So, if both Trump and Pence have been near people who then tested positive...

[RhodeIslandOne]

17. He did, when Reagan was shot.

https://en.wikipedia.org/wiki/Alexander_Haig

In 1981, following the March 30 assassination attempt on Reagan, Haig asserted before reporters, "I am in control here"[30] as a result of Reagan's hospitalization, indicating that, while President Reagan had not "transfer[red] the helm," Haig was in fact directing White House crisis management until Vice President Bush arrived in Washington to assume that role.

Constitutionally, gentlemen, you have the president, the vice president, and the secretary of state in that order, and should the president decide he wants to transfer the helm to the vice president, he will do so. He has not done that. As of now, I am in control here, in the White House, pending return of the vice president and in close touch with him. If something came up, I would check with him, of course.
— Alexander Haig, "Alexander Haig", autobiographical profile in Time magazine, April 2, 1984[31]

The U.S. Constitution, including both the presidential line of succession and the 25th Amendment, dictates what happens when a president is incapacitated. The Speaker of the House (at the time, Tip O'Neill, Democrat) and the president pro tempore of the Senate (at the time, Strom Thurmond, Republican), precede the secretary of state in the line of succession. Haig later clarified,

I wasn't talking about transition. I was talking about the executive branch, who is running the government. That was the question asked. It was not, "Who is in line should the president die?"
— Alexander Haig, "Alexander Haig" interview with 60 Minutes II April 23, 2001