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A stretched logistic equation for pandemic spreading

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  • Consolini, Giuseppe
  • Materassi, Massimo

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.

Suggested Citation

  • Consolini, Giuseppe & Materassi, Massimo, 2020. "A stretched logistic equation for pandemic spreading," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    • Handle: RePEc:eee:chsofr:v:140:y:2020:i:c:s0960077920305105
    DOI: 10.1016/j.chaos.2020.110113
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    References listed on IDEAS

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    1. Fanelli, Duccio & Piazza, Francesco, 2020. "Analysis and forecast of COVID-19 spreading in China, Italy and France," Chaos, Solitons & Fractals, Elsevier, vol. 134(C).
    2. Postnikov, Eugene B., 2020. "Estimation of COVID-19 dynamics “on a back-of-envelope”: Does the simplest SIR model provide quantitative parameters and predictions?," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
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    Cited by:

    1. Pelinovsky, E. & Kokoulina, M. & Epifanova, A. & Kurkin, A. & Kurkina, O. & Tang, M. & Macau, E. & Kirillin, M., 2022. "Gompertz model in COVID-19 spreading simulation," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    2. Lei Zhang & Guang-Hui She & Yu-Rong She & Rong Li & Zhen-Su She, 2022. "Quantifying Social Interventions for Combating COVID-19 via a Symmetry-Based Model," IJERPH, MDPI, vol. 20(1), pages 1-15, December.

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