The coronavirus is killing residents in southeast Louisiana at higher rates than in other parts of the U.S., a new analysis shows, adding urgency to efforts to slow its spread through an already unhealthy population.

Two Louisiana parishes, the state’s equivalent of counties, have the most virus-related deaths per capita nationwide, according to Gary Wagner, an economics professor at the University of Louisiana at Lafayette who is tracking the epidemic for the state. St. John the Baptist Parish has the highest rate, followed...