If I were a super dumb and dishonest political leader, I'd fake being ill to elicit sympathy from my opponents, then I would emerge after a couple of weeks, stronger than ever, and claim no virus can beat a real man.
If I were campaigning to be reelected, it would allow me to relax instead of doing all the hard work/communication/ travelling that demands. I'd just stay in my comfy chair and eat snacks.
If I secretly didn't want to be re-elected, it would give me an excuse to retire.
I don't know if it's possible to get away with such a big lie, but it's worth trying.
Although in Boris Johnson's case, I'm not sure he faked it, because a couple of days before he announced he had the covid, I half-dreamt he was going to die. (I don't know. It's just the way he looks. Like if there's a bug around, it's going to climb on him affectionately.)