Parvo is insanely contagious. Your "mongrel" dog probably has it since it hasn't been vaccinated but isn't showing symptoms yet. The parvo virus can already be inside an animal but it can take up to weeks to start affecting the dog. Take it to the vet to get tested for parvo and tell the vet that it has had direct contact with a parvo infected dog. I would take it to an emergency vet as soon as possible, like tonight. I've had bad experiences with parvo. I was fostering a shelter dog that unbeknownst to us, had parvo. The shelter told us it was seen by a vet and diagnosed with kennel cough. But when symptoms were severe we took it to a vet and it was diagnosed with parvo. The poor dog died and gave parvo to our ferret as well which eventually had to be put down after treatment didn't work. It's a terrible virus that causes a very painful death. Better to be safe than sorry. Call things off of your busy schedule if you have to. An emergency vet is more expensive but can see patients any time, without an appointment. Parvo is seriously not a thing to take lightly. If parvo is treated VERY early on, the dog may have a small chance of survival. But if it's caught in later stages, after symptoms are already arising, it's very unlikely the dog will survive.