MATHEMATICAL MODELING OF MICROORGANISM GROWTH (ANALYTICAL APPROACH)

This work is a report "Mathematical modeling of the growth of microorganisms", written at the suggestion of the teacher of mathematics L.S. Akinfieva in 1982, when the author was a student of the 10th grade of a specialized (with in-depth study of biology) school No. 11 in Moscow. All students of this class were asked to write reports (as a "gift for the 60th anniversary of the USSR") within the framework of the general theme "Mathematics in my future profession." The report contains the basic equations of the kinetics of growth and dying of microorganisms, as well as their consumption of a nutrient substrate (Malthus, Monod's equations, Herbert's model). In addition to the equations of microbiological kinetics themselves, some methods of obtaining their approximate solutions in the form of explicit functions (without using numerical methods) are demonstrated.