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. Author manuscript; available in PMC: 2018 Jun 1.
Published in final edited form as: Theor Popul Biol. 2017 Apr 12;115:45–60. doi: 10.1016/j.tpb.2017.03.003

Table 4. Optimal spacing of releases.

p0 = 0.6 = 0.2 = 0.3

Dispersal D RI Rcrit Tmin D RI Rcrit Tmin
Gaussian 13.06 3.30 2.48 17.60 16.26 4.10 3.19 30.22
Laplace 12.21 3.08 2.35 17.95 16.22 4.09 3.06 31.13
ExpSqrt 11.30 2.85 1.99 19.54 15.11 3.81 2.64 34.87

p0 = 0.8 = 0.2 = 0.3

Dispersal D RI Rcrit Tmin D RI Rcrit Tmin

Gaussian 11.26 2.86 2.05 14.17 13.43 3.39 2.61 24.26
Laplace 10.25 2.60 1.97 14.57 13.39 3.38 2.52 25.09
ExpSqrt 9.34 2.36 1.62 16.25 12.18 3.07 2.16 28.59

All distances are measured in units of σ. Assuming releases over 20% of the target area (i.e., ρ = 0.2 and p0 = 0.6 or 0.8), we compare the spacing, D (distance between adjacent release centers), that produces the shortest time (in generations), Tmin, required to reach 80% coverage as a function of p0, initial infection frequency in release areas, and dispersal shape. The initial radius of these optimal releases, RI=Dρ/π, is compared to the minimum radius, Rcrit, required to initiate an expanding wave for the specified p0 and .