Generalized Logistic Equations in Covid-Related Epidemic Models

The logistic equation on population growth was proposed by Verhulst (Corresp Math Phys 10:113-126, 1838) [22], with the aim to provide a possible correction to the unrealistic exponential growth forecast by T. Malthus, (J Johnson, London, 1872) [13]. Population modeling became of particular interest in the 20 th century to biologists urged by limited means of sustenance and increasing human populations. Verhulst’s scheme was rediscovered by A. Lotka, (Elements of Mathematical Biology. Dover, New York, 1956) [12], as a simple model of a self-regulating population. Subsequently, the use of logistic dynamics spreads across a huge number of different frameworks, especially in diffusion phenomena. The logistic differential equation is a fundamental element in quantitative study of population dynamics, its use also extends to the field of epidemiology: both to describe the evolution of the infected population in deterministic models, and working in conditions of uncertainty it is the deterministic component of stochastic differential equations. This work brings a contribution to the foundational basic research on the logistic equation and its generalizations which hopefully have repercussions for epidemiologic applications.