Mathematical model for comparison of time-killing curves.

The relevance of mathematical modeling to investigations of the bactericidal effects of antimicrobial agents has been emphasized in many studies of killing kinetics. We propose here a descriptive model of general use, with four parameters which account for the lag phase, the initial number of bacteria, and the limit of effectiveness and bactericidal rate of antimicrobial agents. The model has been applied to several kinetic datum sets with amoxicillin, cephalothin, nalidixic acid, pefloxacin, and ofloxacin against two Escherichia coli strains. It is a useful tool to compare killing curves by taking into account model parameter confidence limits. This can be illustrated by studying drug effects, strain effects, and concentration effects. For the antibiotics used here, concentration effects had an influence mainly on the length of the lag phase and the minimum number of living cells observed. It is therefore clear that differences in the killing curves with changes in one or more parameters could occur.