I think you want /r/TheyDidTheMath. The basic information about transmission rates and incubation periods are all well known:

• Receptive anal intercourse; Chance of infection = 0.04–3.0%

• Within 2-4 weeks after HIV infection, many, but not all, people develop flu-like symptoms, often described as “the worst flu ever.” Symptoms can include fever, swollen glands, sore throat, rash, muscle and joint aches and pains, and headache. This is called “acute retroviral syndrome” (ARS) or “primary HIV infection,” [...] During the acute HIV infection stage, you are at high risk of transmitting HIV to your sexual or drug using partners

Just insert the numbers and multiply.

The man being fucked by "Patient Zero" in your scenario has a 0.04 to 3.00% chance of being infected at any particular time that Zero ejaculates. Let's take the mid-point and assume this is a 1.52% chance every time. To reach certainty of infecting Victim One, Patient Zero needs to ejaculate 65.79 times (100 ÷ 1.52 = 65.789). At one ejaculation per hour, that's 2.74 days.

Then, the virus has to incubate for 2 weeks inside Victim One before Victim One is infectious. So, that's 2.74 + 14 days = 16.74 days until Victim One is certain to be infected and infectious.

There are 99 Victims to infect this way. That's 99 x 16.74 = 1,657.26 days to reach certainty that all 99 non-infected people become infected and infectious. We can drop the 14-day incubation period for Victim 99, as we don't need to wait for him to become infectious, so that's 1,643.26 days to reach full infection, or about 30 months, which is 2.5 years. Those men are going to die of exhaustion long before they all catch HIV!

As for whether the infections will go faster in the "pitching" or "catching" direction...

• Receptive anal intercourse; Chance of infection = 0.04–3.0%

• Insertive anal intercourse; Chance of infection = 0.03%

It'll go faster via the receptive partners than via the insertive partners.

And, now I realise that I forgot to allow for the slow infection from Patient Zero via Victim Ninety-Nine, who's fucking him. The two series of infections will probably meet up somewhere around Victim Eighty (or in that vicinity). But, I can't be bothered now doing that extra set of calculations. Go ask /r/TheyDidTheMath.