This could happen...
Actually some of it is happening.
NY just put up a 1 mile quarantine zone.
Travel Restrictions have been implemented and I would expect more of them.
If they want Martial Law they will probably just call it a State of Emergency and you might see things like this...
The suspension of the Constitution, probably starting with the first and second amendment.
Confiscation of firearms; it has happened and it will happen again.
Suspension of Habeas corpus: Imprisonment without due process and without a trial.
Travel Restrictions, including road closures and possibly, even quarantine zones.
Mandatory Curfews and Mandatory Identification.
Automatic search and seizures without a warrant.