Thanks for all of the additional information. Your fellow sounds very, very sick.
It seems unlikely to be from a dog to dog direct contagious disease process because he isn't running a fever and your other dogs are fine.
Panting can indicate poor oxygenation, but in his case I would suspect that he is panting due to nausea and abdominal pain.
With the amount of drool however, his lethargy and him eating very little I suspect he is very, very nauseous and dehydrated.
Blood and mucous in his stools point toward colitis, an inflammation of the large intestine. His trouble passing stools is likely just him feeling a lot of inflammation and like he has stools to pass when in reality there is very little there. So it isn't that he is having trouble passing anything, there probably isn't anything to pass.
I am concerned about a toxin exposure, and possible secondary internal organ compromise, possibly a tick borne disease, or ingesting something that has led to a partial or complete gastrointestinal obstruction.
His bad odor can be indicative of internal organ failure, or exposure to a toxin.
Unfortunately he sounds beyond home care, none of the things I am concerned about are easily treatable at home. He needs hands on veterinary care.
They can rehydrate him with intravenous fluids, give him injectable medication to settle his nausea and run diagnostic testing including a complete blood count, biochemistry profile, urinalysis and testing for tick borne diseases. Depending upon physical exam results they may want to take radiographs as well.
I like to give options for things to try at home, but in this case I think they would be a waste of money and precious time getting him the help he needs.
If you don't know of an emergency veterinarian near you here is a link to help you find one:
I am sorry, as I am sure you were hoping to help him at home, but I feel he is much too sick for that. Best of luck to you and your fellow.