K - College of Natural Resources - University of California, Berkeley

* ( P )
a
SI
2
+ bP
l
a =
k
SI
*
SI
I
+ c = 0
⎛ l
⎜
⎜1−
⎝ l
SI
SS
⎞ l
⎟ +
⎠ k
⎛ π S I ⎞
S + π I
b = −
⎜
⎟
⎝ π Sπ
I ⎠
c = SI
kS
kI
and π S = and π I = .
k + l
k + l
S
SI
I
SI
where
SI
S
⎛ l
⎜
⎜1−
⎝ l
SI
II
2
⎞ ⎛ lSI
⎟ +
⎜
⎜1−
⎠ ⎝ lSSl
We consider four cases, in which infection status has varying influence on
pairing behavior (i.e. different sets of the pair formation and dissolution rates kS, kI, lSS,
lSI and lII have distinct values). When pair dissolution rates are equal (lSS=lSI=lII=l), a=0
*
in Equation (A7) and P = −c
b . Otherwise the quadratic formula was used to find
SI
II
⎞
⎟
⎠
(A7)
*
* 1
2
P SI . For a0) so solutions are
*
always real. Exact solutions for P in all four cases can be expressed in the form
shown in Equation (4), and full expressions are shown in Table 1. All solutions have
been checked numerically to ensure their validity.
Calculation of R0 and i∞
SI
The basic reproductive number, R0, is the expected number of secondary cases
caused by a typical infectious individual in a wholly susceptible population. As such, it
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