Here in India’s capital, where areas of standing water contribute to the epidemic’s growth, hospitals are overrun and feverish patients are sharing beds and languishing in hallways. At Kalawati Saran Hospital, a pediatric facility, a large crowd of relatives lay on mats and blankets under the shade of a huge banyan tree outside the hospital entrance recently.

Among them was Neelam, who said her two grandchildren were deathly ill inside. Eight-year-old Sneha got the disease first, followed by Tanya, 7, she said. The girls’ parents treated them at home but then Sneha’s temperature rose to 104 degrees, a rash spread across her legs and shoulders, and her pain grew unbearable.

“Sneha has been given five liters of blood,” said Neelam, who has one name. “It is terrible.”

Officials say that 30,002 people in India had been sickened with dengue fever through October, a 59 percent jump from the 18,860 recorded for all of 2011. But the real number of Indians who get dengue fever annually is in the millions, several experts said.

“I’d conservatively estimate that there are 37 million dengue infections occurring every year in India, and maybe 227,500 hospitalizations,” said Dr. Scott Halstead, a tropical disease expert focused on dengue research.

A senior Indian government health official, who agreed to speak about the matter only on the condition of anonymity, acknowledged that official figures represent a mere sliver of dengue’s actual toll. The government only counts cases of dengue that come from public hospitals and that have been confirmed by laboratories, the official said. Such a census, “which was deliberated at the highest levels,” is a small subset that is nonetheless informative and comparable from one year to the next, he said.