To add to Caliope's post, without antibiotics and cleaning products that sterilize (i.e., Lysol, etc.), or even an understanding of how to sterilize the "sick room," infants did not fare well against the common childhood illnesses that are preventable, treatable, and survived today. Mumps, measles, chicken pox, small pox, whooping cough, diptheria, and anything that causes rapid dehydration (esp. vomiting or diarrhea) were devastating to young families. The rH factor also took many young lives, as did premature birth and birth defects. At the plague level, Yellow Fever ran through Ohio often when canals were still in use, as well as in the kind of wet weather that lately has given us outbreaks of West Nile Virus. There's a cemetery in Licking Co., not far from Fresno, where an entire family of about 9 died within a week of Yellow Fever. Often, in such cases, you'll see the youngest died first, then the older kids, then the adult(s) who were caring for them.
My husband and I enjoy documenting entire old rural cemeteries and have found many sad stories in the stones like this. It's not unusual to find one parent and all children together, then find in another location that the surviving parent moved and started a second family, as though it was just to painful to stay where their first one had collapsed around them. Another oddity is to find the first child died and was buried, and the parents moved before having more. I mention this because a lot of people researching their families are surprised to find that their grandparents had other kids or spouses till they spot a Find A Grave or similar entry for them. I hear from a lot of these searchers, thanking us for finding their "lost" family members. That kind of feedback is what encourages us to do more than just record the stone and dates, but to also try to find family and cause information.
Sorry for the lecturette, but you asked a great question.