Humans and dogs do not share many diseases. Flu are too different in both species. All the cases would be spatially related in this case. With most cases in a small area instead some animals falling ill here and there.
The carrier doesn't have to get sick with the disease to spread it; most of our insect-transmitted diseases don't affect the insect in any manner after all.
It sounded like you can rule out transmission through insects due to the patterns.
Transmission through latent infection of Humans would also be strange. Dog to Dog would be more probable. Of course, Humans accidentally transfer pathogens from animal to animal all the time.
