Supplementary Methods
Details of the parasite-interaction model
We modelled the dynamics of a parasite community consisting of three parasite species
(P1, P2 and P3) within a single (average) host individual. The burden of parasite species i
wss increased by a constant uptake rate, i and decreased at a per capita rate i. Each
parasite stimulated an immune response Ii, which increased at rate i proportional to that
parasite’s density and decreased at rate i. This immune response had a detrimental
impact on that parasite, by reducing its uptake rate in an exponential fashion, so that the
uptake rate of the parasite in the face of host immunity was i e  i I i where i determined
the strength of the immune response’s impact on parasite uptake. We incorporated
interactions between parasite species via the host’s immune response by allowing each
species (j) to modify the level of immune response raised against one other parasite (i) at
a per capita rate j. Hence, if j was positive, parasite species j reduced Ii, leading to a
positive effect on parasite species i. Conversely, if j was negative, parasite j increased
stimulation of the immune response, leading to a negative impact on parasite i.
Finally, we incorporated vaccination (V) as a dynamic variable, which was
applied at initial level V0 and decayed at rate V. This vaccine wss assumed to be
species-specific, targeted solely at parasite 1 and it worked, like host immunity, by
modifying the uptake rate of species 1 in an exponential fashion, according to the
parameter . Hence, the full model is:
dP1
 1e ( 1I1 V)  1P1
dt
dPi
 i e  i Ii   i Pi
dt
for i = 2,3
dI i
  i Pi   i I i   j P j
dt
where j = 3 when i = 1, j = 1 when i = 2, j = 2 when
i=3
dV
   V V following an initial application level of V0.
dt
All parameter values used in the simulations are listed in Table A1. For the
simulations, we initially ran the model with no vaccine and record the equilibrium levels
of the three parasite species, assuming parasite 1 had a negative impact on parasite 2 (1 =
–1), parasite 2 had a positive impact on parasite 3 (2 = +1) and the impact of parasite 3
on parasite 1 was allowed to vary between –1 and +1. Once the parasites had reached
equilibrium, we applied the vaccine and recorded the post-vaccine equilibrium levels.
The graphs in the main text show the change in abundance following vaccination of each
parasite species:
i = Post-vaccination level of species i
Pre-vaccination level of species i
Table A1. Parameter definitions and values used in the simulation model
Parameter
Definition
Value
i
Uptake rate of parasite i
1, i
i
Mortality rate of parasite i
1/12, i
i
Stimulation rate of immune response i
1, i
i
Decay rate of immune response i
0, i
i
Impact of specific immune response on parasite i
-1, i
j
Modification of immune system i by parasite j
-1
i = 2, j = 1
1
i = 3, j = 2
from –1 to +1
i = 1, j = 3
V0
Initial application dose of vaccine
10
V
Decay rate of vaccine
0

Impact of vaccine on parasite 1
-0.5