The Constitution separates takings into two categories: physical and regulatory. A physical taking is, just like it sounds, when a government takes property away from an owner. It is fairly easy to identify physical takings, such as when DOT or a municipality takes property to build or expand public roads. A physical taking is unlikely – I am not aware of any governmental bodies in the U.S. physically taking property in response to the pandemic – but conceivably a municipality could take a building for quarantine or medical purposes. Should that occur, the municipality would need to pay the owner fair market value of the property taken. Since most of the buildings or spaces suitable for such uses are public buildings or spaces (e.g., the tents in Central Park in New York City), it is improbable that municipalities will need to compensate in such a way.
On the other hand, regulatory takings could, in theory, apply to certain federal, state and local responses to the pandemic. Certain businesses deemed nonessential and specifically ordered to close undoubtedly will take a financial hit. Hair salons, theaters, and gyms, among others, forced to close could make an argument for lost income as a result of government measures to curb the spread of COVID-19 by claiming governments have violated the U.S. and Maine Constitutions in doing so. The Fifth Amendment provides protection against federal takings, while the Fourteenth Amendment protects against state and local takings.
Given what the CDC, the Maine CDC, and most public and private medical professionals have stated concerning COVID-19, governmental stay at home orders, forced closures, and so on are almost certainly a “valid use of police power,” which powers are given to states under the Tenth Amendment to act for the well-being of the public. The most important thing will be to make sure any emergency actions or orders strictly follow a local emergency planning ordinance and the municipal charter.