TABLE 2

Description of model parameters in bacterium-phage systemm

ParameterMeaningRangeBaselineReference(s)
γGrowth rate of bacteria under ideal conditions, normalized to 1a11 (5.1e−3 min−1)93, 94
λProportion growth rate change due to productive chronic infection(0.5, 3)b172
KCarrying capacity of bacteria, normalized to 1c11 (4e7 CFU/ml)95, 96
ηInfection rate(0, 40)20 (0.10 min−1)d41
κBacterial death rate due to antibiotic, relative to antibiotic lysis induction rate(0, 3.5)e193, 97
AAmplitude of stress (rate at which antibiotic induces lysis) introduced with one antibiotic dose(0, 2)1.1 (5.6e−3 min−1)f93, 98
kMetabolic decay rate of antibiotic within the system(1e−3, 0.6)g0.3 (1.7e−3 min−1)h93, 99, 100
{ti}Vector of antibiotic administration times55
δRate at which infection leads to phage production (eclipse and rise phase)(1.5, 7.3)i4 (2.0e−2 min−1)101, 102
fTFraction of bacteria infected with VT that become latently infected(0, 1)0.01103, 104
fCFraction of bacteria infected with VC that become latently infected(0, 1)0.01j
βTBurst size for bacteria infected with VT(10, 1,000)100101, 102, 105109
βCPhage production rate for bacteria infected with VC(5, 200)10 (5.1e−2 min−1)k
βmaxMaximum phage production rate for bacteria infected with VC under maximum stress(10, 10,000)100 (0.51 min−1)34
dRate of free phage degradation(0.9, 3.6)l1 (5.1e−3 min−1)110
  • a Growth rate is approximately 5.1e−3 min−1 for P. aeruginosa grown in vitro but is highly variable in cystic fibrosis patients.

  • b Estimates based on Escherichia coli and M13 phage.

  • c Stable bacterial density in sputum is highly variable in patients with cystic fibrosis; a study of viable P. aeruginosa densities in sputum of 12 patients not undergoing treatment ranged from 5.3e3 CFU/ml to 1.8e11 CFU/ml; log differences between control/placebo and treatment are more commonly reported. We select a carrying capacity near the geometric mean of that range; see the supplemental material for details.

  • d Estimate based on E. coli and λ phage; see the supplemental material for details.

  • e Estimate for antibiotic levofloxacin (upper limit on death rate may include death by phage induction).

  • f Estimated from in vitro experiment using antimicrobial peptides and meropenem; see the supplemental material for details.

  • g Low estimate is for meropenem in vitro; high estimate is for ciprofloxacin in vivo (human).

  • h Antibiotic is levofloxacin (half-life approximately 6.9 h); see the supplemental material for details.

  • i Low estimate is for PAXYB1 phage and PAO1 host, and high estimate is for PAK_P3 phage and PAO1 host; see the supplemental material for details.

  • j Guess based on temperate phage.

  • k Guess based on author experience.

  • l Low estimate is for phage extracted from Raunefjorden, and high estimate is for phage extracted from Bergen Harbor (strains unknown).

  • m See equations S1 to S15 in Text S1 in the supplemental material. Due to nondimensionalization of density and time, all variables and parameters are nondimensional; all densities are relative to the bacterial carrying capacity, and all rates are relative to the growth rate of bacteria under ideal conditions. Commonly used density and time units are noted in parentheses for baseline rates.