What is the meaning of this quote? "the most valuable end of government is the liberty of its inhabitants. no possible advantages can compensate for the loss of this privilege."

I'd take it to mean that the most valuable, or special, or rare, whichever term you'd rather use, virtue of the government is the liberty and freedom of it's inhabitants.

The idea that the people under the government could have a good level of freedom and liberty over themselves and etc. is considered to be a rather large advantage, since some governments are, as you can see, quite hell-bent on controlling their people, and their people's every move. There are many examples of this over the World. So, I think that the statement is trying to say that where there is a government that gives the people under the government a good amount of liberty, control, and freedom, that government is quite valuable, and rare, and you don't see this very often.

The central idea is that the hiv/aids epidemic is serious.