Figure 2.

Post-border spatial dispersal modelling¹⁰. After an individual invasive species enters location $L$, the probability of its survival and establishment at location $L$ is $p_L^E$. The cost of non-survival is zero. The probability of it being detected after establishment with surveillance cost $S_L$ spent at location $L$ is $p_L^D(S_L)$. Once detected, it will be eradicated with eradication cost $Z_L^E$; if not, it will become widespread at location $L$, or even move to other potential locations $m=1,2,\dots ,n\backslash L$ with probability $p_L^S{w}_L^m$ ($p_L^S$ is a common coefficient that is specific to location $L$, $w_L^m$ is a spatial connection weight between location $L$ and $m$) and another loop process starts. It is assumed that when the invasive species becomes widespread at location $L$, the invasive species could be detected with 100% probability. The following eradication conducted with budget $Z_L^W$ (much higher than $Z_L^E$), may fail with probability $1-p_L^{\mathit{Suc}}$. It should be noticed that ${\sum }_{m=1}^N{w}_L^m=1,m\in \{1,2,\dots ,n\}\backslash L$.