Table 1 Mathematical model parameters
Symbol | Description | Value | Source |
|---|---|---|---|
Biological | |||
\({\nu }_{S}\) | Coefficient for amplified susceptibility to colonization after therapy with regular antimicrobial | 3 | [39] |
\({\nu }_{i}\) | Coefficient for amplified infectiousness | 2, sensitivity: 1, 3 | [40] |
ω | Susceptibility/infectiousness amplification factor for neutral antimicrobials with respect to regular ones | 0.5 | |
λ | Probability of clearing resistance to regular antimicrobials following treatment with restricted antimicrobials | 0.8 | Assumption (expert guess) |
α | Rate of spontaneous clearance of colonization (year−1)1 | 1.4 | |
δ | Delay between end of treatment with restricted antimicrobials and complete resolution of colonization (months) | 1 | Assumption (expert guess) |
1/\({\varphi }_{c}\) | Average time to spontaneous clearance of infection in the community (days)2 | 30 | [45] |
Transmission | |||
\({\beta }_{h}\) | human to human transmission colonization rate in hospitals (year−1) | 10.9 (95% CI: 5.8–20.9) | Model fit |
\({\beta }_{c}\) | human to human transmission colonization rate in the community (year−1) | 0.67 (95% CI: 0.56–0.79) | Model fit |
ε3 | External force of colonization equivalent (% by 2015) | 49.04 (95% CI:6–100), sensitivity: 0–60% | Model fit; exogenous values |
Antimicrobial consumption | |||
Treatment rate (treatments per year per inhabitant/patient, range) | |||
Hospital setting | |||
\({\rm T}_{h,1}\) | Regular antimicrobials | 0.18–0.27 | ANRESIS |
\({\rm T}_{h,2}\) | Restricted antimicrobials | 0.02–0.04 | ANRESIS |
\({\rm T}_{h,3}\) | Neutral antimicrobials | 0.26–0.34 | ANRESIS |
Community setting | |||
\({\rm T}_{c,1}\) | Regular antimicrobials | 0.71 -0.80 | ANRESIS |
\({\rm T}_{c,2}\) | Restricted antimicrobials | 0.0031–0.0032 | ANRESIS |
\({\rm T}_{c,3}\) | Neutral antimicrobials | 1.5–1.71 | ANRESIS |
Average treatment duration (days) | |||
\({\tau }_{1}\) | Regular antimicrobials | 8 | Assumption based on clinical routine |
\({\tau }_{2}\) | Restricted antimicrobials | 5 | Assumption based on clinical routine |
\({\tau }_{3}\) | Neutral antimicrobials | 8 | Assumption based on clinical routine |
θ | Hospitalisation rate | 0.061–0.069 | ANRESIS |
μh | Average length of hospitalization (days) | 10 | ANRESIS (set to reproduce data) |
\({\kappa }_{h/c}^{2}\) | Fraction of infections resulting in antibiotic therapy that were caused by Klebsiella pneumoniae in hospitals/community5 | 7% | |
\({\rho }_{h}\) | Fraction of infections caused by Klebsiella pneumoniae that were treated with restricted antibiotics (in hospitals)6 | 0.026 | ANRESIS |
\({\rho }_{c}\) | Fraction of infections caused by Klebsiella pneumoniae that were treated with restricted antibiotics (in the community)6 | 0.019 | ANRESIS |