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

can be calculated as the product of the total rate of transmission per I individual times
the expected duration of infectiousness, in the limit S→N (Anderson and May 1991).
*
From Equation (A4), with P substituted from Equation (4), we find for our model:
R
0
= lim
S → N
SI
( transmission
rate per I individual×
duration of infectiousness)
⎛ S
= lim⎜
β pairφκ
( s,
i)
S → N
⎝ N
β pair
= lim κ
σ + µ S → N
( φ ( s,
i)
)
1 ⎞
× ⎟
σ + µ ⎠
From the expressions φκ(s,i) in Table 1, it is readily shown that
k
lim [ φκ ( s,
i)
] = π = for all cases. Therefore R0 takes the same form for all four
l
S → N
I
I
kI
+
SI
levels of infection-induced behavioral shifts, as shown in Equation (5).
We can also calculate the equilibrium density of infectives, I∞, by finding the
(A8)
⎛ dI ⎞
non-zero solution to ⎜ ⎟ = 0 . From this we can calculate the steady-state endemic
⎝ dt ⎠
I * ≠0
I ∞
prevalence, i∞
= . Results are shown in Table 1.
N
Calculation of steady-state fraction in partnerships
When disease does not influence pair-formation dynamics, we can simply model
the density of unpartnered individuals, X, and of partnerships, P:
dX
= −kX
+ 2lP
dt
dP 1 = 2 kX − lP
dt
42
(A9)