NEW DELHI — An epidemic of dengue fever in India is fostering a growing sense of alarm even as government officials have publicly refused to acknowledge the scope of a problem that specialists say is threatening hundreds of millions of people, not just in India but around the world.

India has become the focal point for a mosquito-borne plague that is sweeping the globe. Reported in just a handful of countries in the 1950s, dengue is now endemic in half the world’s nations.