I have Differential equation sytems as follow:

r := 10^(-2);k := 10^12;c1 := 5*10^(-11);c2 := 10^(-13);mu := 8;lambda := 4.16;a := 2*10^3;q := 300;s0 := 3*10^5;d := 10^(-3);rho := 10^(-12);gama := 10^2;delta := 10^4;b := 5*10^6;

eq1 := {N(0) = 2*10^10, P(0) = 5*10^7, Q(0) = 0, diff(N(t), t) = r*N(t)*(1 - N(t)/k) - c1*N(t)*P(t) - mu*N(t)*Q(t)/(a + Q(t)), diff(P(t), t) = s(t) + s0 - d*P(t) + rho*N(t)*P(t)/(gama + N(t)) - c2*N(t)*P(t) - delta*P(t)*Q(t)/(b + Q(t)), diff(Q(t), t) = q(t) - lambda*Q(t)}. I replace I with P.

N(t):The number of cancer cells; P(t): The number of immune cells (Healthy T-Lymphocuyes); Q(t): The amount of chemotherapeutic agent in bloodstream; q(t): Source terms standing for chemotherapy.

My question is how to get the first two figures below based on these information: q_infinity means constant chemotherapy infusion, while s_infinity means constant immunotherpy.

I got the plot for Q(t) as follow:

Please anyone has any suggestions to help. Thank you very much.

Hi, I am trying to plot the phase potrait for this as follow:

s0 := 3*10^5;
d := 10^(-3);
delta := 10^4;
b := 5*10^6;
lamda := 4.16;

DEplot([diff(I(t), t) = s0 + I(t)*(-d - delta*Q(t)/(b + Q(t))), diff(Q(t), t) = -lamda*Q(t)], [I(t), Q(t)], t = 0 .. 10, I = 0 .. 100, 0, Q = 0 .. 100, 0, dirfield = 400, arrows = smalltwo, number = 2, [[0, 4, 0.1], [0, 0.2, 4.1], [0, 7, 0.2], [0, 0.2, 7]], color = red, linecolor = blue, numsteps = 100)

But, there is an error saying "Error, (in DEtools/DEplot) vars must be declared as a list, e.g. [x(t),y(t),...]". However, I did the same for other problem and worked well tho. I have no idea what the problem is for above.