Initial Comp at epidemic start time w/ unknown infection time; unable to infer its lineages' coalescent waiting times

[gtng92]

Drawing coalescent waiting times from linear population growth dynamics. Current implementation implies that the final piece remains at a constant population size with a slope of zero. First infected compartment in epidemic has no recorded infection time, I originally assumed the initial infection time to be arbitrarily large.

Instead, I'm going to implement it so the maximum time is right before it hits the saturation point (before the population size goes constant). Since there shouldn't be any transmissions possible after this point in time (since we are only doing births and no deaths).

[ArtPoon]

Rewording the problem: this is an issue at the root of the outer tree, where we are at the last infected individual carrying two or more lineages (one of which was just traced back through a transmission event). If individuals are immortal (no death rate specified), then we have way of asserting a time frame of that root individual's infection, so we can't say much about their within-host population dynamics that we need to simulate the coalescent process. So I propose to impose this constraint:

• without a death rate, coalescent rates must be uniform (constant within-host population sizes)
• with a death rate, varying coalescent rates are permitted because it should be possible to draw a waiting time to infection of the root compartment.

[ArtPoon]

We are proceeding with option 1 for now, until death rates are implemented.