I want to plot parameters and time , with influence three others paramaters , but i dont know how to plot

i have this matlab code ,

i want to make plotting like this picture

tau vs phi , in my code it is same label , but u from this picture is v from my code . I dont know how to plot tau as function of phi , whre phi is which loss of 10% x[4] in my code, according 0.6 to 0.54, so in interval of phi=[0,250] what time tau get decrease of x[4] from initial value 0.6 to 0.54. with variant of v . thank you

 function hdot = glioma0(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr)
    % Define the system of ODEs for glioma0
    hdot = zeros(7, 1);
    v = 0.0;
    Phi = 3.3e-3;

    H = 0;
    if x(6) > 0 || x(7) > 0
        H = 1;
    end

    hdot(1) = Pg * x(1) * (1 - x(1)) - beta1 * x(1) * (x(2) + x(3)) - (d10 + d11 * x(4) + d12 * x(7)) * (x(1) * x(6)) / (a1 + x(1));
    hdot(2) = Ps * x(2) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta2 * x(1) * x(2) - u * x(2) * H - v * H * x(2) - (d20 + d21 * x(4) + d22 * x(7)) * x(2) * x(6) / (a2 + x(2));
    hdot(3) = Pr * x(3) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta3 * x(1) * x(3) + u * x(2) * H - v * H * x(3);
    hdot(4) = mu * (x(2) + x(3)) + pe * x(4) * (1 - x(4)) - d4 * x(4) * x(7) / (a4 + x(4));

    if hdot(1) < 0
        hdot(5) = alpha * hdot(1) * x(5) - (d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    elseif hdot(1) > 0
        hdot(5) = -(d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    end
    hdot(6) = Phi - (psi + c1 * x(1) / (a1 + x(1)) + c2 * x(2) / (a2 + x(2)) + c5 * x(5) / (a5 + x(5))) * x(6);
    hdot(7) = delta - (gamma + c4 * x(4) / (a4 + x(4))) * x(7);
end

function hdot = glioma01(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr)
    % Define the system of ODEs for glioma01
    hdot = zeros(7, 1);
    v = 0.03;
    Phi = 3.3e-3;

    H = 0;
    if x(6) > 0 || x(7) > 0
        H = 1;
    end

    hdot(1) = Pg * x(1) * (1 - x(1)) - beta1 * x(1) * (x(2) + x(3)) - (d10 + d11 * x(4) + d12 * x(7)) * (x(1) * x(6)) / (a1 + x(1));
    hdot(2) = Ps * x(2) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta2 * x(1) * x(2) - u * x(2) * H - v * H * x(2) - (d20 + d21 * x(4) + d22 * x(7)) * x(2) * x(6) / (a2 + x(2));
    hdot(3) = Pr * x(3) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta3 * x(1) * x(3) + u * x(2) * H - v * H * x(3);
    hdot(4) = mu * (x(2) + x(3)) + pe * x(4) * (1 - x(4)) - d4 * x(4) * x(7) / (a4 + x(4));

    if hdot(1) < 0
        hdot(5) = alpha * hdot(1) * x(5) - (d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    elseif hdot(1) > 0
        hdot(5) = -(d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    end
    hdot(6) = Phi - (psi + c1 * x(1) / (a1 + x(1)) + c2 * x(2) / (a2 + x(2)) + c5 * x(5) / (a5 + x(5))) * x(6);
    hdot(7) = delta - (gamma + c4 * x(4) / (a4 + x(4))) * x(7);
end

function hdot = glioma1(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr)
    % Define the system of ODEs for glioma1
    hdot = zeros(7, 1);
    v = 0.003;
    Phi = 3.3e-3;

    H = 0;
    if x(6) > 0 || x(7) > 0
        H = 1;
    end

    hdot(1) = Pg * x(1) * (1 - x(1)) - beta1 * x(1) * (x(2) + x(3)) - (d10 + d11 * x(4) + d12 * x(7)) * (x(1) * x(6)) / (a1 + x(1));
    hdot(2) = Ps * x(2) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta2 * x(1) * x(2) - u * x(2) * H - v * H * x(2) - (d20 + d21 * x(4) + d22 * x(7)) * x(2) * x(6) / (a2 + x(2));
    hdot(3) = Pr * x(3) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta3 * x(1) * x(3) + u * x(2) * H - v * H * x(3);
    hdot(4) = mu * (x(2) + x(3)) + pe * x(4) * (1 - x(4)) - d4 * x(4) * x(7) / (a4 + x(4));

    if hdot(1) < 0
        hdot(5) = alpha * hdot(1) * x(5) - (d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    elseif hdot(1) > 0
        hdot(5) = -(d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    end
    hdot(6) = Phi - (psi + c1 * x(1) / (a1 + x(1)) + c2 * x(2) / (a2 + x(2)) + c5 * x(5) / (a5 + x(5))) * x(6);
    hdot(7) = delta - (gamma + c4 * x(4) / (a4 + x(4))) * x(7);
end

% Initial conditions
x0 = [0.6; 0.6; 0.0; 0.0; 0.6; 0.0; 0.0];

% Time span
t = 0:1:1000;

% Parameters
Pg = 0.0068;
Ps = 0.012;
Pr = 0.002;
pe = 0.002;
beta1 = 1.8e-2;
beta2 = 1.8e-3;
beta3 = 1.8e-3;
d4 = 0.71;
u = 0.01;
a1 = 1;
a2 = 1;
a4 = 1;
a5 = 1;
c1 = 0.0002;
c2 = 0.032;
c4 = 0.032;
c5 = 0.0012;
d10 = 4.7e-8;
d11 = 4.0e-8;
d12 = 3.9e-8;
d20 = 7.8e-2;
d21 = 0.04;
d22 = 7.5;
d50 = 4.7e-3;
d51 = 4.0e-3;
d52 = 3.9e-3;
tau = 0.15;
mu = 0.004;
psi = 0.01813;
delta = 2.4e-4;
gamma = 0.136;
alpha = 2;

% Solve the ODEs for glioma0
[t, y0] = ode45(@(t, x) glioma0(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr), t, x0);

% Solve the ODEs for glioma01
[t, y01] = ode45(@(t, x) glioma01(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr), t, x0);

% Solve the ODEs for glioma1
[t, y1] = ode45(@(t, x) glioma1(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr), t, x0);

% Plot the results
figure;
plot(t, y0(:, 5), 'r', 'LineWidth', 2, 'DisplayName', '\rho=0');
hold on;
plot(t, y1(:, 5), 'b', 'LineWidth', 2, 'DisplayName', '\rho=0.003');
plot(t, y01(:, 5), 'k', 'LineWidth', 2, 'DisplayName', '\rho=0.03');

% Add labels and legend
xlabel('Time (Days)');
ylabel('Concentration of Cell g_4(t)');
legend('Location', 'Best');
title('Glioma Model');
grid on;
hold off;

Answer 1

[Les Beckham]

Note that, in Matlab, functions must be defined at the end of a script.

Your code seems to run just fine after reordering it.

Can you please explain what isn't working the way you want it to?

This part of your question is very confusing:

tau vs phi , in my code it is same label , but u from this picture is v from my code . I dont know how to plot tau as function of phi , whre phi is which loss of 10% x[4] in my code, according 0.6 to 0.54, so in interval of phi=[0,250] what time tau get decrease of x[4] from initial value 0.6 to 0.54. with variant of v . thank you

% Initial conditions
x0 = [0.6; 0.6; 0.0; 0.0; 0.6; 0.0; 0.0];

% Time span
t = 0:1:1000;

% Parameters
Pg = 0.0068;
Ps = 0.012;
Pr = 0.002;
pe = 0.002;
beta1 = 1.8e-2;
beta2 = 1.8e-3;
beta3 = 1.8e-3;
d4 = 0.71;
u = 0.01;
a1 = 1;
a2 = 1;
a4 = 1;
a5 = 1;
c1 = 0.0002;
c2 = 0.032;
c4 = 0.032;
c5 = 0.0012;
d10 = 4.7e-8;
d11 = 4.0e-8;
d12 = 3.9e-8;
d20 = 7.8e-2;
d21 = 0.04;
d22 = 7.5;
d50 = 4.7e-3;
d51 = 4.0e-3;
d52 = 3.9e-3;
tau = 0.15;
mu = 0.004;
psi = 0.01813;
delta = 2.4e-4;
gamma = 0.136;
alpha = 2;

% Solve the ODEs for glioma0
[t, y0] = ode45(@(t, x) glioma0(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr), t, x0);

% Solve the ODEs for glioma01
[t, y01] = ode45(@(t, x) glioma01(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr), t, x0);

% Solve the ODEs for glioma1
[t, y1] = ode45(@(t, x) glioma1(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr), t, x0);

% Plot the results
figure;
plot(t, y0(:, 5), 'r', 'LineWidth', 2, 'DisplayName', '\rho=0');
hold on;
plot(t, y1(:, 5), 'b', 'LineWidth', 2, 'DisplayName', '\rho=0.003');
plot(t, y01(:, 5), 'k', 'LineWidth', 2, 'DisplayName', '\rho=0.03');

% Add labels and legend
xlabel('Time (Days)');
ylabel('Concentration of Cell g_4(t)');
legend('Location', 'Best');
title('Glioma Model');
grid on;
hold off;

 function hdot = glioma0(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr)
    % Define the system of ODEs for glioma0
    hdot = zeros(7, 1);
    v = 0.0;
    Phi = 3.3e-3;

    H = 0;
    if x(6) > 0 || x(7) > 0
        H = 1;
    end

    hdot(1) = Pg * x(1) * (1 - x(1)) - beta1 * x(1) * (x(2) + x(3)) - (d10 + d11 * x(4) + d12 * x(7)) * (x(1) * x(6)) / (a1 + x(1));
    hdot(2) = Ps * x(2) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta2 * x(1) * x(2) - u * x(2) * H - v * H * x(2) - (d20 + d21 * x(4) + d22 * x(7)) * x(2) * x(6) / (a2 + x(2));
    hdot(3) = Pr * x(3) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta3 * x(1) * x(3) + u * x(2) * H - v * H * x(3);
    hdot(4) = mu * (x(2) + x(3)) + pe * x(4) * (1 - x(4)) - d4 * x(4) * x(7) / (a4 + x(4));

    if hdot(1) < 0
        hdot(5) = alpha * hdot(1) * x(5) - (d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    elseif hdot(1) > 0
        hdot(5) = -(d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    end
    hdot(6) = Phi - (psi + c1 * x(1) / (a1 + x(1)) + c2 * x(2) / (a2 + x(2)) + c5 * x(5) / (a5 + x(5))) * x(6);
    hdot(7) = delta - (gamma + c4 * x(4) / (a4 + x(4))) * x(7);
end

function hdot = glioma01(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr)
    % Define the system of ODEs for glioma01
    hdot = zeros(7, 1);
    v = 0.03;
    Phi = 3.3e-3;

    H = 0;
    if x(6) > 0 || x(7) > 0
        H = 1;
    end

    hdot(1) = Pg * x(1) * (1 - x(1)) - beta1 * x(1) * (x(2) + x(3)) - (d10 + d11 * x(4) + d12 * x(7)) * (x(1) * x(6)) / (a1 + x(1));
    hdot(2) = Ps * x(2) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta2 * x(1) * x(2) - u * x(2) * H - v * H * x(2) - (d20 + d21 * x(4) + d22 * x(7)) * x(2) * x(6) / (a2 + x(2));
    hdot(3) = Pr * x(3) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta3 * x(1) * x(3) + u * x(2) * H - v * H * x(3);
    hdot(4) = mu * (x(2) + x(3)) + pe * x(4) * (1 - x(4)) - d4 * x(4) * x(7) / (a4 + x(4));

    if hdot(1) < 0
        hdot(5) = alpha * hdot(1) * x(5) - (d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    elseif hdot(1) > 0
        hdot(5) = -(d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    end
    hdot(6) = Phi - (psi + c1 * x(1) / (a1 + x(1)) + c2 * x(2) / (a2 + x(2)) + c5 * x(5) / (a5 + x(5))) * x(6);
    hdot(7) = delta - (gamma + c4 * x(4) / (a4 + x(4))) * x(7);
end

function hdot = glioma1(t, x, Pg, Ps, pe, beta1, beta2, a1, a2, a4, a5, c1, c2, c4, c5, u, d10, d11, d12, d20, d21, d22, d50, d51, d52, d4, tau, mu, beta3, psi, delta, gamma, alpha, Pr)
    % Define the system of ODEs for glioma1
    hdot = zeros(7, 1);
    v = 0.003;
    Phi = 3.3e-3;

    H = 0;
    if x(6) > 0 || x(7) > 0
        H = 1;
    end

    hdot(1) = Pg * x(1) * (1 - x(1)) - beta1 * x(1) * (x(2) + x(3)) - (d10 + d11 * x(4) + d12 * x(7)) * (x(1) * x(6)) / (a1 + x(1));
    hdot(2) = Ps * x(2) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta2 * x(1) * x(2) - u * x(2) * H - v * H * x(2) - (d20 + d21 * x(4) + d22 * x(7)) * x(2) * x(6) / (a2 + x(2));
    hdot(3) = Pr * x(3) * (1 - (x(2) + x(3)) / (1 + tau * x(4))) - beta3 * x(1) * x(3) + u * x(2) * H - v * H * x(3);
    hdot(4) = mu * (x(2) + x(3)) + pe * x(4) * (1 - x(4)) - d4 * x(4) * x(7) / (a4 + x(4));

    if hdot(1) < 0
        hdot(5) = alpha * hdot(1) * x(5) - (d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    elseif hdot(1) > 0
        hdot(5) = -(d50 + d51 * x(4) + d52 * x(7)) * x(5) * x(6) / (a5 + x(5));
    end
    hdot(6) = Phi - (psi + c1 * x(1) / (a1 + x(1)) + c2 * x(2) / (a2 + x(2)) + c5 * x(5) / (a5 + x(5))) * x(6);
    hdot(7) = delta - (gamma + c4 * x(4) / (a4 + x(4))) * x(7);
end

[Latifah]

yes, thank you, i want to make plot tau (time which the brains of patients with glioma have a loss of $10 \%$ in the neurons concentration ( $n=0.54$ )) vs phi (infusion rate chemotherapy) with three v values .

According to Peters et al. there is an overall age-related loss of neurons [x[5], about $10 \%$, from the cerebral cortex. With this in mind, we compute the time $\tau$ in which the brains of patients with glioma have a loss of $10 \%$ in the neurons concentration ( $n=0.54$ ). i want to shows the time $\tau$ for a neuron to achieve the concentration $n=0.54$ (because in my model the initial value of x[5] is 0.6 as a function of $\Phi$. For $v=0$ and $\phi=1-250,

exmple result : \tau$ is equal to 3926 days, while $\tau$ is much less for $v=10^{-3}$ (red line) and $u=3*10^{-2}$ (black line). We obtain $\tau$ equal to 3672 and 2910 days for $u$ equal to $#*10^{-3}$ and $10^{-2}$, respectively. Then, it is possible to conclude an important effect on $\tau$.

note: tau is not my paramaters , but as a function of phi

[Latifah]

the code you wrote from my previouse question is example for x[5] vs time t, please help me from that codes

[Les Beckham]

I still don't understand what you are trying to do. Show the code you have written that isn't working. In the code you posted, tau and phi are constant scalars. A plot of those is not going to be very useful.

[Latifah]

I apologize, 'tau' here is not tau about parameters, think of replacing 'tau' with t=time, and phi=[0-400], so the phi value is plotted with phi=[0-400]

[Les Beckham]

That still doesn't make sense. Where is the code that you are using to try to plot your desired plot? What isn't working? Does the code that you posted have anything to do with what you want to do? Which variables in that code are you wanting to plot? Don't make us guess what you are trying to do.