Hello Ernie & Lenora,
First of all I'm sorry you went through this experience. I hope your following Airbnb experiences are much better.
I have been on similar situations, but I have managed to detect this before they arrive, so I just tell them through the Airbnb chat that since Airbnb is a trust system third-party bookings are not allowed as you cannot hold the OTHER guest responsible for what happens in your home.
The following step is to involve Airbnb to let them know this is not a booking that follows the rules and then flag the profile.
When someone books even if they book for one person almost as an instant reply I ask exactly who is staying and that "I notice you booked for one, does that mean you're staying alone?" especially because we do not allow visitors.
There are emergency Airbnb phone numbers you can call if you feel you are not safe, of course they first suggest you contact the police but in this case it was not necessary. Do you ask for a security deposit?
Good luck.