THE DOSING SCHEDULE DECIDES WHETHER RESISTANCE WINS Science Journaling Club, Volume 2 Issue 1, Fall 2025 Everything below is simulation output. No bacteria were involved, no patients were involved, and none of it is medical advice. ============================================================================== master seed : 20250915 python : 3.12.3 numpy : 2.4.2 ------------------------------------------------------------------------------ psi_max_S 1.0000 /h psi_max_R 0.9000 /h (cost c = 0.100) psi_min -4.0000 /h kappa 1.5000 MIC_S 1.0000 mg/L MIC_R 16.0000 mg/L (ratio 16.0) K 1e+09 cells mu 1e-09 /birth t_half 3.0000 h k_elim 0.231049 /h dt 0.0200 h burn-in 48.0 h follow-up 168.0 h ============================================================================== VALIDATION 1 MUTANT SELECTION WINDOW, DETERMINISTIC CORE ============================================================================== Stochasticity off. Bisection to 1e-14 on the net growth rate of each strain at density zero. The concentration where a strain's net growth crosses zero is that strain's MIC by definition, so recovering the two input MICs is a check that the pharmacodynamic function was coded correctly and that the window edges are where we think they are. quantity club value input/analytic difference ------------------------------------------------------------------------------ lower MSW edge, psi_S(C)=0 1.000000000000 1.000000000000 -2.89e-15 upper MSW edge, psi_R(C)=0 16.000000000000 16.000000000000 0.00e+00 Mutant selection window produced by the model: [1.000000000000, 16.000000000000] mg/L, width 15.000000000 mg/L Mutant selection window fed in: [1.000000000000, 16.000000000000] mg/L, width 15.000000000 mg/L agreement to 2.9e-15 mg/L, which is the bisection tolerance. ============================================================================== VALIDATION 2 MINIMAL SELECTIVE CONCENTRATION, CLOSED FORM ============================================================================== The traditional window starts at MIC_S because that is where the sensitive strain stops growing. Relative selection for resistance starts earlier, at the concentration where psi_R first exceeds psi_S. The closed form is derived in msc_closed_form() in this file and was solved by hand before the code was written. quantity club value input/analytic difference ------------------------------------------------------------------------------ MSC, bisection vs closed form 0.190003079618 0.190003079618 -2.72e-15 MSC in units of MIC_S 0.190003079618 0.190003079618 -2.72e-15 Selective window produced by the model : [0.190003, 16.000000] mg/L that is : [MIC_S/5.26, 16 x MIC_S] Gullberg et al. (2011) measured minimal selective concentrations of MIC/4 to MIC/230 for real drug-strain pairs. Ours sits at MIC/5.3, inside that published range but at its weak-selection end. ============================================================================== VALIDATION 3 DENSE SCAN OF THE WINDOW ============================================================================== Scanning C from 0 to 40 mg/L in 40001 steps and asking two questions at each point: does R gain on S (psi_R > psi_S), and does R actually grow in absolute numbers (psi_R > 0)? Both must be true inside the window and at no point outside it. points scanned : 40001 points where R gains on S but C <= MSC : 0 points where R does not gain but C > MSC : 0 mismatches, 'R gains' vs C > MSC : 0 mismatches, 'R grows' vs C < MIC_R : 0 mismatches, 'R gains and grows' vs in window : 0 verdict : PASS C (mg/L) psi_S (/h) psi_R (/h) psi_R-psi_S in window ------------------------------------------------------------------------------ 0.000000 1.000000 0.900000 -0.100000 no 0.050000 0.986064 0.899807 -0.086256 no 0.100000 0.960782 0.899455 -0.061326 no 0.190003 0.898574 0.898574 0.000000 no 0.500000 0.593948 0.893917 0.299969 yes 1.000000 0.000000 0.882834 0.882834 yes 2.000000 -1.071068 0.851756 1.922823 yes 4.000000 -2.333333 0.765957 3.099291 yes 8.000000 -3.248894 0.538930 3.787825 yes 16.000000 -3.705882 0.000000 3.705882 no 24.000000 -3.835493 -0.533063 3.302430 no 40.000000 -3.922174 -1.406571 2.515602 no ============================================================================== VALIDATION 4 ZERO FITNESS COST, DRUG ABSENT ============================================================================== With c = 0 the resistant strain must never decline when there is no drug. Deterministic run, 500 h, C = 0, N_S(0) = 1e8, N_R(0) = 1e3, cost set to zero, mutation switched off. minimum change in N_R over any step : 0.000000e+00 cells minimum net growth rate of R : 0.000000e+00 /h N_R at t = 0 / t = 500 h : 1.000000e+03 -> 9.999900e+03 verdict : PASS, R never declines For contrast, the same run with the real cost c = 0.10: N_R at t = 0 / t = 500 h : 1.000000e+03 -> 1.928750e-18 R declines once the population fills the niche, which is what a cost is. Decay rate over the last 100 h: 0.100000 /h against the input 0.100000. ============================================================================== VALIDATION 5 ZERO MUTATION SUPPLY ============================================================================== mu = 0, N_R(0) = 0, 2000 stochastic replicates on a schedule that breeds resistance readily when mutation is on (D = 8 mg/L, tau = 24 h, 7 days). One resistant cell anywhere means the bookkeeping is wrong. replicates : 2000 largest N_R seen in any replicate : 0 replicates with any resistant cell ever : 0 replicates classified as resistance : 0 P(treatment success) with no mutation : 1.0000 verdict : PASS ============================================================================== VALIDATION 6 STANDING RESISTANCE AT MUTATION-SELECTION BALANCE ============================================================================== Before treatment the model runs 48 h of drug-free burn-in from N_S = K, N_R = 0. The deterministic balance is mu*K/c, approached with relaxation time 1/c = 10 h, so the accepted value at 48 h is the finite-time solution mu*K/c * (1 - exp(-c t)). quantity club value input/analytic difference ------------------------------------------------------------------------------ mean standing N_R at dose 1 10.1233 9.9177 0.2055 asymptotic balance mu*K/c - 10.0000 - standard error of the mean : 0.1571 cells difference in standard errors : 1.31 replicates with zero standing R : 282 of 4000 (7.05%) median standing N_R : 7.0 cells variance of standing N_R : 98.7 cells analytic variance lambda*d/(d-b)^2 : 100.0 cells verdict : PASS, within 3 standard errors ============================================================================== VALIDATION 7 TAU-LEAPING STEP SIZE ============================================================================== One cell (D = 8 mg/L, tau = 12 h, 7 days, full adherence) run at three step sizes with 2000 replicates each. A leap that is too coarse makes the outcome probabilities drift with dt. dt (h) n P(success) P(resistance) seconds ------------------------------------------------------------------------------ 0.080 2000 0.1000+-0.0067 0.9000+-0.0067 1.0 0.040 2000 0.1090+-0.0070 0.8910+-0.0070 1.4 0.020 2000 0.1035+-0.0068 0.8965+-0.0068 5.7 P(success) at dt = 0.04 against dt = 0.02 differs by 0.0055, which is 0.56 standard errors. dt = 0.02 h is used for everything below. ============================================================================== EXPERIMENT 1 DOSE SIZE BY DOSING INTERVAL, PERFECT ADHERENCE ============================================================================== 7-day course, adherence 1.0, 2000 replicates per cell, 25 cells, 50000 simulated courses. D is the concentration jump per dose in mg/L, so with MIC_S = 1 mg/L the column is also D/MIC_S. Brackets are 95% Wilson score intervals, which stay honest when a cell reads 0 or 1. D tau n AUC P(success) +-SE [95% Wilson] P(resistance) +-SE [95% Wilson] t_clear ------------------------------------------------------------------------------ 2.0 4.0 42 363.6 0.0515 +-0.0049 [0.0426,0.0621] 0.9485 +-0.0049 [0.9379,0.9574] 21.28 h 2.0 6.0 28 242.4 0.0375 +-0.0042 [0.0300,0.0468] 0.9625 +-0.0042 [0.9532,0.9700] 45.52 h 2.0 8.0 21 181.8 0.0000 +-0.0000 [0.0000,0.0019] 0.9935 +-0.0018 [0.9889,0.9962] - 2.0 12.0 14 121.2 0.0000 +-0.0000 [0.0000,0.0019] 1.0000 +-0.0000 [0.9981,1.0000] - 2.0 24.0 7 60.6 0.0000 +-0.0000 [0.0000,0.0019] 0.5555 +-0.0111 [0.5336,0.5772] - 4.0 4.0 42 727.1 0.0825 +-0.0062 [0.0712,0.0954] 0.9175 +-0.0062 [0.9046,0.9288] 10.46 h 4.0 6.0 28 484.7 0.0725 +-0.0058 [0.0619,0.0847] 0.9275 +-0.0058 [0.9153,0.9381] 14.38 h 4.0 8.0 21 363.6 0.0850 +-0.0062 [0.0736,0.0980] 0.9150 +-0.0062 [0.9020,0.9264] 19.41 h 4.0 12.0 14 242.4 0.0790 +-0.0060 [0.0680,0.0916] 0.9210 +-0.0060 [0.9084,0.9320] 49.65 h 4.0 24.0 7 121.2 0.0000 +-0.0000 [0.0000,0.0019] 1.0000 +-0.0000 [0.9981,1.0000] - 8.0 4.0 42 1454.2 0.1105 +-0.0070 [0.0975,0.1250] 0.8895 +-0.0070 [0.8750,0.9025] 7.26 h 8.0 6.0 28 969.5 0.1030 +-0.0068 [0.0904,0.1171] 0.8970 +-0.0068 [0.8829,0.9096] 8.30 h 8.0 8.0 21 727.1 0.0970 +-0.0066 [0.0848,0.1108] 0.9030 +-0.0066 [0.8892,0.9152] 9.88 h 8.0 12.0 14 484.7 0.0960 +-0.0066 [0.0839,0.1097] 0.9040 +-0.0066 [0.8903,0.9161] 14.36 h 8.0 24.0 7 242.4 0.0890 +-0.0064 [0.0773,0.1023] 0.9110 +-0.0064 [0.8977,0.9227] 54.12 h 16.0 4.0 42 2908.5 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 24.76 h 16.0 6.0 28 1939.0 0.2090 +-0.0091 [0.1917,0.2274] 0.7910 +-0.0091 [0.7726,0.8083] 6.56 h 16.0 8.0 21 1454.2 0.1945 +-0.0089 [0.1777,0.2124] 0.8055 +-0.0089 [0.7876,0.8223] 6.92 h 16.0 12.0 14 969.5 0.1865 +-0.0087 [0.1700,0.2042] 0.8135 +-0.0087 [0.7958,0.8300] 6.94 h 16.0 24.0 7 484.7 0.1945 +-0.0089 [0.1777,0.2124] 0.8055 +-0.0089 [0.7876,0.8223] 6.92 h 32.0 4.0 42 5816.9 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 5.62 h 32.0 6.0 28 3878.0 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 6.02 h 32.0 8.0 21 2908.5 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 5.98 h 32.0 12.0 14 1939.0 0.6515 +-0.0107 [0.6303,0.6721] 0.3485 +-0.0107 [0.3279,0.3697] 5.74 h 32.0 24.0 7 969.5 0.6870 +-0.0104 [0.6663,0.7069] 0.3130 +-0.0104 [0.2931,0.3337] 5.76 h Pharmacokinetic summaries of the same 25 regimens at steady state, from the concentration curve alone with no population model in them: D tau Cmax Cmin fT>MIC_S fT>MIC_R fT in window ------------------------------------------------------------------------------ 2.0 4.0 3.316 1.316 1.0000 0.0000 1.0000 2.0 6.0 2.667 0.667 0.7075 0.0000 1.0000 2.0 8.0 2.374 0.374 0.4677 0.0000 1.0000 2.0 12.0 2.133 0.133 0.2733 0.0000 0.8723 2.0 24.0 2.008 0.008 0.1257 0.0000 0.4252 4.0 4.0 6.632 2.632 1.0000 0.0000 1.0000 4.0 6.0 5.333 1.333 1.0000 0.0000 1.0000 4.0 8.0 4.748 0.748 0.8427 0.0000 1.0000 4.0 12.0 4.267 0.267 0.5233 0.0000 1.0000 4.0 24.0 4.016 0.016 0.2507 0.0000 0.5502 8.0 4.0 13.264 5.264 1.0000 0.0000 1.0000 8.0 6.0 10.667 2.667 1.0000 0.0000 1.0000 8.0 8.0 9.495 1.495 1.0000 0.0000 1.0000 8.0 12.0 8.533 0.533 0.7733 0.0000 1.0000 8.0 24.0 8.031 0.031 0.3757 0.0000 0.6752 16.0 4.0 26.527 10.527 1.0000 0.5471 0.4529 16.0 6.0 21.333 5.333 1.0000 0.2075 0.7925 16.0 8.0 18.991 2.991 1.0000 0.0927 0.9073 16.0 12.0 17.067 1.067 1.0000 0.0233 0.9767 16.0 24.0 16.063 0.063 0.5007 0.0007 0.7994 32.0 4.0 53.055 21.055 1.0000 1.0000 0.0000 32.0 6.0 42.667 10.667 1.0000 0.7075 0.2925 32.0 8.0 37.982 5.982 1.0000 0.4677 0.5323 32.0 12.0 34.133 2.133 1.0000 0.2733 0.7267 32.0 24.0 32.125 0.125 0.6257 0.1257 0.7994 Which pharmacokinetic index predicts the outcome? Spearman rank correlation of each index against P(success) across all 25 cells. index rho vs P(ok) rho vs P(res) ------------------------------------------------------------------------------ total AUC over the course 0.9333 -0.7994 AUC per interval / MIC_S 0.9570 -0.8492 Cmax / MIC_S 0.9809 -0.8497 Cmax / MIC_R 0.9809 -0.8497 fraction of time above MIC_S 0.6078 -0.4374 fraction of time above MIC_R 0.8807 -0.8452 fraction of time in the window -0.4818 0.6519 Best single predictor of treatment success: Cmax / MIC_S (rho = +0.9809). Total drug delivered over the course has rho = +0.9333, so on this grid how much drug you give predicts the outcome far less well than when the concentration sits above the resistant strain's MIC. Mechanism check. Splitting every replicate in the grid by whether any resistant cell was standing at the moment the first dose was taken: replicates starting with zero standing resistance : 3479 of which treatment succeeded : 2365 (0.6798) replicates starting with resistance already there : 46521 of which treatment succeeded : 11688 (0.2512) odds ratio : 6.33 ============================================================================== EXPERIMENT 2 MATCHED TOTAL EXPOSURE ============================================================================== Dosing interval fixed at 8 h. The product (number of doses) x (dose size) is held at 288 mg/L, so every row delivers the same total drug and the same area under the concentration curve. Only the shape of the schedule changes. 2000 replicates per row. days doses D AUC P(success) +-SE [95% Wilson] P(resistance) +-SE [95% Wilson] ------------------------------------------------------------------------------ 2 6 48.000 1246.5 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 3 9 32.000 1246.5 0.9950 +-0.0016 [0.9908,0.9973] 0.0050 +-0.0016 [0.0027,0.0092] 4 12 24.000 1246.5 0.4340 +-0.0111 [0.4124,0.4558] 0.5660 +-0.0111 [0.5442,0.5876] 5 15 19.200 1246.5 0.2615 +-0.0098 [0.2427,0.2812] 0.7385 +-0.0098 [0.7188,0.7573] 7 21 13.714 1246.5 0.1665 +-0.0083 [0.1508,0.1835] 0.8335 +-0.0083 [0.8165,0.8492] 10 30 9.600 1246.5 0.1080 +-0.0069 [0.0951,0.1224] 0.8920 +-0.0069 [0.8776,0.9049] 14 42 6.857 1246.5 0.0890 +-0.0064 [0.0773,0.1023] 0.9110 +-0.0064 [0.8977,0.9227] Best row : 2 days at D = 48.000, P(success) = 1.0000 Worst row : 14 days at D = 6.857, P(success) = 0.0890 Difference: 0.9110, which is 143.1 standard errors, on identical drug. Resistance runs from 0.0000 (2 days) to 0.9110 (14 days), a factor of 911000000. ============================================================================== EXPERIMENT 3 COURSE LENGTH AT A FIXED DOSE ============================================================================== The matched-exposure ladder changes two things at once, the dose and the length. This experiment changes only the length. D = 32 mg/L every 8 h, stopped after 1, 2, 3, 5, 7, 10 or 14 days. Total drug therefore rises fourteen-fold down the table. 2000 replicates per row. days doses AUC P(success) +-SE [95% Wilson] P(resistance) +-SE [95% Wilson] med t_clear ------------------------------------------------------------------------------ 1 3 415.5 0.8670 +-0.0076 [0.8514,0.8812] 0.1330 +-0.0076 [0.1188,0.1486] 5.88 h 2 6 831.0 0.9670 +-0.0040 [0.9582,0.9740] 0.0330 +-0.0040 [0.0260,0.0418] 6.02 h 3 9 1246.5 0.9955 +-0.0015 [0.9915,0.9976] 0.0045 +-0.0015 [0.0024,0.0085] 6.04 h 5 15 2077.5 0.9990 +-0.0007 [0.9964,0.9997] 0.0010 +-0.0007 [0.0003,0.0036] 6.06 h 7 21 2908.5 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 6.00 h 10 30 4155.0 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 6.04 h 14 42 5816.9 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 6.06 h 1 day against 14 days on the same dose: P(success) 0.8670 vs 1.0000, a difference of 0.1330, which is 17.52 standard errors. The extra 13 days cost 5401 mg/L of exposure, 13 times the first day's. Median time to clearance across all rows: 5.88 to 6.06 h. In this model the drug finishes inside the first day and every later dose is acting on a population that is already gone. ============================================================================== EXPERIMENT 4 MISSED DOSES ============================================================================== Adherence is only interesting on a regimen that works when taken properly, so the reference is D = 32 mg/L every 8 h, the schedule that cleared every replicate in Experiment 1. Each scheduled dose is taken independently with probability a. 2000 replicates per level, two course lengths, 3 days and 7 days. course length 3 days (9 scheduled doses) a missed AUC taken P(success) +-SE [95% Wilson] P(resistance) +-SE [95% Wilson] ------------------------------------------------------------------------------ 1.00 0.00 1246.5 0.9945 +-0.0017 [0.9902,0.9969] 0.0055 +-0.0017 [0.0031,0.0098] 0.95 0.45 1184.2 0.9560 +-0.0046 [0.9461,0.9641] 0.0440 +-0.0046 [0.0359,0.0539] 0.90 0.90 1121.8 0.9135 +-0.0063 [0.9004,0.9250] 0.0865 +-0.0063 [0.0750,0.0996] 0.85 1.35 1059.5 0.9005 +-0.0067 [0.8866,0.9129] 0.0995 +-0.0067 [0.0871,0.1134] 0.80 1.80 997.2 0.8555 +-0.0079 [0.8394,0.8702] 0.1445 +-0.0079 [0.1298,0.1606] 0.70 2.70 872.5 0.8160 +-0.0087 [0.7984,0.8324] 0.1840 +-0.0087 [0.1676,0.2016] 0.60 3.60 747.9 0.7935 +-0.0091 [0.7752,0.8107] 0.2060 +-0.0090 [0.1888,0.2243] 0.50 4.50 623.2 0.7720 +-0.0094 [0.7531,0.7899] 0.2270 +-0.0094 [0.2092,0.2459] course length 7 days (21 scheduled doses) a missed AUC taken P(success) +-SE [95% Wilson] P(resistance) +-SE [95% Wilson] ------------------------------------------------------------------------------ 1.00 0.00 2908.5 1.0000 +-0.0000 [0.9981,1.0000] 0.0000 +-0.0000 [0.0000,0.0019] 0.95 1.05 2763.0 0.9800 +-0.0031 [0.9729,0.9853] 0.0200 +-0.0031 [0.0147,0.0271] 0.90 2.10 2617.6 0.9350 +-0.0055 [0.9233,0.9450] 0.0650 +-0.0055 [0.0550,0.0767] 0.85 3.15 2472.2 0.9060 +-0.0065 [0.8924,0.9180] 0.0940 +-0.0065 [0.0820,0.1076] 0.80 4.20 2326.8 0.8595 +-0.0078 [0.8436,0.8740] 0.1405 +-0.0078 [0.1260,0.1564] 0.70 6.30 2035.9 0.8150 +-0.0087 [0.7974,0.8314] 0.1850 +-0.0087 [0.1686,0.2026] 0.60 8.40 1745.1 0.7915 +-0.0091 [0.7731,0.8087] 0.2085 +-0.0091 [0.1913,0.2269] 0.50 10.50 1454.2 0.7670 +-0.0095 [0.7480,0.7850] 0.2330 +-0.0095 [0.2150,0.2520] Seven-day course, adherence 1.00 -> 0.80: P(success) changes by -0.1405 (18.08 standard errors) and P(resistance) by +0.1405. Three-day course, adherence 1.00 -> 0.80: P(success) changes by -0.1390 and P(resistance) by +0.1390. Control. The same average amount of drug delivered on a schedule with no gaps in it: every dose taken, but each dose scaled down by a. If adherence hurt only by cutting the total, these two would match. a ragged schedule (missed doses) smooth schedule (smaller doses) ------------------------------------------------------------------------------ 0.80 ok 0.8595 res 0.1405 ok 0.4980 res 0.5020 0.70 ok 0.8150 res 0.1850 ok 0.3710 res 0.6290 0.60 ok 0.7915 res 0.2085 ok 0.2525 res 0.7475 0.50 ok 0.7670 res 0.2330 ok 0.2015 res 0.7985 ============================================================================== ARITHMETIC WHAT ONE MISSED DOSE BUYS THE RESISTANT STRAIN ============================================================================== No simulation in this section. It is the pharmacokinetics and the pharmacodynamic function integrated by hand, to show where the missed dose results come from. Elimination rate k = ln2/t_half = 0.231049 /h. short sharp arm: D = 32.0000 mg/L every 8 h steady-state peak Cmax = D / (1 - exp(-k tau)) = 37.9818 mg/L steady-state trough Cmin = 5.9818 mg/L time from peak down to MIC_R = 3.7417 h (0.4677 of a 8 h interval) time from peak down to MIC_S = 15.7417 h (1.0000 of a 8 h interval) time from peak down to MSC = 22.9294 h (1.0000 of a 8 h interval) on schedule ( 8.0 h): resistant x 5.5975e-01, sensitive x 3.2419e-13 one dose missed (16.0 h): resistant x 3.8606e+02, sensitive x 4.3216e-18 the gap multiplies the resistant strain by a further 6.8971e+02 gaps needed to take 9.9 standing mutants to 1e6 cells: 1.93 long mild arm: D = 6.8571 mg/L every 8 h steady-state peak Cmax = D / (1 - exp(-k tau)) = 8.1389 mg/L steady-state trough Cmin = 1.2818 mg/L time from peak down to MIC_R = never above it time from peak down to MIC_S = 9.0745 h (1.0000 of a 8 h interval) time from peak down to MSC = 16.2622 h (1.0000 of a 8 h interval) on schedule ( 8.0 h): resistant x 4.7462e+02, sensitive x 2.5048e-07 one dose missed (16.0 h): resistant x 5.9426e+05, sensitive x 1.1862e-05 the gap multiplies the resistant strain by a further 1.2521e+03 gaps needed to take 9.9 standing mutants to 1e6 cells: 0.87 Reading those two lines together: on the short sharp schedule a resistant cell is worse off at the end of every interval than at the start, and a single missed dose reverses that. On the long mild schedule it gains ground on every interval whether or not a dose is missed, which is why missing doses barely changes that arm at all. ============================================================================== EXPERIMENT 5 MONTE CARLO CONVERGENCE ============================================================================== One cell run long, D = 8 mg/L every 12 h for 7 days, full adherence, 20000 replicates, with the running estimate recorded as trials pile up. P(success) = 0.10395 +- 0.00216 P(resistance) = 0.89605 +- 0.00216 P(persist) = 0.00000 +- 0.00000 wall clock = 62.5 s n P(success) se P(resist) se |p_n - p_N|/se ------------------------------------------------------------------------------ 100 0.10000 0.03000 0.90000 0.03000 0.13 250 0.07600 0.01676 0.92400 0.01676 1.67 500 0.10600 0.01377 0.89400 0.01377 0.15 1000 0.10500 0.00969 0.89500 0.00969 0.11 2000 0.10800 0.00694 0.89200 0.00694 0.58 4000 0.10675 0.00488 0.89325 0.00488 0.57 8000 0.10625 0.00345 0.89375 0.00345 0.67 12000 0.10292 0.00277 0.89708 0.00277 0.37 16000 0.10356 0.00241 0.89644 0.00241 0.16 20000 0.10395 0.00216 0.89605 0.00216 0.00 Relative standard error on P(success) falls from 30.00% at n = 100 to 2.08% at n = 20000, a factor of 14.45 for a factor of 200 in trials. The 1/sqrt(n) prediction for that factor is 14.14. ============================================================================== EXPERIMENT 6 WHERE A DIFFERENT MODELLING CHOICE CHANGES THE ANSWER ============================================================================== Two arms carried through every sensitivity run: the short sharp arm (D = 32 mg/L q8h for 3 days) and the long mild arm (D = 6.857 mg/L q8h for 14 days). They deliver identical total drug. 1000 replicates per cell. The baseline row is the model as specified above. variant short: ok / resistance long: ok / resistance ------------------------------------------------------------------------------ baseline 0.9900 / 0.0100 0.1100 / 0.8900 fitness cost c = 0.02 0.9850 / 0.0150 0.0390 / 0.9610 fitness cost c = 0.30 0.9980 / 0.0020 0.2120 / 0.7880 fitness cost c = 0.50 0.9970 / 0.0030 0.3070 / 0.6930 MIC_R = 4 x MIC_S 1.0000 / 0.0000 0.6020 / 0.3980 MIC_R = 8 x MIC_S 1.0000 / 0.0000 0.1680 / 0.8320 MIC_R = 32 x MIC_S 0.1950 / 0.8050 0.0810 / 0.9190 inoculum K = 1e7 1.0000 / 0.0000 0.9780 / 0.0220 inoculum K = 1e8 0.9980 / 0.0020 0.7980 / 0.2020 mutation rate mu = 1e-10 1.0000 / 0.0000 0.7880 / 0.2120 mutation rate mu = 1e-8 0.9390 / 0.0610 0.0000 / 1.0000 immune clearance 0.10 /h 1.0000 / 0.0000 0.1250 / 0.8750 immune clearance 0.30 /h 1.0000 / 0.0000 0.2730 / 0.7270 immune clearance 0.50 /h 1.0000 / 0.0000 0.4470 / 0.5530 Baseline gap in P(success), short minus long : +0.8800 Smallest gap across all variants : +0.0220 (inoculum K = 1e7) Largest gap across all variants : +0.9460 (fitness cost c = 0.02) Variants where the short arm stops winning : none ============================================================================== EXPERIMENT 7 TWO TRAJECTORIES RECORDED IN FULL ============================================================================== Single replicates recorded every 0.1 h so the article can draw them. Panel A: D = 32 mg/L every 8 h, 3 days. Peaks above MIC_R. Panel B: D = 8 mg/L every 24 h, 7 days. Sits inside the window. panel A: standing N_R at dose 1 = 5, outcome = cleared panel A: max N_R = 5, final N_S = 0, final N_R = 0 panel A: peak C = 37.982 mg/L, last recorded C = 0.000 mg/L panel A: cleared at t = 6.02 h panel B: standing N_R at dose 1 = 5, outcome = resistance established panel B: max N_R = 908258952, final N_S = 0, final N_R = 908211768 panel B: peak C = 8.031 mg/L, last recorded C = 0.000 mg/L DATA BLOCK trajectoryA t_hours C_mgL N_S N_R (every 0.5 h) 0.00 32.0000 1025903986 5 0.50 28.5088 124788863 2 1.00 25.3984 18413935 1 1.50 22.6274 2820016 1 2.00 20.1587 439888 0 2.50 17.9594 69172 0 3.00 16.0000 11197 0 3.50 14.2544 1910 0 4.00 12.6992 324 0 4.50 11.3137 59 0 5.00 10.0794 16 0 5.50 8.9797 5 0 6.00 8.0000 1 0 6.50 7.1272 0 0 7.00 6.3496 0 0 7.50 5.6569 0 0 8.00 37.0397 0 0 8.50 32.9986 0 0 9.00 29.3984 0 0 9.50 26.1910 0 0 10.00 23.3335 0 0 10.50 20.7878 0 0 11.00 18.5198 0 0 11.50 16.4993 0 0 12.00 14.6992 0 0 12.50 13.0955 0 0 13.00 11.6668 0 0 13.50 10.3939 0 0 14.00 9.2599 0 0 14.50 8.2497 0 0 15.00 7.3496 0 0 15.50 6.5478 0 0 16.00 37.8334 0 0 16.50 33.7057 0 0 17.00 30.0284 0 0 17.50 26.7522 0 0 18.00 23.8335 0 0 18.50 21.2333 0 0 19.00 18.9167 0 0 19.50 16.8529 0 0 20.00 15.0142 0 0 20.50 13.3761 0 0 21.00 11.9168 0 0 21.50 10.6166 0 0 22.00 9.4583 0 0 22.50 8.4264 0 0 23.00 7.5071 0 0 23.50 6.6881 0 0 24.00 37.9584 0 0 24.50 33.8171 0 0 25.00 30.1276 0 0 25.50 26.8406 0 0 26.00 23.9123 0 0 26.50 21.3034 0 0 27.00 18.9792 0 0 27.50 16.9085 0 0 28.00 15.0638 0 0 28.50 13.4203 0 0 29.00 11.9561 0 0 29.50 10.6517 0 0 30.00 9.4896 0 0 30.50 8.4543 0 0 31.00 7.5319 0 0 31.50 6.7102 0 0 32.00 37.9781 0 0 32.50 33.8346 0 0 33.00 30.1432 0 0 33.50 26.8546 0 0 34.00 23.9247 0 0 34.50 21.3145 0 0 35.00 18.9890 0 0 35.50 16.9173 0 0 36.00 15.0716 0 0 36.50 13.4273 0 0 37.00 11.9623 0 0 37.50 10.6572 0 0 38.00 9.4945 0 0 38.50 8.4587 0 0 39.00 7.5358 0 0 39.50 6.7136 0 0 40.00 37.9812 0 0 40.50 33.8374 0 0 41.00 30.1457 0 0 41.50 26.8567 0 0 42.00 23.9266 0 0 42.50 21.3162 0 0 43.00 18.9906 0 0 43.50 16.9187 0 0 44.00 15.0728 0 0 44.50 13.4284 0 0 45.00 11.9633 0 0 45.50 10.6581 0 0 46.00 9.4953 0 0 46.50 8.4593 0 0 47.00 7.5364 0 0 47.50 6.7142 0 0 48.00 37.9817 0 0 48.50 33.8378 0 0 49.00 30.1461 0 0 49.50 26.8571 0 0 50.00 23.9269 0 0 50.50 21.3165 0 0 51.00 18.9908 0 0 51.50 16.9189 0 0 52.00 15.0730 0 0 52.50 13.4285 0 0 53.00 11.9635 0 0 53.50 10.6582 0 0 54.00 9.4954 0 0 54.50 8.4595 0 0 55.00 7.5365 0 0 55.50 6.7143 0 0 56.00 37.9817 0 0 56.50 33.8379 0 0 57.00 30.1461 0 0 57.50 26.8571 0 0 58.00 23.9270 0 0 58.50 21.3165 0 0 59.00 18.9909 0 0 59.50 16.9189 0 0 60.00 15.0731 0 0 60.50 13.4286 0 0 61.00 11.9635 0 0 61.50 10.6583 0 0 62.00 9.4954 0 0 62.50 8.4595 0 0 63.00 7.5365 0 0 63.50 6.7143 0 0 64.00 37.9817 0 0 64.50 33.8379 0 0 65.00 30.1461 0 0 65.50 26.8572 0 0 66.00 23.9270 0 0 66.50 21.3165 0 0 67.00 18.9909 0 0 67.50 16.9189 0 0 68.00 15.0731 0 0 68.50 13.4286 0 0 69.00 11.9635 0 0 69.50 10.6583 0 0 70.00 9.4954 0 0 70.50 8.4595 0 0 71.00 7.5365 0 0 71.50 6.7143 0 0 72.00 5.9818 0 0 72.50 5.3291 0 0 73.00 4.7477 0 0 73.50 4.2297 0 0 74.00 3.7683 0 0 74.50 3.3571 0 0 75.00 2.9909 0 0 75.50 2.6646 0 0 76.00 2.3739 0 0 76.50 2.1149 0 0 77.00 1.8841 0 0 77.50 1.6786 0 0 78.00 1.4954 0 0 78.50 1.3323 0 0 79.00 1.1869 0 0 79.50 1.0574 0 0 80.00 0.9421 0 0 80.50 0.8393 0 0 81.00 0.7477 0 0 81.50 0.6661 0 0 82.00 0.5935 0 0 82.50 0.5287 0 0 83.00 0.4710 0 0 83.50 0.4196 0 0 84.00 0.3739 0 0 84.50 0.3331 0 0 85.00 0.2967 0 0 85.50 0.2644 0 0 86.00 0.2355 0 0 86.50 0.2098 0 0 87.00 0.1869 0 0 87.50 0.1665 0 0 88.00 0.1484 0 0 88.50 0.1322 0 0 89.00 0.1178 0 0 89.50 0.1049 0 0 90.00 0.0935 0 0 90.50 0.0833 0 0 91.00 0.0742 0 0 91.50 0.0661 0 0 92.00 0.0589 0 0 92.50 0.0525 0 0 93.00 0.0467 0 0 93.50 0.0416 0 0 94.00 0.0371 0 0 94.50 0.0330 0 0 95.00 0.0294 0 0 95.50 0.0262 0 0 96.00 0.0234 0 0 96.50 0.0208 0 0 97.00 0.0185 0 0 97.50 0.0165 0 0 98.00 0.0147 0 0 98.50 0.0131 0 0 99.00 0.0117 0 0 99.50 0.0104 0 0 100.00 0.0093 0 0 100.50 0.0083 0 0 101.00 0.0074 0 0 101.50 0.0066 0 0 102.00 0.0058 0 0 102.50 0.0052 0 0 103.00 0.0046 0 0 103.50 0.0041 0 0 104.00 0.0037 0 0 104.50 0.0033 0 0 105.00 0.0029 0 0 105.50 0.0026 0 0 106.00 0.0023 0 0 106.50 0.0021 0 0 107.00 0.0018 0 0 107.50 0.0016 0 0 108.00 0.0015 0 0 108.50 0.0013 0 0 109.00 0.0012 0 0 109.50 0.0010 0 0 110.00 0.0009 0 0 110.50 0.0008 0 0 111.00 0.0007 0 0 111.50 0.0007 0 0 112.00 0.0006 0 0 112.50 0.0005 0 0 113.00 0.0005 0 0 113.50 0.0004 0 0 114.00 0.0004 0 0 114.50 0.0003 0 0 115.00 0.0003 0 0 115.50 0.0003 0 0 116.00 0.0002 0 0 116.50 0.0002 0 0 117.00 0.0002 0 0 117.50 0.0002 0 0 118.00 0.0001 0 0 118.50 0.0001 0 0 119.00 0.0001 0 0 119.50 0.0001 0 0 DATA BLOCK trajectoryB t_hours C_mgL N_S N_R (every 0.5 h) 0.00 8.0000 1025862817 5 0.50 7.1272 170918140 5 1.00 6.3496 36581516 5 1.50 5.6569 8673904 5 2.00 5.0397 2228764 5 2.50 4.4898 622865 11 3.00 4.0000 189354 12 3.50 3.5636 63500 22 4.00 3.1748 23663 30 4.50 2.8284 9613 45 5.00 2.5198 4294 68 5.50 2.2449 2220 104 6.00 2.0000 1272 156 6.50 1.7818 760 241 7.00 1.5874 526 372 7.50 1.4142 383 586 8.00 1.2599 319 898 8.50 1.1225 278 1373 9.00 1.0000 270 2061 9.50 0.8909 266 3176 10.00 0.7937 283 4898 10.50 0.7071 342 7645 11.00 0.6300 435 11963 11.50 0.5612 560 18634 12.00 0.5000 759 28942 12.50 0.4454 1068 45072 13.00 0.3969 1478 70208 13.50 0.3536 2089 109394 14.00 0.3150 3020 171150 14.50 0.2806 4466 266918 15.00 0.2500 6735 415316 15.50 0.2227 10258 647517 16.00 0.1984 15816 1009629 16.50 0.1768 24716 1575121 17.00 0.1575 38841 2457502 17.50 0.1403 61729 3829343 18.00 0.1250 97978 5963415 18.50 0.1114 156058 9279600 19.00 0.0992 249430 14408802 19.50 0.0884 397833 22300774 20.00 0.0787 634599 34345061 20.50 0.0702 1006230 52514976 21.00 0.0625 1579923 79401501 21.50 0.0557 2448568 118130210 22.00 0.0496 3714560 171780080 22.50 0.0442 5465033 242174885 23.00 0.0394 7740150 328221363 23.50 0.0351 10480541 424755556 24.00 8.0312 13509197 523082832 24.50 7.1550 2185868 533120019 25.00 6.3744 373374 554104750 25.50 5.6790 67373 581506080 26.00 5.0594 12792 612630784 26.50 4.5074 2629 645292197 27.00 4.0156 559 677759245 27.50 3.5775 129 708701475 28.00 3.1872 47 737234081 28.50 2.8395 16 762916408 29.00 2.5297 7 785442972 29.50 2.2537 1 804990390 30.00 2.0078 0 821689635 30.50 1.7888 0 835825688 31.00 1.5936 0 847735755 31.50 1.4197 0 857699060 32.00 1.2648 0 866045265 32.50 1.1268 0 872948783 33.00 1.0039 0 878736699 33.50 0.8944 0 883554350 34.00 0.7968 0 887570773 34.50 0.7099 0 890900694 35.00 0.6324 0 893737890 35.50 0.5634 0 896090371 36.00 0.5020 0 898101038 36.50 0.4472 0 899722544 37.00 0.3984 0 901074844 37.50 0.3549 0 902204822 38.00 0.3162 0 903179714 38.50 0.2817 0 903967387 39.00 0.2510 0 904637982 39.50 0.2236 0 905237317 40.00 0.1992 0 905670606 40.50 0.1775 0 906062981 41.00 0.1581 0 906403456 41.50 0.1409 0 906715277 42.00 0.1255 0 906939264 42.50 0.1118 0 907158336 43.00 0.0996 0 907372210 43.50 0.0887 0 907488016 44.00 0.0791 0 907599746 44.50 0.0704 0 907653442 45.00 0.0627 0 907787571 45.50 0.0559 0 907844896 46.00 0.0498 0 907925422 46.50 0.0444 0 907992966 47.00 0.0395 0 908030396 47.50 0.0352 0 908046730 48.00 8.0314 0 908082332 48.50 7.1551 0 793702252 49.00 6.3745 0 740137309 49.50 5.6790 0 717912858 50.00 5.0594 0 713587650 50.50 4.5075 0 719937736 51.00 4.0157 0 732544130 51.50 3.5776 0 748424357 52.00 3.1873 0 765734941 52.50 2.8395 0 783046778 53.00 2.5297 0 799499375 53.50 2.2537 0 814682680 54.00 2.0078 0 828289466 54.50 1.7888 0 840254205 55.00 1.5936 0 850661699 55.50 1.4198 0 859644803 56.00 1.2649 0 867309072 56.50 1.1269 0 873785485 57.00 1.0039 0 879279089 57.50 0.8944 0 883927880 58.00 0.7968 0 887830281 58.50 0.7099 0 891080140 59.00 0.6324 0 893828945 59.50 0.5634 0 896130539 60.00 0.5020 0 898111725 60.50 0.4472 0 899718538 61.00 0.3984 0 901069490 61.50 0.3549 0 902170843 62.00 0.3162 0 903133158 62.50 0.2817 0 903961028 63.00 0.2510 0 904615466 63.50 0.2236 0 905171935 64.00 0.1992 0 905619601 64.50 0.1775 0 906009206 65.00 0.1581 0 906399337 65.50 0.1409 0 906681888 66.00 0.1255 0 906957086 66.50 0.1118 0 907155463 67.00 0.0996 0 907342287 67.50 0.0887 0 907441409 68.00 0.0791 0 907542581 68.50 0.0704 0 907657819 69.00 0.0627 0 907740725 69.50 0.0559 0 907840119 70.00 0.0498 0 907898725 70.50 0.0444 0 907970398 71.00 0.0395 0 907995890 71.50 0.0352 0 908016233 72.00 8.0314 0 908049210 72.50 7.1551 0 793695928 73.00 6.3745 0 740165833 73.50 5.6790 0 717954364 74.00 5.0594 0 713666482 74.50 4.5075 0 720033846 75.00 4.0157 0 732607132 75.50 3.5776 0 748448628 76.00 3.1873 0 765682923 76.50 2.8395 0 782965927 77.00 2.5297 0 799420051 77.50 2.2537 0 814604607 78.00 2.0078 0 828208249 78.50 1.7888 0 840221219 79.00 1.5936 0 850693438 79.50 1.4198 0 859691053 80.00 1.2649 0 867338669 80.50 1.1269 0 873833776 81.00 1.0039 0 879305394 81.50 0.8944 0 883941663 82.00 0.7968 0 887838239 82.50 0.7099 0 891103013 83.00 0.6324 0 893863152 83.50 0.5634 0 896146133 84.00 0.5020 0 898042403 84.50 0.4472 0 899656829 85.00 0.3984 0 901017514 85.50 0.3549 0 902194899 86.00 0.3162 0 903154549 86.50 0.2817 0 903937547 87.00 0.2510 0 904606278 87.50 0.2236 0 905187840 88.00 0.1992 0 905661421 88.50 0.1775 0 906046628 89.00 0.1581 0 906425793 89.50 0.1409 0 906698969 90.00 0.1255 0 906920020 90.50 0.1118 0 907136794 91.00 0.0996 0 907293661 91.50 0.0887 0 907431566 92.00 0.0791 0 907546460 92.50 0.0704 0 907642289 93.00 0.0627 0 907731054 93.50 0.0559 0 907784200 94.00 0.0498 0 907842716 94.50 0.0444 0 907906785 95.00 0.0395 0 907935505 95.50 0.0352 0 907958969 96.00 8.0314 0 908030555 96.50 7.1551 0 793631959 97.00 6.3745 0 740108628 97.50 5.6790 0 717901615 98.00 5.0594 0 713572340 98.50 4.5075 0 719920327 99.00 4.0157 0 732497193 99.50 3.5776 0 748437954 100.00 3.1873 0 765663657 100.50 2.8395 0 782970345 101.00 2.5297 0 799450676 101.50 2.2537 0 814598861 102.00 2.0078 0 828249291 102.50 1.7888 0 840262079 103.00 1.5936 0 850653396 103.50 1.4198 0 859682824 104.00 1.2649 0 867328365 104.50 1.1269 0 873789791 105.00 1.0039 0 879260453 105.50 0.8944 0 883899090 106.00 0.7968 0 887794181 106.50 0.7099 0 891068696 107.00 0.6324 0 893865232 107.50 0.5634 0 896167307 108.00 0.5020 0 898109621 108.50 0.4472 0 899737620 109.00 0.3984 0 901115996 109.50 0.3549 0 902256494 110.00 0.3162 0 903169763 110.50 0.2817 0 903979114 111.00 0.2510 0 904635535 111.50 0.2236 0 905206628 112.00 0.1992 0 905682210 112.50 0.1775 0 906094035 113.00 0.1581 0 906476128 113.50 0.1409 0 906678462 114.00 0.1255 0 906897735 114.50 0.1118 0 907100112 115.00 0.0996 0 907293774 115.50 0.0887 0 907462788 116.00 0.0791 0 907594264 116.50 0.0704 0 907661709 117.00 0.0627 0 907697664 117.50 0.0559 0 907843888 118.00 0.0498 0 907862377 118.50 0.0444 0 907963526 119.00 0.0395 0 907977190 119.50 0.0352 0 908045866 120.00 8.0314 0 908030932 120.50 7.1551 0 793657499 121.00 6.3745 0 740110263 121.50 5.6790 0 717897151 122.00 5.0594 0 713603696 122.50 4.5075 0 719939410 123.00 4.0157 0 732542548 123.50 3.5776 0 748451140 124.00 3.1873 0 765682204 124.50 2.8395 0 783012189 125.00 2.5297 0 799496172 125.50 2.2537 0 814649426 126.00 2.0078 0 828248691 126.50 1.7888 0 840251438 127.00 1.5936 0 850667547 127.50 1.4198 0 859652065 128.00 1.2649 0 867341212 128.50 1.1269 0 873845244 129.00 1.0039 0 879317317 129.50 0.8944 0 883942865 130.00 0.7968 0 887835850 130.50 0.7099 0 891088458 131.00 0.6324 0 893825015 131.50 0.5634 0 896119882 132.00 0.5020 0 898077811 132.50 0.4472 0 899725011 133.00 0.3984 0 901086969 133.50 0.3549 0 902266319 134.00 0.3162 0 903236006 134.50 0.2817 0 904004550 135.00 0.2510 0 904681314 135.50 0.2236 0 905237512 136.00 0.1992 0 905636035 136.50 0.1775 0 906049301 137.00 0.1581 0 906399530 137.50 0.1409 0 906664748 138.00 0.1255 0 906905885 138.50 0.1118 0 907117884 139.00 0.0996 0 907273818 139.50 0.0887 0 907431371 140.00 0.0791 0 907550757 140.50 0.0704 0 907667589 141.00 0.0627 0 907783727 141.50 0.0559 0 907874444 142.00 0.0498 0 907905617 142.50 0.0444 0 907927505 143.00 0.0395 0 907956306 143.50 0.0352 0 907975276 144.00 8.0314 0 908012285 144.50 7.1551 0 793636294 145.00 6.3745 0 740107952 145.50 5.6790 0 717880950 146.00 5.0594 0 713555892 146.50 4.5075 0 719906646 147.00 4.0157 0 732529377 147.50 3.5776 0 748426443 148.00 3.1873 0 765688066 148.50 2.8395 0 782968154 149.00 2.5297 0 799421158 149.50 2.2537 0 814565779 150.00 2.0078 0 828209616 150.50 1.7888 0 840213442 151.00 1.5936 0 850685348 151.50 1.4198 0 859692949 152.00 1.2649 0 867306957 152.50 1.1269 0 873814407 153.00 1.0039 0 879299508 153.50 0.8944 0 883945376 154.00 0.7968 0 887875274 154.50 0.7099 0 891156123 155.00 0.6324 0 893892824 155.50 0.5634 0 896186066 156.00 0.5020 0 898156190 156.50 0.4472 0 899783088 157.00 0.3984 0 901105499 157.50 0.3549 0 902234925 158.00 0.3162 0 903181804 158.50 0.2817 0 903993150 159.00 0.2510 0 904650548 159.50 0.2236 0 905228777 160.00 0.1992 0 905698371 160.50 0.1775 0 906103771 161.00 0.1581 0 906479535 161.50 0.1409 0 906724560 162.00 0.1255 0 906955198 162.50 0.1118 0 907154613 163.00 0.0996 0 907309620 163.50 0.0887 0 907448110 164.00 0.0791 0 907529702 164.50 0.0704 0 907634305 165.00 0.0627 0 907715704 165.50 0.0559 0 907838037 166.00 0.0498 0 907890118 166.50 0.0444 0 907988530 167.00 0.0395 0 908030010 167.50 0.0352 0 908051076 168.00 0.0314 0 908040184 168.50 0.0279 0 908095817 169.00 0.0249 0 908146655 169.50 0.0222 0 908135346 170.00 0.0198 0 908102294 170.50 0.0176 0 908098525 171.00 0.0157 0 908126049 171.50 0.0140 0 908142271 172.00 0.0125 0 908164466 172.50 0.0111 0 908148010 173.00 0.0099 0 908166249 173.50 0.0088 0 908173076 174.00 0.0078 0 908153168 174.50 0.0070 0 908192795 175.00 0.0062 0 908204196 175.50 0.0055 0 908202302 176.00 0.0049 0 908200944 176.50 0.0044 0 908162875 177.00 0.0039 0 908159312 177.50 0.0035 0 908179268 178.00 0.0031 0 908166300 178.50 0.0028 0 908166829 179.00 0.0025 0 908177194 179.50 0.0022 0 908194459 180.00 0.0020 0 908185816 180.50 0.0017 0 908173984 181.00 0.0016 0 908192902 181.50 0.0014 0 908177351 182.00 0.0012 0 908201580 182.50 0.0011 0 908188843 183.00 0.0010 0 908187187 183.50 0.0009 0 908216599 184.00 0.0008 0 908216741 184.50 0.0007 0 908225534 185.00 0.0006 0 908190718 185.50 0.0006 0 908197686 186.00 0.0005 0 908227591 186.50 0.0004 0 908235102 187.00 0.0004 0 908222151 187.50 0.0003 0 908210703 188.00 0.0003 0 908177652 188.50 0.0003 0 908189512 189.00 0.0002 0 908205503 189.50 0.0002 0 908233471 190.00 0.0002 0 908189993 190.50 0.0002 0 908175617 191.00 0.0002 0 908177202 191.50 0.0001 0 908184269 192.00 0.0001 0 908218509 192.50 0.0001 0 908243223 193.00 0.0001 0 908209042 193.50 0.0001 0 908219227 194.00 0.0001 0 908194350 194.50 0.0001 0 908149058 195.00 0.0001 0 908083305 195.50 0.0001 0 908105153 196.00 0.0000 0 908157471 196.50 0.0000 0 908153520 197.00 0.0000 0 908146495 197.50 0.0000 0 908155508 198.00 0.0000 0 908148479 198.50 0.0000 0 908172990 199.00 0.0000 0 908185838 199.50 0.0000 0 908196583 200.00 0.0000 0 908195920 200.50 0.0000 0 908185388 201.00 0.0000 0 908183575 201.50 0.0000 0 908176748 202.00 0.0000 0 908167553 202.50 0.0000 0 908178605 203.00 0.0000 0 908173888 203.50 0.0000 0 908179019 204.00 0.0000 0 908223731 204.50 0.0000 0 908197314 205.00 0.0000 0 908215685 205.50 0.0000 0 908194837 206.00 0.0000 0 908200241 206.50 0.0000 0 908173403 207.00 0.0000 0 908172043 207.50 0.0000 0 908185238 208.00 0.0000 0 908151896 208.50 0.0000 0 908155027 209.00 0.0000 0 908141863 209.50 0.0000 0 908130423 210.00 0.0000 0 908157911 210.50 0.0000 0 908157071 211.00 0.0000 0 908143893 211.50 0.0000 0 908135876 212.00 0.0000 0 908194681 212.50 0.0000 0 908185440 213.00 0.0000 0 908240415 213.50 0.0000 0 908232218 214.00 0.0000 0 908199595 214.50 0.0000 0 908212590 215.00 0.0000 0 908221635 215.50 0.0000 0 908206740 ============================================================================== MACHINE-READABLE BLOCKS FOR THE FIGURES AND THE LATEX ============================================================================== BLOCK grid D tau P_ok SE P_res SE P_persist SE fT_s fT_r fT_win Cmax 2.0 4.0 0.05150 0.00494 0.94850 0.00494 0.00000 0.00000 1.0000 0.0000 1.0000 3.316 2.0 6.0 0.03750 0.00425 0.96250 0.00425 0.00000 0.00000 0.7075 0.0000 1.0000 2.667 2.0 8.0 0.00000 0.00000 0.99350 0.00180 0.00650 0.00180 0.4677 0.0000 1.0000 2.374 2.0 12.0 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.2733 0.0000 0.8723 2.133 2.0 24.0 0.00000 0.00000 0.55550 0.01111 0.44450 0.01111 0.1257 0.0000 0.4252 2.008 4.0 4.0 0.08250 0.00615 0.91750 0.00615 0.00000 0.00000 1.0000 0.0000 1.0000 6.632 4.0 6.0 0.07250 0.00580 0.92750 0.00580 0.00000 0.00000 1.0000 0.0000 1.0000 5.333 4.0 8.0 0.08500 0.00624 0.91500 0.00624 0.00000 0.00000 0.8427 0.0000 1.0000 4.748 4.0 12.0 0.07900 0.00603 0.92100 0.00603 0.00000 0.00000 0.5233 0.0000 1.0000 4.267 4.0 24.0 0.00000 0.00000 1.00000 0.00000 0.00000 0.00000 0.2507 0.0000 0.5502 4.016 8.0 4.0 0.11050 0.00701 0.88950 0.00701 0.00000 0.00000 1.0000 0.0000 1.0000 13.264 8.0 6.0 0.10300 0.00680 0.89700 0.00680 0.00000 0.00000 1.0000 0.0000 1.0000 10.667 8.0 8.0 0.09700 0.00662 0.90300 0.00662 0.00000 0.00000 1.0000 0.0000 1.0000 9.495 8.0 12.0 0.09600 0.00659 0.90400 0.00659 0.00000 0.00000 0.7733 0.0000 1.0000 8.533 8.0 24.0 0.08900 0.00637 0.91100 0.00637 0.00000 0.00000 0.3757 0.0000 0.6752 8.031 16.0 4.0 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.0000 0.5471 0.4529 26.527 16.0 6.0 0.20900 0.00909 0.79100 0.00909 0.00000 0.00000 1.0000 0.2075 0.7925 21.333 16.0 8.0 0.19450 0.00885 0.80550 0.00885 0.00000 0.00000 1.0000 0.0927 0.9073 18.991 16.0 12.0 0.18650 0.00871 0.81350 0.00871 0.00000 0.00000 1.0000 0.0233 0.9767 17.067 16.0 24.0 0.19450 0.00885 0.80550 0.00885 0.00000 0.00000 0.5007 0.0007 0.7994 16.063 32.0 4.0 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.0000 1.0000 0.0000 53.055 32.0 6.0 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.0000 0.7075 0.2925 42.667 32.0 8.0 1.00000 0.00000 0.00000 0.00000 0.00000 0.00000 1.0000 0.4677 0.5323 37.982 32.0 12.0 0.65150 0.01065 0.34850 0.01065 0.00000 0.00000 1.0000 0.2733 0.7267 34.133 32.0 24.0 0.68700 0.01037 0.31300 0.01037 0.00000 0.00000 0.6257 0.1257 0.7994 32.125 BLOCK matched days D n_doses AUC P_ok SE P_res SE 2 48.0000 6 1246.49 1.00000 0.00000 0.00000 0.00000 3 32.0000 9 1246.49 0.99500 0.00158 0.00500 0.00158 4 24.0000 12 1246.49 0.43400 0.01108 0.56600 0.01108 5 19.2000 15 1246.49 0.26150 0.00983 0.73850 0.00983 7 13.7143 21 1246.49 0.16650 0.00833 0.83350 0.00833 10 9.6000 30 1246.49 0.10800 0.00694 0.89200 0.00694 14 6.8571 42 1246.49 0.08900 0.00637 0.91100 0.00637 BLOCK duration days n_doses AUC P_ok SE P_res SE 1 3 415.50 0.86700 0.00759 0.13300 0.00759 2 6 830.99 0.96700 0.00399 0.03300 0.00399 3 9 1246.49 0.99550 0.00150 0.00450 0.00150 5 15 2077.48 0.99900 0.00071 0.00100 0.00071 7 21 2908.47 1.00000 0.00000 0.00000 0.00000 10 30 4154.96 1.00000 0.00000 0.00000 0.00000 14 42 5816.95 1.00000 0.00000 0.00000 0.00000 BLOCK adherence days a P_ok SE P_res SE 3 1.00 0.99450 0.00165 0.00550 0.00165 3 0.95 0.95600 0.00459 0.04400 0.00459 3 0.90 0.91350 0.00629 0.08650 0.00629 3 0.85 0.90050 0.00669 0.09950 0.00669 3 0.80 0.85550 0.00786 0.14450 0.00786 3 0.70 0.81600 0.00866 0.18400 0.00866 3 0.60 0.79350 0.00905 0.20600 0.00904 3 0.50 0.77200 0.00938 0.22700 0.00937 7 1.00 1.00000 0.00000 0.00000 0.00000 7 0.95 0.98000 0.00313 0.02000 0.00313 7 0.90 0.93500 0.00551 0.06500 0.00551 7 0.85 0.90600 0.00653 0.09400 0.00653 7 0.80 0.85950 0.00777 0.14050 0.00777 7 0.70 0.81500 0.00868 0.18500 0.00868 7 0.60 0.79150 0.00908 0.20850 0.00908 7 0.50 0.76700 0.00945 0.23300 0.00945 BLOCK smooth a P_ok SE P_res SE 0.80 0.49800 0.01118 0.50200 0.01118 0.70 0.37100 0.01080 0.62900 0.01080 0.60 0.25250 0.00971 0.74750 0.00971 0.50 0.20150 0.00897 0.79850 0.00897 BLOCK convergence n P_ok SE P_res SE 100 0.10000 0.03000 0.90000 0.03000 250 0.07600 0.01676 0.92400 0.01676 500 0.10600 0.01377 0.89400 0.01377 1000 0.10500 0.00969 0.89500 0.00969 2000 0.10800 0.00694 0.89200 0.00694 4000 0.10675 0.00488 0.89325 0.00488 8000 0.10625 0.00345 0.89375 0.00345 12000 0.10292 0.00277 0.89708 0.00277 16000 0.10356 0.00241 0.89644 0.00241 20000 0.10395 0.00216 0.89605 0.00216 BLOCK sensitivity variant short_ok short_res long_ok long_res baseline 0.9900 0.0100 0.1100 0.8900 fitness_cost_c_=_0.02 0.9850 0.0150 0.0390 0.9610 fitness_cost_c_=_0.30 0.9980 0.0020 0.2120 0.7880 fitness_cost_c_=_0.50 0.9970 0.0030 0.3070 0.6930 MIC_R_=_4_x_MIC_S 1.0000 0.0000 0.6020 0.3980 MIC_R_=_8_x_MIC_S 1.0000 0.0000 0.1680 0.8320 MIC_R_=_32_x_MIC_S 0.1950 0.8050 0.0810 0.9190 inoculum_K_=_1e7 1.0000 0.0000 0.9780 0.0220 inoculum_K_=_1e8 0.9980 0.0020 0.7980 0.2020 mutation_rate_mu_=_1e-10 1.0000 0.0000 0.7880 0.2120 mutation_rate_mu_=_1e-8 0.9390 0.0610 0.0000 1.0000 immune_clearance_0.10_/h 1.0000 0.0000 0.1250 0.8750 immune_clearance_0.30_/h 1.0000 0.0000 0.2730 0.7270 immune_clearance_0.50_/h 1.0000 0.0000 0.4470 0.5530 BLOCK pd C psi_S psi_R 0.0000 1.000000 0.900000 0.2500 0.848485 0.897848 0.5000 0.593948 0.893917 0.7500 0.301520 0.888837 1.0000 0.000000 0.882834 1.2500 -0.294610 0.876043 1.5000 -0.573651 0.868556 1.7500 -0.832954 0.860442 2.0000 -1.071068 0.851756 2.2500 -1.288136 0.842542 2.5000 -1.485177 0.832839 2.7500 -1.663649 0.822680 3.0000 -1.825177 0.812094 3.2500 -1.971401 0.801106 3.5000 -2.103888 0.789740 3.7500 -2.224092 0.778018 4.0000 -2.333333 0.765957 4.2500 -2.432798 0.753578 4.5000 -2.523543 0.740896 4.7500 -2.606503 0.727927 5.0000 -2.682506 0.714685 5.2500 -2.752282 0.701185 5.5000 -2.816473 0.687440 5.7500 -2.875647 0.673461 6.0000 -2.930306 0.659261 6.2500 -2.980892 0.644851 6.5000 -3.027796 0.630241 6.7500 -3.071366 0.615442 7.0000 -3.111911 0.600463 7.2500 -3.149704 0.585313 7.5000 -3.184991 0.570002 7.7500 -3.217989 0.554539 8.0000 -3.248894 0.538930 8.2500 -3.277882 0.523185 8.5000 -3.305110 0.507311 8.7500 -3.330720 0.491315 9.0000 -3.354839 0.475205 9.2500 -3.377583 0.458987 9.5000 -3.399056 0.442668 9.7500 -3.419354 0.426254 10.0000 -3.438561 0.409751 10.2500 -3.456758 0.393166 10.5000 -3.474015 0.376504 10.7500 -3.490397 0.359770 11.0000 -3.505964 0.342970 11.2500 -3.520770 0.326110 11.5000 -3.534866 0.309193 11.7500 -3.548298 0.292226 12.0000 -3.561107 0.275213 12.2500 -3.573333 0.258158 12.5000 -3.585012 0.241065 12.7500 -3.596177 0.223940 13.0000 -3.606858 0.206785 13.2500 -3.617084 0.189606 13.5000 -3.626881 0.172405 13.7500 -3.636273 0.155187 14.0000 -3.645284 0.137955 14.2500 -3.653935 0.120713 14.5000 -3.662244 0.103464 14.7500 -3.670231 0.086212 15.0000 -3.677912 0.068959 15.2500 -3.685303 0.051708 15.5000 -3.692419 0.034463 15.7500 -3.699275 0.017226 16.0000 -3.705882 0.000000 16.2500 -3.712254 -0.017212 16.5000 -3.718402 -0.034408 16.7500 -3.724337 -0.051585 17.0000 -3.730068 -0.068741 17.2500 -3.735606 -0.085873 17.5000 -3.740959 -0.102980 17.7500 -3.746135 -0.120059 18.0000 -3.751143 -0.137108 18.2500 -3.755991 -0.154125 18.5000 -3.760684 -0.171108 18.7500 -3.765230 -0.188055 19.0000 -3.769636 -0.204965 19.2500 -3.773907 -0.221836 19.5000 -3.778048 -0.238666 19.7500 -3.782066 -0.255453 20.0000 -3.785965 -0.272197 20.2500 -3.789750 -0.288895 20.5000 -3.793426 -0.305546 20.7500 -3.796997 -0.322148 21.0000 -3.800467 -0.338701 21.2500 -3.803840 -0.355204 21.5000 -3.807120 -0.371654 21.7500 -3.810310 -0.388051 22.0000 -3.813414 -0.404394 22.2500 -3.816435 -0.420681 22.5000 -3.819375 -0.436912 22.7500 -3.822239 -0.453086 23.0000 -3.825028 -0.469201 23.2500 -3.827746 -0.485257 23.5000 -3.830394 -0.501254 23.7500 -3.832976 -0.517189 24.0000 -3.835493 -0.533063 24.2500 -3.837948 -0.548875 24.5000 -3.840343 -0.564624 24.7500 -3.842680 -0.580309 25.0000 -3.844961 -0.595929 25.2500 -3.847188 -0.611485 25.5000 -3.849362 -0.626976 25.7500 -3.851485 -0.642401 26.0000 -3.853560 -0.657759 26.2500 -3.855587 -0.673051 26.5000 -3.857567 -0.688275 26.7500 -3.859503 -0.703431 27.0000 -3.861396 -0.718520 27.2500 -3.863247 -0.733540 27.5000 -3.865057 -0.748491 27.7500 -3.866828 -0.763373 28.0000 -3.868561 -0.778186 28.2500 -3.870257 -0.792929 28.5000 -3.871917 -0.807603 28.7500 -3.873542 -0.822206 29.0000 -3.875132 -0.836739 29.2500 -3.876691 -0.851202 29.5000 -3.878217 -0.865594 29.7500 -3.879712 -0.879915 30.0000 -3.881176 -0.894166 30.2500 -3.882612 -0.908346 30.5000 -3.884019 -0.922455 30.7500 -3.885398 -0.936493 31.0000 -3.886750 -0.950459 31.2500 -3.888076 -0.964355 31.5000 -3.889376 -0.978179 31.7500 -3.890652 -0.991933 32.0000 -3.891903 -1.005615 BLOCK window MSC MIC_S MIC_R 0.190003080 1.000000000 16.000000000 ============================================================================== TOTALS ============================================================================== simulated treatment courses in this run : 178002 replicates in the largest single cell : 20000 master seed : 20250915 wall clock : 498.0 s Reminder: this is a model. It contains no patients, no bacteria and no clinical data, and nothing in it is advice about taking medicine.