Dear expert ,thank You.
Of course, we have no reason to believe that this study is limited. The equations are common.
In any case, we need to check the specific objects of study.
This study is a continuation of a general theory:
Continuous process are a special case of periodic processes. Periodic processes may be decribed by S-shaped curves.
This has a lot of interesting results.
In the other group we discuss common properties of S- shaped curves:
Please, about vaccines see:
Modeling the bacterial vaccine strains growth for the cells survival control in suspensions to improve the product at the freeze-drying and at the storage.
Our studies on the effect of Salmonella culture growth rate on cell survival under adverse external influences  showed that during GIP(growth inhibition phase), if there is a lack of dissolved oxygen, the accumulation of stable cells occurs at a constant specific rate equal to that of the growth delay (A = m/a). The share of stable cells within the population is obviously equal to that of nonproliferating cells, which consume energy only for viability maintenance. Methods for the definition of parameters of the structured model describing substrate consumption and metabolite biosynthesis on the basis of preliminary calculated parameters of the unstructured model were designed. Thus, the proposed structured model assumes that within a growing population there are two groups of cells essentially differing in their physiology. Group I represents newly generated (young) cells and group II contains cells being in a state of active proliferation. Although the cells of group I are often called ‘resting’ cells , in our opinion these are the cells of ‘zero age’ , i.e. the cells being in phase G1
or in phase V as designated for eukaryotes and prokaryotes, respectively. Group I cells exhibit minimal physiological functions, and for each cell these functions are constant. A
characteristic feature of the cells is that they consume energy substrates only for their viability maintenance. In  these cells are called ‘stable’.
All this is important to consider when considering your question.
 Klykov S P, Paderin J P, Sadikov M M, Chuprunov V P,
Derbyshev V V and Gusev V V 1996 Effect of culture
growth rate on Salmonella survival Biotechnology 1 35–9
 Pirt S J 1975 Principles of Microbe and Cell Cultivation
 Bailey J E and Ollis D F 1986 Biochemical Engineering
Fundamentals 2nd edn (New York: McGraw-Hill)