Why have quirky grammar when the alternatives are simple and it is your role to convey science to lay people in a convenient and easy to understand way? We know 'HIV virus' is a tautology that should be avoided and usually it is just an unnecessary word.
"..the number of HI-virus particles in the blood" creates a new acronym, HI, and need only be 'HIV particles in the blood' or simply 'virus particles in the blood'. You don't have to even use the correct term for a virus particle, virion.
".. in spite of activation by the HI-virus" should just be 'activation by HIV' and after all that is exactly what acronym HIV stands for. It is wrong and confusing to use two thirds of an acronym currently in use as whole - especially one as well known as HIV. There are several cases of this and they are all redundant.

The inability to cope with these basics has me wondering about the legitimacy of the simplification of the material - like the questionable distinction of real and unreal functions of telomerase. And macrophages being "special immune cells". "The virus can survive inside these cells – beyond the reach of drugs." I think you are conflating anitretroviral effects with virus latency in different cells. Macrophages make good viral reservoirs not because they keep out antiretrovirals (that's not true) but because they are good at keeping HIV integrated into the host DNA without much activation, without production of viral proteins that would alert the immune system to its infected status.