How should we handle progressives who spread coronavirus fake news?

Here’s a thought experiment: Imagine there was a burgeoning global pandemic in a world in which there was also a universally accessible publishing platform without editors or regulation. Now, imagine some of the most influential contributors on that platform were spreading misinformation about the response to the contagion. Their conduct carries obvious risks: governments are dependent on public trust to ensure life-saving advice is heeded. In health emergencies, government can usually expect citizens’ in-built cynicism to be tempered by concern about the crisis at hand. But what if influential users of the publishing platform, through negligence or malice, caused public confidence to corrode in dangerous ways? What if the population started to disregard government advice and so frustrated efforts to contain the virus? Is there then a case for punitive regulation or even censorship of the publishing platform?

I ask because my hypothetical isn’t as hypothetical as it might be.