Sorry, but we cannot check just any equations. But suppose these are correct. What you also need is a good initial point. If you start too far away from an equilibrium it will not be able to find it, that is the newton iterations will not converge. So you may first do a simulation (like in the first tutorial) to observe the behaviour and get an idea of what the system is doing.
While I understand how you want to enter your system, the GUI does not work this way. The problem is that we chose to work with scalar state variables. Not with vector-valued ones. In our recent work to work with delays we sort of have an option for vector-valued variables but it is far from automated. Work in progress, if anyone has time. For now, what you can do, is to create a simple system with the correct number of state variables and parameters but no irrelevant ODEs. After creating the file,...
In versions 7p5 and 7p6, we have disabled this menu item for this switch as it is not there, indeed. In the version for maps (MatContM) we have implemented the switch GPD to LPC of double period, but we never created the file for the continuous-time case. If you want to proceed, you better start a bit away from the GPD point and switch to the doubled cycle from a regular point on the PD curve to detect the LPC point from regular one-parameter continuation. You may have to try starting from both sides...
No clue, I do not manage to reproduce this error, so cannot help.
Your screenshot suggests your Matlab working folder is not correct, that is also what the error/warning indicates; It cannot find the files. Change it from "Matlab> dengue_matcont" to a folder where you have placed the matcont files.
Have a look at the manual; Chapter 4 on the structure of the ODEFILE, and how to add it in the GUI.
EEG is not a variable, but an expression, so remove that from the coordinates, and put it before the differential equations, not after. If you need the value of "EEG" then add it as a user function, or compute it afterwards.
The expressions (ZP to vf) should come before the differential equations. It is code, if you compute those intermediate quantities after you use them, who could tell what value they should have.