[Mathematical model of the zone formation in polyene antibiotic diffusion in an inoculated gel]

A mathematical model of inhibition growth zone formation on diffusion of polyenic antibiotics in gel is described. Dynamic equations for the zone formation describing the changes in time of the microbial population density (test microbe) in the presence of the diffusing antibiotics, as well as equations for diffusion of the antibiotics with an account of their inactivation were developed. Extreme cases of no inactivation of the drug by the test microbe are discussed. For the cases of spontaneous inactivation of the drugs due to instability of their molecules there were developed expressions showing correlation between the zone size and antibiotic initial concentration in the hole and other parameters characterizing the antibiotic and test microbe.