An epidemiological model for proliferative kidney disease in salmonid populations

Parasites & Vectors

Table 2 List of parameters

Parameter	Definition	Dimension
Bryozoans
Constant
ρ	Inverse of carrying capacity	[M^-1L^-3]
β _B	Exposure rate	[L³T^-1]
φ	Fraction of B _C generating uninfected statoblasts	[−]
ψ	Recovery rate	[T^-1]
π _B	Rate of contamination operated by B _O	[M^-1T^-1]
σ _B	Probability of survival over winter for B _S, B _C	[−]
σ _O	Probability of survival over winter for B _O	[−]
ν	Biomass generated by one statoblast	[M]
Temperature-dependent
r	Baseline growth rate of B _S, B _C	[T^-1]
r _O	Baseline growth rate of B _O	[T^-1]
d _CO	Rate of covert-to-overt transition	[T^-1]
d _OC	Rate of overt-to-covert transition	[T^-1]
Time and temperature-dependent
f _B	Statoblast production rate	[M^-1T^-1]
Fish
Constant
μ _F	Natural mortality rate	[T^-1]
β _F	Exposure rate	[L³T^-1]
ε	Fraction of acute infections	[−]
γ	Rate of recovery from acute infection	[T^-1]
ζ	Rate of complete recovery	[T^-1]
π _F	Rate of contamination operated by F _I	[T^-1]
κ	Relative rate of contamination operated by F _C	[−]
σ _F	Probability of survival over winter	[−]
η	Baseline reproduction rate	[−]
ξ	Strength of density dependence	[L^-3]
Temperature-dependent
h	Rate of development of the disease	[T^-1]
a	PKD-caused mortality rate	[T^-1]
Parasite
μ _Z	Spore decay rate	[T^-1]
Rescaled parameters
\( {\pi}_B^{*}={\beta}_F{\pi}_B \)	Synthetic rate of contamination operated by B _O	[L³M^-1T^-2]
\( {\pi}_F^{*}={\beta}_B{\pi}_F \)	Synthetic rate of contamination operated by F _I	[L³T^-2]

ISSN: 1756-3305