Right, but you'd just base your growth rate on what you know surely?
The higher the unknown cases, the more known cases you should have.
So would you bother trying to work out what the unknown cases were at all?
You do not. Give me time to type.
So the problem is, that you are faced with this:
'Exponential' is this hockey stick curve thingy:
That comes as a result of 'one person "converting" tree others" - in a short period of time'.
And that at one point (== hospitals getting full) you need to get the the downward slope again you also see in that graph (which I did'nt mark)).
Getting to that downward slope FAST, is very costly. (Basically halting your economy.)
Developing strategies, how to get to the downward slope, has to be done - before you reach that point.
Modeling is about giving you a rough Idea, when you reach that point (where drastic measures are necessary (and if)). And what to do then. (Roughly telly you, what what measure would do.)
Mitigation (masks, handwashing) is about, trying to never let the hockeystick appear (not letting one person infect 3 others).
And getting on the downward slope fast is 'in no way free, easy, or a natural given' (at some point it is, because "most of the fuel is burned" - then you plateau, but that can be at case numbers, way too high for certain other societal systems (hospitals, ...)).
--
Watch this movie if you want to see the 'hollywood version' of solving pestilence in the middle ages.
https://www.imdb.com/title/tt2101473/?ref_=nm_flmg_act_39
Hero walzes in the day after the plague hit town. Realizes its fleas on rats that are transmitting the disease, by looking at three dead people. Ben Kingsley and a group of 50 good guys make rat poison. A week later the curve goes down, the city is saved, and its back to power games..
In reality - you try to mitigate longterm costs (== you having to do harsh things to get the curve on the downwards slope again), while giving people developing vaccines more time to scale up production (== solve the issue structurally (rat poison in the Ben Kingsley movie..
).
Models are there to show you "decision packages" at certain 'stages'. You have several ones of those. (And a priest cast (scientists) that presents that to political leaders. Little better than priests, maybe..
) Who then decide on when to implement what.
if hospitals not overrun yet (or in danger to be). Less harsh measures can still be deployed. (If growth rate is not that exponential (meaning time until caserate doubles, is not three days or some incredibly small amount of time)).