Ph. Berg et al., A PHARMACODYNAMIC MODEL FOR THE ACTION OF THE ANTIBIOTIC IMIPENEM ON PSEUDOMONAS-AERUGINOSA POPULATIONS IN-VITRO, Bulletin of mathematical biology, 58(5), 1996, pp. 923-938
The standard method for measuring in vitro antibiotic efficacy is base
d on a point observation of bacterial activity 18 hours after inoculat
ion. The method, while simple, forgoes significant information by igno
ring the dynamics of the interactions between antibiotic and bacteria.
This paper proposes a simple dynamic model describing these interacti
ons. The model consists of two non-linear differential equations of th
e S-system type. Its parameter values are estimated, through the minim
ization of residual errors, from data on the effect of the carbapenem
antibiotic imipenem on Pseudomonas aeruginosa. The model adequately de
scribes the dynamic behavior of the bacterial populations in the prese
nce of the antibiotic: beginning with drug administration, then throug
h the decline of the bacterial population and possibly ending with bac
terial resurgence.