On Static, Dynamic and Stochastic Kinetic Models of Peaking Microbial Growth in a Closed or Resources-limited Habitat

A peaking static (isothermal) microbial growth curve recorded in an isolated habitat is viewed as a manifestation of a conflict between the tendency of healthy cells to multiply by division, and the habitat’s progressive depletion of resources and deterioration which is intensified by the rising population’s density. This scenario can be described mathematically by the product of a monotonically rising growth term such as a stretched exponential (Weibull) term, representing the habitat’s uninterrupted growth potential, by a stretched exponential (Weibull) decay term, representing the fall of the cells’ survival probability and increased mortality rate. An alternative is to have the growth potential represented by the Verhulst/logistic differential rate model, and the decline by a superimposed falling log-logistic algebraic term that becomes negative as growth turns into mortality. Yet another alternative is a scaled version of a beta-distribution function-based model, which captures both the rise and fall regimes in a single algebraic expression. For dynamic (notably non-isothermal) growth, a convenient model has the basic structure of the static Verhulst/logistic rate model equation, except that its parameters are entered as functions of time. In contrast with the other model equations the Verhulst/logistic mode conversion from a static to dynamic state does not require the use of inverse functions, and hence special programming.

Graphical Abstract