Probably never.When should i use this option in the city management ???,
what is the advantages and disadvantages?
Never stop city growth because citizens are becoming sick.
This is all true. However, I often find myself using the stop growth option because (a) the city in question is building something important that isn't a Settler or a Worker and (b) if I juggle tile assignments to freeze growth then I'll end up in a sub-optimal situation (e.g. cottages not being worked, lower commerce, etc.). Frankly, assigning citizens to low-food tiles to freeze growth poses the same problem as turning on this option: you have to remember to change that to get the city growing again.The disadvantages are that it wastes all excess food once the bar is filled (really bad), and if you forget about and leave it on it will paralyse your cities, possibly making them completely worthless. You can get far better effects by building a worker/settler, or by picking tiles and specialist slots to use yourself when you want to slow growth down.
The thing to remember is that a city that has grown to its happiness cap and is still producing excess food is a prime candidate for use of the whip (i.e. the Slavery civic). With the food bar full (or filling fast), one of the citizens you whip away will be replaced quickly.
I know, I was merely replying to the question in the topic title.If your referring to me read my post again. I said unhappy not unhealthy.
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) no much hummer for making army,,,so any help please?

When should i use this option in the city management ???,
what is the advantages and disadvantages?
increases
income
maintenance costs for a large army)
from certain causes (such as lacking protection, lacking emancipation, war weariness, and fighting with enemy of the same faith, among others)
maintenance costs
growth, and if you don't have a granary, might go right back to previous population but at 0 food accumulated
doing nothing, but that food wasn't getting you anything anyways, so don't worry if you grow past the
capCan't you just unclick some weak food tiles to make specialists to keep it from going over the limit. Then you are still growing, but slower, and can use the specalists.
Sometimes it will lead to inferior tile usage (lack of hammers or commerce) and even rarer but still a possibility there is no way to get it to Stagnate. Its either growth or starvation. Its these times that the prevent growth button is useful.