The worst-hit will be the very old, who are susceptible to heart disease and stroke, and the very young, whose lungs are taxed so badly by polluted air that they cannot develop normally. Children are more vulnerable because they are smaller, with shallower breaths and higher heart rates; they breathe more air.

In the very different homes of Vaishnavi and Mehtab, four parents are waiting to see what the rest of this winter will do to their children.

Vaishnavi’s father, Ravi — who, like many in India, does not use a last name — remembers the day when he woke up and smelled something burning. The rubber casing of an electrical wire is burning, that was his first thought. He splashed his eyes with water to stop the stinging.

On the ride into central Delhi, where he sells trinkets on a street corner, he passed columns of smoke: gray-blue wisps from piles of trash, and black pillars from fields where farmers were burning the straw left over from their rice harvests.

Scientists had been tracking the progress of a mass of smoke via NASA satellite images, as it rose off farmers’ fields in the nearby states of Punjab and Haryana and floated across the plains toward the city, a two-day drift. In Delhi, it merged with emissions from cars, coal-fired power plants, open-air burning of trash and dust from construction.

This year, the crop-burning emissions happened to arrive on the eve of Diwali, the Hindu festival of lights, when smoke from millions of celebratory fireworks typically send concentrations of the harmful PM 2.5 particles skyrocketing. Ravi has worked on the same corner since he was a child, and his mother worked there before him. He had never seen a smog so thick that it obscured the Shangri-La Hotel. He knew something was not right: He felt dizzy, as if he had been sniffing glue.

What worried him more was his only child, Vaishnavi, just 18 months old, whose spasmodic nighttime cough no longer quieted with the arrival of morning. He bought her a surgical mask for 40 rupees — about 60 cents — from a merchant at an intersection, but she kept pulling it off. On the way home, he furiously jumped out of the auto-rickshaw and confronted a man burning a pile of trash on the road. “Please don’t burn this, my daughter is crying,” he said.