I meant within the bounds of a biurification graph. The 'average' will be based on the background population level for that organism.
Mmmm, how to explain this.
Lets take ebola as an example. Its deadly, it kills about half its hosts. It doesn't want a stable population growth. If it does that it will infect everyone eventually. Those who survive have antebodies, many pass those to their children during pregnancy and breast feeding and those who survive have children genetically predisposed to beating it.
Eventually it will have infected everyone and have no place to go. those who had it have antebodies and kill it, those who are new are the types who survive it anyway. It wants to kill. A postulating corpse it the best way for it to spread.
It wants to boom bust. Infect a small area, but once that area is saturated it wants a boom to infect new areas where it can continue in smaller numbers until that area is no longer of use. Then boom again.
A growth rate within a biurification graph from 3.57 (its going to be higher for a virus) to 4 is going to ensure it always stays in those boundaries. Over 4 it could go below and extinct itself. But there is also an upper limit because it must stay below 4 and so can't boom hard enough to infect the world in one go. IE, no pandemic.

so some examples.
Spanish influenza came out of nowhere (unlike ebola). Stable population growth, infected and killed millions, but disappeared. Why, everyone got it, all those left were immune. It disappeared. Extinct.
Black death (plague). Still exists but has a higher base level of population. remains relatively stable but can almost disappear and sometime boom in a massive way. (largely quelled now by modern medicine and hygiene).
Ebola. Small background population, is booming right now. Is as big as is likely to get. A pandemic will only ever be a new disease. Not an existing one.
I don't think I can explain it better. If you are interested, follow the breadcrumbs and research chaos theory in populations of organisms.