A stretched logistic equation for pandemic spreading. (November 2020)

• Record Type: Journal Article
• Authors: Consolini, Giuseppe; Materassi, Massimo
• Is Part Of: Chaos, solitons and fractals. Volume 140(2020)
• Publication Date: 2020-11
• Subjects: Pandemic spreading -- Logistic regression -- Complex dynamics -- COVID-19; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2020.110113
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: In this brief work we present a novel approach to the logistic dynamics of populations and epidemic spreading that can take into account of the complex nature of such a process in several real situations, where due to different agents the dynamics is no longer characterized by a single characteristic timescale, but conversely by a distribution of time scales, rendered via a time-dependent growth rate. In detail, a differential equation containing a power-law time dependent growth rate is proposed, whose solution, named Stretched Logistic Function, provides a modified version of the usual logistic function. The model equation is inspired by and applied to the recent spreading on COVID-19 disease in Italy, showing how the real dynamics of infection spreading is characterized by a time dependent dynamics. A speculative discussion of the Stretched Logistic Function in relation to diffusion processes is attempted.