Yes. Regardless of previous infection, the U.S. Centers for Disease Control and Prevention says people should plan on getting vaccinated when it's their turn.

"It's a pretty straightforward question," said Johns Hopkins infectious disease specialist Dr. Amesh Adalja. "Yes, you need to get vaccinated."

After someone recovers, their immune system should keep them from getting sick again right away.

"Your immune system is able to identify the virus, and protect itself," said Dr. Saskia Popescu, an infectious disease expert at George Mason University. 

Scientists still don't know exactly how long this immunity lasts or how strong it is, though recent research suggests the protection could last for several months.

It's impossible to know how long a person might be immune, said Dr. Prathit Kulkarni, an infectious disease expert at Baylor College of Medicine. "There's no way to calculate that."

Vaccines, by contrast, are designed to bring about a more consistent and optimal immune response. And they should boost whatever preexisting immunity a person might have from an infection, experts say. 

"Since we're in this pandemic, and don't have a handle on it, the safer approach is to vaccinate," Kulkarni said. "You don't lose anything and you stand to benefit."

If you've been infected in the last three months, the CDC says it's OK to delay vaccination if you want to let others go first while supplies are limited.

"All things being equal you would want the person with no protection to go first," Adalja said.