It's a case that would have challenged Sherlock Holmes.

Infant botulism, a disease that causes serious respiratory symptoms -- and death to 2 to 3 percent of its victims -- is on the rise in the United States, although the reasons for the increase have researchers stumped.

Among the mysteries challenging medical detectives looking for answers to infant botulism are:

*Why the disease appears in three major pockets -- California, southeastern Pennsylvania and Utah. (Locally last year there was one case in Alexandria, and none reported in the District.) Investigators are looking at everything from possible regional variations in the bacteria that causes botulism to diet differences that might account for the varying rates.

*How the illness is spread. Diet seems to play an important role in some cases. Culprits identified so far are honey and corn syrup, which carry bacterial spores that can germinate in a baby's still immature intestine, colonize and produce a harmful toxin. But foods explain at most only about one in three cases.

*Why breast-feeding seems to offer some protection against the disease -- except among the Pennsylvania cases. There, all 44 of the infants who developed the disease between 1976 and 1983 were breast-fed, according to a report published earlier this year in the journal Pediatrics.

*What role infant botulism may play in sudden infant death syndrome (SIDS). Autopsies suggest that perhaps as many as eight of every 100 babies who die of SIDS may actually have had respiratory failure caused by infant botulism. SIDS kills 8,000 infants yearly in the United States.

Compared with the number of cases of other infectious childhood diseases -- including measles, mumps and chicken pox -- infant botulism is but a drop in the bucket. Only 99 cases were reported last year to the federal government's Centers for Disease Control in Atlanta. But those 99 cases represented a record year for the disease, a trend that worries researchers like Dr. Stephen Arnon, chief of California's Infant Botulism Research Project.

"Infant botulism is sort of a prototype of infant infections that have escaped detection," Arnon says. "But there's a provocative suggestion that whatever is going on with infant botulism . . . may give us the clues to understand the larger problem of crib death."

"Clearly babies who were thought to have died of SIDS, on more specific examination, were indeed found to have had botulism," says Dr. Allen Merritt, chairman of the Medical Research Board of the National SIDS Foundation. "It may represent a small proportion of babies with SIDS, but nonetheless, it is assisting us in being able to understand that part of the cause of SIDS."

Mention botulism and most people picture bulging cans of tainted food. This deadly food poisoning is caused by the toxins produced by the bacteria Clostridium botulinum. Those toxins are among the deadliest substances known to man. Usually people get the disease by eating improperly canned foods, which provides an ideal medium for the bacteria to grow and thrive.

But the route of transmission for infant botulism is different. The bacteria spread through spores -- a kind of bacterial seed present in the air, in soil and dust and in a variety of foods, including the surface of fresh vegetables and fruits.

Adults and older children ingest these spores without harm. But for unknown reasons, explains California's Arnon, until almost a year of age, "the infant intestinal tract permits the spores to grow."

The result is a disease that begins with a kind of listlessness, gradual loss of body control, irritability and constipation. Because the infection is still fairly uncommon -- and because there's usually no fever -- it can easily be overlooked by both parents and physicians.

"The most fearsome complication is respiratory arrest," explains Arnon, who describes how one baby "stopped breathing right in his mother's arms." Fortunately, the mother was a nurse and started giving artificial respiration while her husband called the hospital. Had the baby stopped breathing while alone in its crib, it probably would have died, Arnon said.

Despite these potentially dire complications, about 98 percent of the hospitalized victims survive. "Not," says Arnon, "because this a mild illness, but rather because it's a statement of the quality of supportive care that our top-flight hospitals can deliver."

The average hospital stay for an infant botulism victim is about a month, usually in an intensive care unit. "The majority are on respirators," says Arnon. A study of health care costs in California found that the treatment price ranged from $2,600 to $163,000. "And that's just the hospital bill," says Arnon.

Experts say many of the infections could be prevented by eliminating spore-carrying foods from a baby's diet. So far, researchers have identified honey as a clear culprit, corn syrup as a likely suspect and molasses as possible agent.

"There's a whole new generation of moms out there who haven't gotten the word" that those foods can be dangerous, says Arnon.

Five years ago, the Center for Science in the Public Interest unsuccessfully petitioned the Food and Drug Administration to require warning labels on honey which would have read: "Do not feed infants under 1 year old. Serious illness may result." Last year, Best Foods, one of the major manufacturers of corn syrup, published a special pamphlet on the disease for pediatricians.

"It's an important illness, one we feel is being underreported," says CDC's Dr. John Spika.