Gompertz and Verhulst Flameworks for Growth AND Decay Description

Verhulst logistic curve either grows OR decays, depending on the growth rate param eter sign. A similar situation is found in the Gompertz law about human mortality. It is aimed to encompass into ONE simple differential equation the growth AND decay features of, e.g., population sizes, or numbers. Previous generalizations of Verhulst or Gompertz functions are recalled. It is shown that drastic growth or decay jumps or turnovers can be readily described through drastic changes in values of the growth or decay rate. However smoother descriptions can be found if the growth or decay rate is modified in order to take into account some time or size dependence. Similar arguments can be carried through, but not so easily, for the so called carrying capacity, indeed leading to more elaborate algebraic work.