Devising a model for inflation for a closed points system
If your points are exchangable for rewards, the fundamental value of the points is entirely driven by the exchange rate between points and the rewards. (People may value the points more or less than the fundamental value for any number of reasons.)

This means that the inflation rate is entirely driven by the administered exchange rate - up until the point the program runs out of rewards. If you want to prevent the possibility of running out of rewards, the total supply of points must be held less than the redemption value.

This is similar to the operation of a gold standard. In the classical gold standard, a country’s currency (in principle) is exchangeable at a fixed rate against gold. (In practice, the implementation of gold standards changed over time.) You should be able to find a lot of resources on gold standard systems.

If you have a fixed supply of rewards, and you want to keep the exchange rate stable, you would need to find a way to drain points from the system - a tax. 

In terms of motivating people, the major question is the value of the rewards. If people don’t want your rewards, your points will have little value.