Trade
As with exploration, espionage, terrain improvement, city founding and diplomacy, the Civilisation model for trade requires laborious pushing of units around the map. The player interventions in trade should be as follows:
Construction of infrastructure (roads, railways, canals, ports, marketplaces, etc) that promote trade.
Setting the tax rate on imports/exports per trading partner (higher tax gives more revenue but reduces volume, also diplomatic impact) (this also affects flow across the country)
Piracy
Banning imports/exports per trading partner (as a diplomatic measure) (this also prevents flow across the country)
War (reduces trade as a consequence)
Build monuments (promotes trade via prestige)
There was no trade between the Incans and the Aztecs. As such, the trade model should limit trade based upon regions that are relatively impassable. For your example, no trade routes should for over desert tiles that don't contain oases, or over tundra, or over dense rainforests.
Commodities
Can trade be modelled without modelling commodities? The disadvantage of commodities is that it can create too much of an imbalance, particularly where these are one-commodity-per-tile. A potential solution is to have multiple commodities per tile, which should reduce imbalance.
Passage
Trade that passes across the country is treated as an import and export.
Instantaneous
Assume trade is instantaneous. So the impact of actions upon trade levels are instantaneous.
The data
For each province, each turn, for each commodity:
value of exports to every other (known) province of the world
route that it takes
value of demand
This could be quite computationally intensive, as it would require iterative calculations such that local demand is satisfied first (or perhaps demand from rich provinces).
Can show trade on the map as a layer, with the width of the arrow showing the flow. This will highlight trade chokepoints, which are strategically important.
The value of exports to every other province in the world is related to:
distance (travel time)
populations
relationships
diplomatic status (war/peace)
active conflict (i.e. the presence of military units)
piracy
trade rates
trade bans
tech level
infrastructure (speed/latency)
infrastructure (capacity/bandwidth)
There is only one route used from one province to one other (this may not be the same in reverse). The route is dependent upon the variables above, with the exception of population.
Trade pact
Agreement for one Country to drop import tax to X% if the other drops import tax to Y%.
What do we want the trade model to include?
tax - definitely
diplomacy - definitely
currencies and exchange rates - probably not
balance of payments - probably not
impact on GDP - definitely
A highly abstracted trade model
A potential highly abstracted trade model would be to have all production of various commodities (including excess food production) automatically converted to "production units" at the market rate. That market is determined by the sum of all the trading relationships between all the players (whether trade is allowed by treaty, and whether it is possible, given blockades).
Key principles for trade
For a proper trade model, the following key principles apply:
location matters (location of production, location of consumption)
supply and demand matter
every commodity must have a mechanism of construction and of consumption
commodities matter (it is necessary for something to be in one place but not another in order for trade to happen)