I'm not sure there is a mathematical model for cryptocurrencies. I think there are several factors you have to take into account.
One, will those who accept bitcoin always continue to do so? There's no law that says they have to keep doing so, but some merchants may make a legal commitment to do so. I don't have any knowledge in this area. Note that regular currencies have value because they are backed by law.
Two, can those who accept bitcoin change the price of their goods and services drastically? One of the requirements of a currency is a store of value. If merchants can change prices at whim and suffer no consequences, then bitcoin wouldn't be a good store of value. Regular currencies don't have this problem because the government tries to regulate its value via central banks.
If the above two conditions are satisfied, then it's possible to derive the value of cryptocurrencies by comparing their purchasing power. For example, if one bitcoin can buy 10 apples and $20 can buy the same number of apples, then one bitcoin would be worth $20. But if the two conditionals are not satisfied, then I'm not aware of how to value bitcoin. Personally, I'd think there's no intrinsic value to them.
Hope that helps,