@ragush Thanks for taking a look.  I'll continue to investigate/work around this issue.

@dharr Thanks for trying.  I should have mentioned I am running a Mac with OSX 13.6.7

@JAMET let me be direct where others have suggested... please upload your maple file so people can run it and help you.  Without it, providing help is not easy and you aren't likely to get the responses you want or need.  Use this button above...

@acer Thank you so much - really appreciate the comments and advice - really helps with the ongoing continuous learning of Maple.

@Ronan Thank you - that was it...

@max125 Similar to what another response mentioned, going through this stepwise, I see that simplify(-27^1/3) returns a different answer than simplify((-27)^1/3).  It seems the order of operations changes (as expected) between the two given the parenthesis in the first example below.  Still doesn't explain why that particular solution is returned.

simplify_test_(v02).mw

@C_R Excellent!! Many Thanks!

@C_R Thank you - this was helful as was the reference you pointed me to.

Though not flexible enough for the general use case with any/all units, the following is sufficient for my use (and can be revised for use with any unit).

Thanks for the help everyone.  Several options here (as always in Maple).

@gkokovidis Thank you - while that certainly works to add gridlines to the plot without altering the shape of the curve, it doesn't quite explain why assigning colors to the gridlines introduces what appears to be a linear peice-wise segment at the lower end of the curve in the 2nd plot spec.  What you have suggested does help though so thanks!

I've included a link to a worksheet here that demonstrates results for several types of functions using a selection of solutions proposed.  You have several options to address your plotting needs and you can see from this worksheet some of the different behaviors exhibited by each.  Hope you find this useful...

plot_with_y_is_0.mw

@sija Glad to have helped.

@SHIVAS 

I suspect that this system of equations may be too complex to solve symbolically using Maple but perhaps someone with more knowledge of both differential equations and Maple could tell you for sure.  Of course this system can be solved numerically if values are assumed for the key equation parameters.  I've done this for you in the attached (assuming a value of 1 for everything).  You may be able to get a general idea from how these DEs interrelate by substituting meaningful values for the parameters and solving numerically.  An example is at the link below:

diff_eq_question_-_numerical_solution.mw

Attached is a model that generates the solution of the exposure-free equilibrium point (solution 4 in the solution list).  Once the differentials are set to 0 in the problem statement, this becomes a system of nonlinear equations rather than a system of ODEs.  While I was able to generate the solution expressions stated in part (i) of your query, I didn't feel I understood the problem enough to help with (ii).  For example how r₁ was to be used unless the exposure-free equlibrium value for S collapses into r₁ but that would be speculation on my part.  Hope this model at least helps with the first part.

diff_eq_question_-_diabetes_or_hypertension.mw

It seems you might need to use the assignment operator ":=" instead of the equal sign "=".

Try "expr := x^4-10*x^2+1".  Without the quotes of course.