  We provide a Galton--Watson model for the growth of a bacterial population in
the presence of antibiotics. We assume that bacterial cells either die or
duplicate, and the corresponding probabilities depend on the concentration of
the antibiotic. Assuming that the mean offspring number is given by $m(c) = 2 /
(1 + \alpha c^\beta)$ for some $\alpha, \beta$, where $c$ stands for the
antibiotic concentration we obtain weakly consistent, asymptotically normal
estimator both for $(\alpha, \beta)$ and for the minimal inhibitory
concentration (MIC), a relevant parameter in pharmacology. We apply our method
to real data, where \emph{Chlamydia trachomatis} bacteria was treated by
azithromycin and ciprofloxacin. For the measurements of \emph{Chlamydia} growth
quantitative PCR technique was used. The 2-parameter model fits remarkably well
to the biological data.
