Table 3. List of all parameters. Maximum likelihood values are provided for parameters that were part of the best model (discrete-time model with all bugs from sites infested at t−1, t and t+1 counted as source). For details on parameters see equation (1) and text.

Symbol	Description	Value in best model
a	Intercept for establishment function (determines the rate of establishment not attributable to other source sites)	0.15
b	Slope of establishment function (determines the increase in the rate of establishment as function of bugs found on other source sites)	0.014
c 1	Distance decay parameter for intervals from November–May [m−1]	0.011
c 2	Distance decay parameter for intervals from May–November [m−1]	0 (not fitted)
pe	Extinction probability for unsprayed sites in discrete-time model	0.5
pes	Extinction probability for sprayed sites in discrete-time model	0.9
pd	Probability to detect infestation at a site in May surveys given the site is infested	NA
pI	Probability of instantaneous extinction due to spraying in continuous-time model	NA
μ	Extinction rate in continuous-time model	NA
ρ	Proportionality factor for establishment on sites sprayed within the same time interval	0.4
γ	Factor for increase of establishment rate after last infestation [year−1]	0.38
α	Factor for instantaneous effect of spraying on establishment rate	NA
β	Decay rate for on establishment rate [year−1]	NA