Zvi Mowshowitz has some interesting models of how truth-telling works, but because he is, er, loquacious, it helps to have shorter versions of his posts to refer to. Which I might do here.
For now, though, I’ll simply link to the levels of simulacra model. In the case of modelling COVID there are some interesting analyses of truth dynamics hypothesised:
To the purely political actor, the implausible lie is better. If the lie is implausible, then those repeating it have sent a costly signal of loyalty, and cut ties with lower levels. You don’t have to worry they repeated the statement because it happens to match the physical world, or that they will refuse to repeat the next one if it fails to match.