< Back to Article
Optimizing strategies for slowing the spread of invasive species
Fig 3
The algorithm finds the optimal treatment, which slows the population’s propagation to a given target speed, v, while minimizing the annual cost of treatment (ACT) (spongy moth population model). The description of the panels is similar to that in Fig 2. (A-D) The algorithm begins with a population front 
that has evolved naturally (A); it finds front shapes that could be slowed with lower annual costs (B-D), until reaching a population front 
for which ACT is minimized. (E-H) The same algorithm as in (A-D) is executed, only here it begins with a piecewise-linear population front (E). As in Fig 2, in both simulations no. 1 (A-D) and no. 2 (E-H) of the algorithm, the population front and the corresponding treatment function converge to a similar shape ((D) is similar to (H)). Units: Distance (x) is shown in units of σ = 10 km: population size (
) is in units of its carrying capacity; treatment cost (
) is in USD per hectare per year; and ACT is given in thousands of USD per one-kilometer strip of land. Parameters are the same in all panels: The target speed is v = 220 m/year, and the dynamics of n follow Eq (2), where b is given by Eqs (6–8) with r = 2, kλ0 = 100, and a = 0.08 USD‒1.
doi: https://doi.org/10.1371/journal.pcbi.1011996.g003