体外杀菌效力的随机建模
Stochastic modeling of in vitro bactericidal potency
摘要：
我们提供了一个高尔顿-沃森模型的细菌种群在抗生素的存在下的增长。我们假设细菌细胞要么死亡，要么复制，相应的概率取决于抗生素的浓度。假设平均后代数由$m(c) = 2 / (1 + αc^β)$给出，其中$c$代表抗生素浓度，我们得到了$(α, β)$和最小抑菌浓度（MIC）（药理学中的相关参数）的弱一致、渐近正态估计。我们将我们的方法应用于实际数据，其中\emph{Chlamydia trachomatis}细菌被阿奇霉素和环丙沙星处理。对于\emph{Chlamydia}生长的测量，使用定量PCR技术。双参数模型非常适合生物学数据。
英文摘要：
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 $m(c) = 2 / (1 + αc^β)$ for some $α, β$, where $c$ stands for the antibiotic concentration we obtain weakly consistent, asymptotically normal estimator both for $(α, β)$ 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.
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