@Adele97 Airbnb does not have the authority to force you to extend a booking if it turns into a quarantine situation, but in some jurisdictions the local laws may require accommodation providers to keep infected patients onsite. This is where it gets tricky, as it's not always clear whether the locality regards Airbnb hosts as public accommodations subject to the same requirements as hotels. Hopefully your city council can clarify what your rights and obligations are in this scenario.
If honoring an incoming booking would require you to let guests in less than 72 hours after a Covid-positive guest has departed, you should be eligible for a penalty-free cancellation under Extenuating Circumstances. I would personally find it morally wrong to terminate a booking prematurely because the guest has fallen sick - which in this context means that I don't think it's acceptable for hosts who can't safely host an infected guest to be hosting at all during this pandemic.
But a grey area emerges on the question of what to do if a guest has to quarantine but can't afford to extend their booking past the checkout date. I don't feel that a host should ever feel forced to provide a free stay, but I guess you'd have to weigh your losses against the danger posed to your community and your guest's health if you put them out on the street. I wonder what Kwame Anthony Appiah would have to say about this...
