Table 1. List of Parameters and their Values.
| Symbol | Interpretation | Value | Units | References |
| λ | Growth rate of bacteria | 2.7726 (without treatment)(i) | day−1 | [27], [28], [29] |
| 2.7726 −1.9 with treatment A (sensitive to A) | ||||
| 2.7726 −2.1 with treatment B (sensitive to B) | ||||
| δ | Division rate of bacteria | 2.7726 | day−1 | This study(ii) |
| μ | Mortality rate of sensitive bacteria | 0 without treatment | day−1 | This study |
| 1.9 with treatment A (for sensitive to A) | day−1 | |||
| 2.1 with treatment B (for sensitive to B) | ||||
| κ | λκ is the carrying capacity of bacteria | 1015/2.7726(iii) | This study | |
| γ | Killing rate of Phagocytes | 33.6038(iii) | day−1 | This study |
| P | Total Number of Phagocytes | 332711(iii) | This study | |
| τ | Recombination rate | 10−3 | day−1 | [41], [43] |
| p | Probability that a plasmid is lost during the division without antibiotic pressure | 0.4(iv) | This study |
In the work from [31], the E. coli generation time in vivo in the gastrointestinal tract was approximately 60 min (λ = 16.6622 day−1) and was quasi-static in the lumen content. However, the authors state that these results are specific to their experimental conditions, without competition with other bacteria. In our model, we chose a longer generation time based on (a) other studies [27]–[29]; and (b) the relevance of our simulations. Indeed, if λ is set at 16.6622 day−1, the bacterial growth was at a rate that antibiotic therapy was totally inefficient, even for susceptible bacteria.
In this study we assume that the mortality rate of bacteria in absence of antibiotics is negligible.
These parameters have been adjusted to maintain an infection threshold of 106 bacteria [32] and a rate of invasion comparable to previous studies [12].
The probability that a plasmid is lost during the division without antibiotic pressure depends on the bacteria and plasmid size. According to several studies, we chose an average parameter representative of E. coli and the common size of plasmid bearing resistance genes [33]–[36]. This probability may vary from 0 to 1 among 50 generations cell. In this model, this parameter was set at a value to provide adequate simulations.