Table 1.
Parameter definitions. The parameter values were those found during the optimisation process in the Results section.
Table 2.
Host survival at the end of each 24-h interval for different ‘fixed dose’ treatments, i.e. 0.9 mg either administered as a single dose, or split equally over 2 days, or split equally over 3 days (n = 45).
PBS = phosphate-buffered saline; Vib 79 = V. anguillarum (bacterium).
Fig 1.
Decay rate of the antibiotic (TET) over time in G. mellonella host.
Biological data of the decay rate of the antibiotic over time in G. mellonella (red points); and fitted curves for the experimental data (black lines) and the estimate for the half-life of the antibiotic (blue lines). The black and blue dotted lines represent the respective 95% confidence intervals.
Fig 2.
Comparison of mathematical model and experimental results for survival rates for different ‘fixed dose’ treatments, with 0.9 mg either administered as a single dose, or split equally over 2 days, or split equally over 3 days: (A) 0.9 mg administered at 2 h; (B) 0.45 mg administered at 2 h and at 24 h; (C) 0.3 mg administered at 2 h, 24 h and 48 h. n = 45 for biological experiments; n = 5000 for mathematical model.
Table 3.
Host survival from the biological validation experiments.
Host survival was recorded at 192 h for five different antibiotic treatment regimens, with both the ‘raw’ data given, along with the ‘normalised’ data, whereby host survival for four of the treatments were increased by 0.28 to bring host survival for (0.45,0.45) and (0.9,0) treatments in line with those in the initial experiments, in Table 2. (n = 90.) Full data in the Supporting Information (S3 Table).
Fig 3.
Survival rates at 192 h for various first doses, d1; where the second dose is (0.9−d1). The mathematical model results are in black; blue circles represent the initial biological experimental data (Table 2), and green circles are the additional biological experiments (Table 3). Red circles represent the normalised data from Table 3 (with each of the four points increased by 0.28). (The model runs for these solutions were increased to 10000 to confirm the accuracy of the results).
Fig 4.
Two-dose treatment regimen with the first dose d1 is taken at 2 h and the second dose 0.9-d1 at t2 h.
Host survival at 192 h is plotted against the size of the first dose d1: and the time of the second dose t2. Model runs = 10000.
Fig 5.
(A) Combined Pareto Fronts for 50 repeat runs; (B) subset of points along the upper edge of combined Pareto Fronts in (A). Both graphs show the trade-off between the total amount of antibiotic used in a treatment regimen and maximum host survival at 192 h. The colours of the points represent the number of (non-zero) antibiotic doses used to achieve that optimal point. Population = 50, generations = 80, model runs = 5000, repetitions = 50.
Table 4.
Optimal treatment regimens from within the Pareto Front (Fig 5B) for different criteria, given host survival at 192 h of at least (a) 0.9, or (b) 0.99.
(*Only 4-dose treatments were found along the upper edge of Pareto Front with host survival more than 0.99).