“We live off tourism, so a stupid comment like saying that Aeolian cockroaches have colonized Naples can become a tragedy,” Mr. Giorgianni said. Lipari did have red cockroaches, he added, “but no more than in any other city. It’s not a problem here.”

Entomologists in Italy are perplexed that the bugs ever got noticed at all. “Every city has cockroaches, and in hot periods they increase their population, but it’s not a new problem,” said Piero Cravedi, director of the Institute of Entomology and Plant Pathology at the Università Cattolica del Sacro Cuore in Piacenza. While ships have been singled out as the likely vehicles for insect travel throughout the world for centuries, “it would be easier for Naples to infest Lipari, rather than the other way around,” Professor Cravedi said.

The uproar was made more acute, perhaps, after the red cockroaches were identified as an American type, and described as having cannibalized the black cockroaches indigenous to Naples. “They ate them up, destroying the native species — it was a battle of the fittest,” said Maria Triassi, a professor in the department of preventive medicine at the Federico II University here, who is not an entomologist but whose concerns were much repeated in the Italian news media, helping to ignite the hysteria.

Entomologists say that different species of cockroaches have cohabited throughout the world for quite some time without any disastrous effects. “We can’t ascribe any particular responsibility to the Americans: it’s the name of the species, but they’ve been endemic to Europe for centuries,” Professor Cravedi said. “I’d exclude that they are newcomers.”

Health authorities in Naples regularly disinfect the city’s gutters and sewers at night; last week, they began disinfecting some neighborhoods during the day as well.

Neapolitans are justly renowned for their ingenuity, said Anna Fusco, who works in a tobacco shop near the San Carlo Opera House, so many had already taken the situation into their own hands. “As with all things, we organize ourselves in Naples,” she said. “Where people live, they’ve been cleaning their own stoops and throwing disinfectant on the ground.”