Periods labelled "famines" were not all that common, but much of the population was living in a sub-acute famine much the time, primarily for political reasons (power imbalances, unelightened decision-makers).
> how does that model explains why eastern Asian [rice-growing areas] ... where able to achieve and sustain far higher population density [than the Eurocentric examples in OP].
The average densities were higher, but until the 20th century, with Beijing* as the primary exception, big cities were in Western Asia, North Africa, and Europe.[1] Many infectious diseases probably need "point" (small area) population sizes greater than those of the villages prevalent in rice-growing areas to take hold.
Rice rulers could afford to burn a village to the ground if there were reports of spreading sickness in it. They'd only lose a small fraction of their tax base, which would soon be replaced. Rulers of large cities, not so much.
Why did rice-growing areas have villages while wheat areas developed cities? I don't know. Possibly something to do with wheat being being grown in drier areas so it could be stored for years without rotting, making large centralised granaries possible.
* And a few other North China cities. I know very little about Beijing, but I don't think the climate there is suitable for rice.
1. https://en.wikipedia.org/wiki/List_of_largest_cities_through...