This was a good chance to review this subject I studied many years ago. Let’s see if I can summarize from the site chalk creek posted and this from the Merck Veterinary Manual:
http://www.merckveterinarymanual.com...m/bc/22108.htm
What is the cause of your calf’s disease? Hard to say. Sometimes it can be a combination of bugs. Possibilities are bacteria like E. coli or Salmonella. Or viruses like corona and rotavirus. Or protozoa like cryptosporidiosis. You can have feces cutured, but results are often confusing, since their presence does not necessarily mean they are the problem. Many of the bugs can be found in healthy calves.
Crypto is supposed to be more mild unless combined with other bugs. The common E. coli usually hits before 5 days old. Salmonella may be likely, as it causes foul smelling diarrhea as you described. It infects all the body, not just the gut, so requires injected antibiotics, but penicillin and other common drugs are ineffective due to overuse and resistance.
The main treatment for severe diarrhea is fluids for dehydration. Dehydration and it’s consequences are usually what kills the calf. If the calf is down and weak, the fluids need to be given IV (in the vein) to do any good. Very dehydrated calves lack sufficient circulation for fluids given orally to be absorbed from the gut. Calves also need energy to recover, so may need to add sugars to fluids and/or keep feeding milk.
Penicillin does not work for viruses, or E. coli, or Salmonella, or protozoa.
Why is this calf more affected than others? Individuals vary in their resistance to disease organisms. Some calves get less colostrum if they are weak from a difficult calving, or from other problems. Or the colostrum may lack protection if the cow is unvaccinated, or from a heifer which hasn’t yet been exposed to disease.
Calves also differ in their exposure to bugs. Many of the organisms causing disease are all around, or in the feces of the cows or other calves. Some bugs have a certain minimum number to cause disease. So if a calf happens to get a mouthful of feces containing these organisms, it will be more likely to get sick. Which is why clean bedding is helpful, and spreading out calves, and general cleanliness.