Basic model where inflation occurs
Quoting Wikipedia:


  the quantity theory of money (QTM) states that money supply has a
  direct, proportional relationship with the price level.


According to this theory an increase in money in circulation increases price levels.

So an "extremely simple mathematical model" (and extremely simplistic) would be something like:

$$ \pi_t = \dfrac{M_t-M_{t-1}}{M_t} $$ where $M$ stands for money supply and $\pi$ stands for inflation.