Fig 1.
Flow diagram of model (1): the green squares represent the (fully) wild population (with females mated once or twice with wild males only); the blue squares represent the double-mated females (with fertile (sterile) and then sterile (fertile) males); the orange squares represent the sterile population (sterile males released and females mated once or twice with sterile males only).
Table 1.
Description of parameters and state variables of model (1).
Table 2.
C. capitata entomological parameter values used in this model (literature selected for demographic parameters were studies using host fruits rather than artificial diet, and field studies when available).
The parameters values for δ and δS are given below in Table 3.
Table 3.
Re-mating rates with and without GRO treatment [36].
Table 4.
Basic Offspring numbers with and without GRO treatment according to Tables 2 and 3.
Fig 2.
Critical ratio for continuous releases as a function of residual fertility—re-mating case 1 with bW,S = 0.5 × bW, bS,W = 0.5 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 3.
Critical ratio for continuous releases as a function of residual fertility—re-mating case 2 with bW,S = 0.4717 × bW and bSW = 0.6553 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 4.
Critical ratio for continuous releases as a function of residual fertility—re-mating case 3 with bWS = 0.1532 × bW and bSW = 0.65 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 5.
Critical ratio for continuous releases as a function of residual fertility—re-mating case 4 with bW,S = bW, bS,W = bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Table 5.
Numerical estimates for εmax, the threshold value for the residual fertility, with and without GRO treatment—Case 1: bW,S = bS,W = 0.5 × bW.
Table 6.
Numerical estimates for εmax with and without GRO treatment—Case 2: bWS = 0.4717 × bW and bSW = 0.6553 × bW.
Table 7.
Numerical estimates for εmax with and without GRO treatment—Case 3: bWS = 0.1532 × bW and bSW = 0.65 × bW.
Table 8.
Numerical estimates for εmax with and without GRO treatment—Case 4: bW,S = bS,W = bW.
Fig 6.
Critical ratio for weekly periodic releases as a function of residual fertility—re-mating 1 with bW,S = 0.5 × bW, bS,W = 0.5 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 7.
Critical ratio for weekly periodic releases as a function of residual fertility—re-mating case 2 with bW,S = 0.4717 × bW and bSW = 0.6553 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 8.
Critical ratio for weekly periodic releases as a function of residual fertility—re-mating case 3 with bWS = 0.1532 × bW and bSW = 0.65 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 9.
Critical ratio for weekly periodic releases as a function of residual fertility—re-mating case 4 with bW,S = bS,W = bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 10.
Critical ratio for periodic releases every 3 days based on residual fertility—re-mating case 1 with bW,S = 0.5 × bW, bS,W = 0.5 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 11.
Critical ratio for periodic releases every 3 days based on residual fertility—re-mating case 2 with bW,S = 0.4717 × bW and bSW = 0.6553 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 12.
Critical ratio for periodic releases every 3 days based on residual fertility—re-mating case 3 with bWS = 0.1532 × bW and bSW = 0.65 × bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 13.
Critical ratio for periodic releases every 3 days based on residual fertility—re-mating case 4 with bW,S = bS,W = bW: A) without GRO-treatment. B) With GRO-treatment. Simulations with different re-mating configurations: the black bullets, with re-mating rates δS > 0 and δ = 0; the red triangles, the NO re-mating case, δS = δ = 0; the green squares, with positive and equal re-mating rates, δS = δ > 0; the blue diamonds, with positive re-mating rates, δS > δ > 0.
Fig 14.
Wild population numbers evolution in time for periodic releases every 3 days and no residual fertility—re-mating case 2 with bW,S = 0.4717 × bW and bSW = 0.6553 × bW: (A) Without GRO-treatment (B) With GRO-treatment.
Fig 15.
Wild population numbers evolution in time for periodic releases every 3 days and 0.2% residual fertility—re-mating case 2 with bW,S = 0.4717 × bW and bSW = 0.6553 × bW,: (A) Without GRO-treatment (B) With GRO-treatment.