The SIS model
Models diseases where re-infection is possible
Gonorrhea, Chlamydia, are exampled from
sexually transmitted infections (and thus appro-
priate for network epidemiology)
A population of susceptible (S) and infectious (I)
When S meets I, there is a probability λ that S
will become I
I becomes S again after some time, or with some
chance per unit of time
Two areas of current research
1.The epidemic threshold (phase transition in λ).
2.The extinction probability as a function of λ.
Both points when N → ∞
The immortality transition
There is another phase transition (threshold)—
when λ = 1. The mean time to extinction
diverges at this point.
It may seem trivial (since it is not an emergent
property in the N → ∞), but we will pretend it is
Our example networks
We could take any small networks with a variety
of network structures, but to honor the network
epidemiology pioneers we use:
D. M. Auerbach, W. W. Darrow, H. W. Jaffe, and
J. W. Curran, Am. J. Med. 76, 487 (1984).
S. Haraldsdottir, S. Gupta, and R. M. Anderson,
J. Acquir. Immune Defic. Syndr. 5, 374 (1992).
Contribution of individual nodes
Measure America Iceland
ki 0.73(4) 0.974(2)
ni 0.82(4) 0.75(5)
mi 0.83(3) 0.965(2)
i 0.64(4) 0.917(6)
max Ki 0.76(5) 0.98(2)
for α 0.17(8) 0.038(5)
max Ri 0.72(6) 0.97(4)
for d 0.99(1) 0.99(1)
a = ζ(G ) / ζ(G)i i