Table 1 The parameters used in the model along with their definitions and simulated values

P1, P2

Parasite species 1 and 2

n/a

S

Susceptible host proportion

Dynamic

I ₁ , I ₂ , I ₁₂

Host proportions infected with P1, P2 and both

Dynamic

E ₁ , E ₂ , E ₁₂

Environment contaminated with P1, P2 and both

Dynamic

λ ₁ , λ ₂

Rate at which new infections are established

0.1216328

β ₁ , β ₂

Rate at which hosts contaminate the environment

1.216328x10^-2, x10^-3

β _{1 | 12} , β _{2 | 12}

Rate at which co-infected hosts contaminate the env.

0.1-10 x β₁, x β₂

α ₁ , α ₂

Relative susceptibility to heterologous parasite infection

0.1-10

μ

Natural mortality rate of hosts (~50 yr life expectancy, parasite-induced host mortality can be modelled by μ_i > 0)

5.479452x10^-5

ν ₁ , ν ₂

Mortality rates of the free-living P1 and P2 stages

0.1

γ ₁ , γ ₂

Host recovery rate from P1 and P2 infection (~2 yr)

1.369863x10^-3

γ _{1 | 12} , γ _{2 | 12}

Recovery rate from P1 and P2 infection when co-infected

1.369863x10^-3