"I am talking about any disaster"
They will all be managed these days under the National Incident Management System (NIMS) and the Incident Command System (ICS) in accord with federal guidelines. Because no one wants to pay for local disasters, and FEMA will not release a cent unless NIMS/ICS guidelines are followed and the correct paperwork is turned in. (They'll release funds, but they'll take them back if the paperwork doesn't pass review.)
So under ICS the first responder on the scene becomes the Incident Commander, and the communications will be whatever they have at hand. That may be whistles, police radios, DPW radios, fire department radios, VHF, UHF low or high band, cell phones...ANYTHING. The Incident Commander stays in charge of the response until someone more senior and capable can be found or shows up, and then command changes hands. Communications will also change, as a formal response structure is set up and a COMMS team can be put in place.
Incident command and communications may also be switched to military resources now. Not just National Guard, but full active military resources. That hasn't happened yet but has been authorized since 2006 under special executive order, after Mr. Bush had to be told why he couldn't send the Army into New Orleans after Katrina.
So, you may want to familiarize yourself with NIMS and ICS. Heavy reading but free on the web. And then you would need a list of every potential "responder" in your area, from the local dog catcher to the closest military bases. There are no "universal" communications, not actually deployed, not yet. It is still very much a hodge-podge of legacy equipment and new gear.