A mathematical model-based analysis of the time–kill kinetics of ceftazidime/avibactam against Pseudomonas aeruginosa

Objectives: To characterize quantitatively the effect of avibactam in potentiating ceftazidime against MDR Pseudomonas aeruginosa by developing a mathematical model to describe the bacterial response to constant concentration time-kill information and validating it using both constant and time-varying concentration-effect data from in vitro and in vivo infection systems. Methods: The time course of the bacterial population dynamics in the presence of static concentrations of ceftazidime and avibactam was modelled using a two-state pharmacokinetic/pharmacodynamic (PK/PD) model, consisting of active and resting states, to account for bactericidal activities, bacteria-mediated ceftazidime degradation and inhibition of degradation by avibactam. Ceftazidime's effect on the bacterial population was described as an enhancement of the death rate of the active population, with the effect of avibactam being to increase ceftazidime potency. Model validation was performed by comparing simulated time courses of bacterial responses with those from in vitro and in vivo experimental exposures of ceftazidime and avibactam that represented those predicted in an average patient dosed with 2 g/0.5 g ceftazidime/avibactam administered every 8 h as 2 h infusions. Results: The two-state model successfully described the bacterial population dynamics, ceftazidime degradation and its inhibition by avibactam. For external validation, the model correctly predicted the bacterial response of P. aeruginosa isolates evaluated in in vitro hollow-fibre and in vivo neutropenic mouse thigh and lung infection models. Conclusions: The PK/PD model and modelled strains successfully replicated the spread in activity when compared with a large selection of P. aeruginosa strains reported in the literature.