Coronavirus in India: Amitabh Bachchan, Bollywood Star, in Hospital for Covid-19

Another explanation, though, might simply be testing — or the lack of it. India has performed far fewer coronavirus tests per capita than many other countries have.

Either way, the Indian authorities keep coming up with innovative ways to fight the virus. At airports, for instance, video cameras have been installed that enable security officers to check passengers’ boarding passes remotely to minimize face-to-face contact. The officers who use electromagnetic wands to screen passengers now use wands attached to four-foot rubber poles to maintain distance. And many Indians, even the poorest, have been wearing face masks for months.

India’s biggest enemy is the density of its population. This country has dozens of cities with more than a million people. Even in smaller towns and villages, many families live in cramped quarters, eight or even 10 people to a room, which makes a highly contagious illness like the coronavirus very hard to stop.

In many of these areas, it is impossible to maintain social distancing. In recent weeks, Mumbai, one of India’s most-packed cities and home to Mr. Bachchan, the movie star, has especially struggled.

The virus started out in Mumbai’s wealthier neighborhoods among the jet-setter crowd. Then it swept through the slums. Now it is gnawing through the entire city, home to 20 million.

On Saturday night, Mr. Bachchan announced via Twitter — where he has 43.2 million followers — that he had tested positive. He was soon admitted to Nanavati Hospital, near the exclusive Juhu neighborhood in Mumbai where he lives, overlooking the Arabian Sea.

It appears that several of his family members have fallen sick as well.

His son, Abhishek Bachchan, also an actor, disclosed that he had contracted the coronavirus. Abhishek’s wife, Aishwarya Rai Bachchan, an actress and model, tested positive, as did their 8-year-old daughter, Aaradhya.