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Optimizing strategies for slowing the spread of invasive species
Fig 2
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) (simple model). (A) The algorithm begins with a population front, 
, that has evolved naturally when the species has propagated at a speed v0 (v0 > v; blue line). The algorithm then finds the treatment function 
for which the speed of the leftward movement of the front does not exceed v in any location. (B-D) The algorithm finds new front shapes, as well as the treatment functions that hold these fronts propagating leftward at a speed v. In each iteration, the algorithm changes 
and 
to those for which the ACT is lower. (E-H) The same algorithm as in (A-D) is executed, only here it begins with a piecewise-linear population front (E). In both simulation no. 1 (A-D) and no. 2 (E-H) of the algorithm, 
and 
converge to a similar shape ((D) is similar to (H)), and we denote 
and 
of this final outcome of the algorithm (shown in (D) and (H)) as nopt and Aopt, respectively. Parameters are the same in all panels: The target speed is v = 10 km/year, and the dynamics of n follow Eq (1), where b and d are given by Eq (3) with r = 2 year–1, k =2, and γ = 1 year‒1; G is given by Eq (4) with σ = 1 km; and R given by Eq (5) with β 1.25 USD‒1 year‒1 and α = 0.2.
doi: https://doi.org/10.1371/journal.pcbi.1011996.g002