,a,nu),tspan_3,S0_3);
[t_4,H_4] = ode45(@(t,s) hill_m4(t,s,K_m,K_5,om,sig,gam,xi,phi,nu,mu,A_0,a),tspan_4,S0_4);


plot(t_2,H_2(:,3),'-.','Linewidth',1.3, 'Color', '#135513', 'Linewidth',1.3')
hold on
plot(t_3,H_3(:,3),':', 'Linewidth',1.3', 'Color', 'blue')
hold on
plot(t_4,H_4(:,4),'--', 'Linewidth',1.3', 'Color', 'red')
title('Molecules of ALT in the Serum', 'FontSize', 18,'Interpreter','Latex')
xlabel('Days', 'FontSize', 15,'Interpreter','Latex')
legend('Model 2', 'Model 3', 'Model 4', 'Interpreter','Latex', 'FontSize', 12)