BILLUND, Denmark — How many rounds of antibiotics does it take to raise a Danish pig?

If it is one of the 35,000 piglets raised each year on Soren Sondergaard’s sprawling farm, odds are the animal will get just a single course before it goes to slaughter.

At times, a quarter or more of his swine arrive at the abattoir without ever having received any antimicrobial drugs at all.

“When I was a boy, we used to pour kilos of antibiotics into their feeding troughs,” said Mr. Sondergaard, 40, whose family has been farming the gently rolling terrain of the Jutland peninsula for generations. “That’s a thing of the past.”

As use of antibiotics in livestock has soared globally, contributing to the rise of drug-resistant germs, Denmark, which ranks among the world’s top pork exporters, has proved that a country can build a thriving industry while sharply cutting back on antibiotic use in pigs.