cbloom rants

3/08/2008

03-08-08 - 1

Sex Sim ADDENDUM : (scroll down and read the first post before this) :

I actually forgot to write about the most interesting thing. When you add actually STD transmission simulation you find that the "supervectors" can cause a critical point where the infection rate becomes nonlinear. This is super interesting, I guess this must be well known in infectious disease.

The simple model of STD's in the system goes like this : people are born in with STD's at some point (this is just to seed the system, I use 0.1% of births infected so it's a very small number and quickly becomes irrelevent). At each coupling, if one partner is infected there's some transmission rate which determines if the other partner is infected. Something like 10% is reasonable for this; remember it's not really just one night of sex, it's a whole relationship. Same basic model as before. We then measure the percentage of people infected at time of death for both normals and sluts.

For example :

```Varying the population fraction of sluts :

population:1000
couplingchance0:0.25
couplingchance1:10
relationduration0:25
relationduration1:4
infectedbirth:0.001
transmissionrate:0.15

fracsluts	normalinf	slutinf	overallinf
0.05	 	0.234 %		0.70%	0.26%
0.10		0.327 %		0.86%	0.38%
0.15	 	0.531 %		1.14%	0.62%
0.20	 	0.995 %		2.06%	1.21%
0.25	 	2.754 %		5.21%	3.37%
0.30	 	10.720 %	18.18%	12.96%
0.35	 	23.612 %	36.35%	28.08%
0.40	 	33.670 %	47.81%	39.33%
0.45	 	42.281 %	56.58%	48.71%

```
You can see the overall infection rate grows slowly and linearly with a small "slut" population, but once the slut population hits a critical point (around 25%) it suddenly jumps. You can see it really well in the graph of slut population vs. overall infection %

The whole system behaves differently on the other side of critial; before critical, infection is roughly linearly proportional to slut fraction. Also the normal infection rate is 1/3 the slut rate. Above critical, the normals quickly catch up and their infection rate is no longer much less than the sluts.

Of course slut population isn't the only thing that causes a critical point, the promiscuity of the sluts can have the same effect, and so can the transmission rate of STD's.

```Varying the transmission rate :

population:1000
couplingchance0:0.25
couplingchance1:10
relationduration0:25
relationduration1:4
popfraction0:0.80
popfraction1:0.20
infectedbirth:0.001

behaviors the same in all case :
normalsex 	fracslut	slutpartners
6.82	 	70.093%		22.129

transmission fraction vs. infected at death :

trans	overall infection
0.10	0.37%
0.11	0.43%
0.12	0.55%
0.13	0.68%
0.14	0.86%
0.15	1.30%
0.16	2.20%
0.17	4.84%
0.18	12.63%
0.19	23.65%
0.20	32.55%

```
You can see the critical point here really radically, infection proceeds in a normal linear way up to a transmission rate around 16% (0.16), and then suddenly hits a point where a massive chunk of the population is infected. And the graph is really striking : Graph of overall population infection vs. transmission rate

This is a bit interesting for thinking about pandemics and plagues too. The difference between an influenza that kills millions and one that spreads a bit then goes away may not actually be that big. If one is slightly above or below the critical point, that produces a massive change in results. What this means is that for near-critical transmission situations, even a slight reduction in the number of vectors can cause a huge drop in infection if you get below the critical point.