“It is like they have a slow stroke,” said Ettore, a local olive producer who would give only his first name because he did not want his company to be associated with the epidemic. “Slowly, it is as if the blood is no longer flowing, and the branches dry out and stop producing olives.”

Standing in the middle of a grove, Ettore, 32, and Mr. Manni, the co-op official, nodded toward a tree with a trunk easily 25 feet in circumference. It is called the Giant of Alliste, and local growers say it is 1,500 years old (a figure scientists say is unlikely). It appears healthy, except for one branch in which the leaves are reddened and curled, an early sign that the bacterium has struck.

Mr. Manni reached down into a patch of grass, picking through weeds until he pinched what appeared to be a glob of spit but was actually the protective casing for the nymph stage of the spittlebug. The spittlebugs will start flying this month and have served as a primary vector of the outbreak, chewing on the leaves of infected trees and then carrying the bacterium to other, healthy trees, like an unseen wildfire. Scientists say no one yet knows the extent of the outbreak because some infected trees may not yet be showing symptoms.

“There are many,” Mr. Manni said, pointing to a few globs in the grass. “Here, here.”

Italian officials, whom olive growers have blamed for reacting too slowly, have divided the affected region into quarantine areas, with the buffer zone extending across the peninsula. Infected trees and plants were supposed to be cut down in one of the quarantine areas north of the buffer zone, while growers in the contaminated region south of the buffer zone were supposed to prune infected trees and cut surrounding grasses to better control insects.

But last week, an Italian administrative court suspended olive tree culling in Puglia. Italy’s Agriculture Ministry has appealed the decision, and culling could resume soon.

Maurizio Martina, Italy’s agriculture minister, said that at most, about 35,000 trees could be uprooted under the government plan — of the estimated 11 million olive trees in the area. So far, the ministry said, officials had cut down only six trees, with farmers culling an additional 100 or so. But the culling numbers could grow far higher assuming the new court ruling is overturned.