This is the area known as "excessive demand medical inadmissibility - A(38)". As a general rule, it requires quite a bit of careful planning to be successful in immigrating if you are HIV positive.
First, note that HIV positivity is not a bar due to "threat to public health/safety" though I've seen people try to make that argument on here. CIC does not normally consider it as such.
The entire issue is around costs. They do not consider your potential contributions as part of the cost analysis (which gives rise to some other complex issues). But because health care is provincially managed, not federally managed, in my experience the CIC officers making these decisions do not have specific insight into those costs, so they just say "this is expensive..."
If you can afford it, you need to work with an attorney specializing in this area. I can recommend two people (both in Toronto) with extensive experience in this area who have been successful assisting applicants in your position.
With that said, I can suggest that a key to being successful with CIC (versus being successful in Federal Court - where you'll need the skills of a good attorney) is to understand the costs involved. This is a combination of the current status of your condition, the treatment (if any) you are taking, and the amount paid for by your province. Cost information can be difficult to obtain (I usually use the costs published by Quebec as it's the only easily available source I've found for such information).
The new medical guides on the CIC website are helpful in understanding the CIC procedures - and their own requirements in a case such as yours - and you should become familiar with them. You can find a wealth of materials here: http://www.cic.gc.ca/english/resources/manuals/index.asp
Pay attention to the Medical section as well as OP 15 (http://www.cic.gc.ca/english/resources/manuals/op/op15-eng.pdf)
My suggestion: don't apply in the PhD stream. Get your PGWP and find an employer that offers extended health care that includes some amount of coverage for the medications that you are presently taking. By pushing the amount paid for by the provincial government down under the excessive demand threshold (currently ~$6300 per year) you eliminate the claim of excessive demand. If you are receiving any treatment through an NGO, you might consider applying in the PhD stream - but part of the CIC criteria for evaluating mitigation plans is whether or not the plan is currently active and whether or not you have availed yourself of provincial payment for such services already.
