@Carl Love Yes, I made a mistake. Your updated worksheet works well. Thank you very much. It is so helpful you gave details explanation since I am a beginner using Maple. 

I am still confused to understand the relation between the immunotherapy infusin rate and the chemo infusion rate.

1. Why after around 75 mg/day chemo infusion the immun infusion rate do not have any effects?

2. Also for the time cured, why in the long term after 10^3, the immuno rate infusion for s_inf=7*10^5 behaves weird (comparison plot 5a and 5b)?   

Thank you very much for your help.

@Carl Love Hi, I tried to mimic your code, but I got

dsol := dsolve(eval({ICs, ODEs}, params), numeric, 'parameters' = [s__inf, q__inf], 'events' = [[N(t) - N__inf, 'halt']]);

Error, invalid input: eval expects its 2nd argument, eqns, to be of type {integer, equation, set(equation)}, but received [r = 0.1e-1, k = 0.1e13, c1, 0.5e-10, c2 = 0.1e-12, mu = 8, lambda = 4.16, a = 0.2e4, q = 300, s0 = 0.3e6, d = 0.1e-2, rho = 0.1e-11, gamma = 0.1e3, delta = 0.1e5, b = 0.5e7, N0 = 0.2e11, P0 = 0.5e8, s(t) = s_inf, q(t) = q_inf]

and

plot([seq(Data[s_inf][() .. (), [1, 3]], s_inf = S_infs)], axis[1, 2] = [mode = log], view = [1.0000000000 .. 100000.0000000000, 1000.0000000000 .. 0.1000000000], legend = [seq(s__infinity = s_inf, s_inf = S_infs)], title = "(a) Chemo does as a function of the infusion rate", axes = boxed, gridlines = false);

Error, Matrix index out of range.

Could you please help me with this issue? Thank you very much.

@Carl Love Thank you very much. Your explanation is really helpful. 

@tomleslie s(t): source of immunotherapy

s0: the natural influx of immune cells to the place of interaction

s_infinity: constant immunotherapy

https://doi.org/10.1016/j.amc.2018.12.008

@Carl Love I have no idea (That is why I am so confused tbh). I will upload the paper i tried to understand to make it sure. A_mathematical_model_for_chemoimmunotherapy_of_chronic_lymphocytic_leukemia

https://doi.org/10.1016/j.amc.2018.12.008

@nm Thank you for the suggestions 

@Kitonum Perfect. I choose the initial condition and the range for P and Q 0 to 100000 to see there is an attractor fixed point tho. Thanks