Mouse studies are always suggestive, but often don't carry over to humans. We can hope they're right, but I wouldn't hold my breath.
Usually rats and mice are used for initial studies because they are inexpensive. These studies are then confirmed in a non rodent animal model (usually dogs), then in non-human primates, then tested in humans.
Only if the treatment is found to be efficacious in rodents will it usually be moved on to NH-primates and then humans.
The CD proteins are likely to be very similar between all these species, so the molecular interactions should be similar enough to maintain efficacy.