Health officials are still working to pinpoint the source of a cyclospora outbreak that has sickened more than 3,000 people in Michigan and Ohio, with investigators saying the culprit has yet to be identified.

Michigan has reported 2,640 confirmed cases, including 44 hospitalizations, while Ohio has recorded 361 cases since June 1.

Combined, at least 46 people have been hospitalized.

The Centers for Disease Control and Prevention said 31 states reported cyclospora infections as of Friday, though it remains unclear whether the cases are connected.

The agency also said "multiple states" have seen an uptick in infections the past two weeks compared with the same period last year.

Health officials say the investigation has been slowed because cyclospora is much harder to trace than more common foodborne pathogens such as salmonella and E. coli.

"For the bacterial pathogens, the technology is quite mature, and the organisms are really very, very simple. It's like reading a children's book versus reading 'War and Peace' — cyclospora being the 'War and Peace,'" Jennifer McEntire, CEO of Food Safety Strategies, told CNN.

"They're all letters of the alphabet, but they are not the same thing," she said.

The Department of Health and Human Services said federal agencies are working alongside state officials to determine what food or other source is responsible.

The Food and Drug Administration and the CDC "are actively engaged with state partners to identify the source of the growing number of illnesses," HHS spokesperson Emily Hilliard told CNN in an emailed statement.

Michigan's chief medical executive, Dr. Natasha Bagdasarian, said investigators are seeing potential leads but have not yet identified the source.

"We have seen some signals. We are looking for signals, and we are seeing some early signals," Bagdasarian told the outlet.

She stressed that no nationwide recall is associated with the outbreak, although some restaurants have voluntarily removed certain fresh ingredients from their menus while the investigation continues.

"There have been proactive measures that were taken to ensure that exposure did not occur," Bagdasarian said.

Cyclospora infections are most commonly linked to contaminated fresh produce or water. Symptoms include persistent watery diarrhea, stomach cramping, bloating, and dehydration, and patients are typically treated with a seven- to 10-day course of antibiotics.

Investigators are interviewing thousands of patients and reviewing restaurant receipts and grocery purchases in an effort to identify a common source.

"It actually requires us looking at every item they've ordered in a restaurant, what was in those menu items, and it requires pulling their shopper cards," Bagdasarian said.

"You can just imagine the sheer amount of effort and work that goes into this," she added.