While I recommend always running a Rakghoul Vaccine stim during the event week to prevent gameplay interruptions, there is not only a hidden, repeatable [DAILY] Quest to get the Rakghoul Plague and infect others on purpose.
While completing the quest only awards a single Rakghoul DNA Canister and Reputation token, it does infact relate to a series of achievements that can only be earned during the event.

The Quest [DAILY] Spreading Infection will pop up as long as you successfully infect 1 other person with your Stage 2 Rakghoul Explosion. To complete the quest you need to explode on at least 3 people that day. It is repeatable every day the Rakghoul event runs.
Exploding on 3 people or more at once will instantly finish and grant you the mission reward even if you aren’t on the quest.

There are four achievements relating to infecting other people during Rakghoul Event weeks using the Rakghoul Infection. The first three are visible and the fourth is secret until you earn it.

The Achievements and their names are as follows:
Calling in Sick: Infected 5 players with the Rakghoul Plague.
Breaking Quarantine: Infected 25 players with the Rakghoul Plague.
An Infectious Personality: Infected 100 players with the Rakghoul Plague.
Mobile Contagion: Infected 1000 players with the Rakghoul Plague.

My strategy for completing Mobile Contagion in 1 day was as follows,

1. Use the Event travel in SOLO activity finder to go to the tunnels.
2. When you load in head to the first Rakghoul Pack, abandon the given Rakghoul mission (important).
3. Get infected then use Fleet Pass.
4. Go up the VIP elevator to the top level cantina, wait until you reach Stage 2 Rakghoul Infection.
5. Jump down onto the spawn point where Fleet Pass users load in, you should get at least 5-10 players.
6. Respawn then repeat steps 1-6 until complete.

I suggest the following guides on the Rakghoul Event if you wish to learn more:
DULFY.net Rakghoul Resurgence Event
Swtorista’s Rakghoul Event Guide