I don't think you need to worry too much about them finding each other because most of your survivors will die, and I think there is almost no chance that the number of survivors will assure the survival of humanity, even if they miraculously find each other. You need a much higher survival rate, which will affect communications and subsequent ability to find each other.
Approaching this only from a medical perspective, given your scenario (1 in 100K survive without restriction by genetics, age, location, etc. and loss of electricity/technology), about 12,500 will be aged 9 and under. Those under 5 will die in days from lack of water; those from 5 to 9 might live longer, but will likely die of disease, dehydration, exposure, malnutrition, etc. unless found by adults, so let's be generous and say 200 live and can someday integrate.
6,000 will be elderly (between 65-99) and will be well more than half women. While they will be helpful repositories of knowledge and can do light work, they cannot do too much, and their life expectancy will be dramatically reduced.
12,000 will be 10-19 years old. Most of those will have little skills or resources to stay alive (they will not know how to forage, let alone farm.) They, too, will be subject to disease and dehydration from unsanitary water and conditions (there are an awful lot of decomposing bodies around), and later by exposure. Being generous, let's say about one third will live more than 9 months. that's 4000, with about 2000 females. About 800 will be of reproductive age.
The golden number here is 28,000. That's the number of people alive between the ages of 19 and 45 (not inclusive). Half will be women of childbearing age. With the 10-19 year old surviving females, (14,000 plus 800) that leaves 14,800 women to repopulate the earth under adverse conditions. Of these, 2% will never conceive (296) and 10.5% will be unable to conceive after having one child (1,554) Of those who do conceive the first time (14,504), one in 100 will die from each pregnancy (the rate in underdeveloped countries) from postpartum hemorrhage, eclampsia, obstructed labor, and sepsis, (145 women) with the rate being 1 in 16 chance of dying from childbirth in her lifetime.
If all the females of childbearing age find males to reproduce with, after the first year of mating (not taking into account a spontaneous abortion rate of 20% before the 14th week), ~14000 babies will be born (half girls), 10% of the women will become infertile, and women will continue to die in childbirth: ~12930 women will be left for a second round. Miscarriages will increase due to decreased nutrition. Women will not have a baby per year in even the best of circumstances; the highest average number of babies per female in developing nations in the 1980s was 8.3. In the worst of circumstances, it will be much less.
In other disasters where a population was forced to become agrarian without technology (e.g. the Cambodia under the Khmer Rouge, after the initial killing of ~3% of the population, close to 25% of the population died in only 4 years (disease, starvation, overwork), and that was in a temperate climate. Your people have to travel to better climates by foot or animal. Think Oregon Trail. Mortality is very significant. A best guess scenario might mean the loss of about 3500 women in maybe 5 years, leaving ~9400 women capable of conceiving.
So, under ideal circumstances of every female mating every year, with the infertility, maternal death (and not even taking into account infant mortality, (which, as in developing nations will be significant), and an overall death rate of
20% in the first 5 years only, you'll be left with too few women and children to come close to repopulation.
If they are spread across the globe and must travel to find each other, the numbers shrink to a small fraction of the best case scenario.
6As a side note, you should probably better leave a lot more people alive, since in the process of gathering together, many of them will die, because they have no experience at all in surviving on their own. – PlasmaHH – 2014-11-07T10:20:18.943
Is there any reason landlines wouldn't work? – Pharap – 2014-11-07T11:36:24.980
3@Pharap: Power will soon be off since people maintaining the infrastructure will cease to do so. – PlasmaHH – 2014-11-07T11:57:16.593
6sounds like The Stand – Jimmery – 2014-11-07T12:44:06.977
Other than distance, I think the largest issue would be that everybody wouldn't share the same priorities. Priority 1 is for survival. Priority 2 would be for happiness, which means a lot of different things to different people. If there were a pressing need to find everybody else, I could see people finding a way, though I don't know how. – DoubleDouble – 2014-11-07T16:16:00.213
You should start watching Walking Dead :P – stackErr – 2014-11-07T18:58:09.410
2You grossly overestimate willingness of the survivors to cooperate. In such situation, small groups (tribes) would compete for best resources. Device would be gun. See my answer why. – Peter M. - stands for Monica – 2014-11-07T23:58:29.010
1Ham Radio can cover a huge area, especially if you start doing digital with error correcting code to punch through noise or weak connections (same sorts of advantages that Morse code had, only moreso). There are emergency preparedness plans which take advantage of that. That provides the long-distance connections. Short-distance: Anything which makes enough noise or light or smoke could be used to draw attention. Medium-distance might be hardest. – keshlam – 2014-11-08T03:03:11.623
It's worth pointing out that in no point in humanity's existence did everyone join together to form one united society. In fact when two groups of people who don't know each other meet they usually go to war. Other times they don't go to war, but don't form one big melting pot. – djechlin – 2014-11-08T15:35:45.157
IOW, your premise is basically that humanity has been fragmented at at war for many centuries, but a giant plague that would set the population back to another point at which humanity has been fragmented and at war, would fix all that. – djechlin – 2014-11-08T15:41:29.863
8One way to improve the basic premise could be to, rather than assume that humanity silently let this plague destroy 99.99999% of the population, have humans make some effort to set up emergency services or meeting locations while it was happening, or spread info about how to remain in touch, e.g. notify public of emergency radio frequencies as it was happening. Otherwise the premise is that everybody simply sat around for 2 weeks until the survivors were simply evenly distributed, which is strange and not how I would expect humans to behave. – Jason C – 2014-11-09T03:03:01.760
The short story: "The Scarlet Plague" covers a similar scenario. http://en.wikipedia.org/wiki/The_Scarlet_Plague It's a bit more realistic than the stand in terms of social and technological decline, also takes into account the emotional scarring the survivors end up with. After all, how many of us would be entirely right in the head after seeing pretty near everyone we love die?
– None – 2014-11-09T01:43:37.303I think you're making an invalid assumption. The survivors would not be trying to figure out how to cross oceans, etc, to find the remaining survivors. They'd be hunkering down, trying to find food for themselves and trying to avoid becoming food for the new dominant species, which would probably be rats. Canned food from supermarkets will only last so long. Without power, gas can't be pumped so they'd be on foot or, if very fortunate, on horseback. Think "tenth century"... – Bob Jarvis - Reinstate Monica – 2014-11-09T15:06:49.927
I'm curious if we (as a community) could approach the question of distributions. I know I translated "spread out evenly" as actually spread out. Others chose to translate it as "uniform distribution" which has clumps. Those clumps greatly improve the survival odds of the species, and are much more natural than the assumption I made. Which approach are you taking in the question? – Cort Ammon – 2014-11-09T22:34:37.820