A fractal viewpoint to COVID-19 infection

TL;DR

This paper introduces a fractal dynamical model for COVID-19 spread, using fractal calculus to accurately describe diverse outbreak patterns and predict key epidemiological milestones.

Contribution

It develops a novel fractal model with conformed derivatives and fractal time, providing new quantitative tools for understanding and predicting COVID-19 dynamics.

Findings

A Burr-XII shaped solution describes outbreak dynamics.

The model fits data from multiple countries with a single function.

Criteria for pandemic peak and herd immunity timing are derived.

Abstract

One of the central tools to control the COVID-19 pandemics is the knowledge of its spreading dynamics. Here we develop a fractal model capable of describe this dynamics, in term of daily new cases, and provide quantitative criteria for some predictions. We propose a fractal dynamical model using conformed derivative and fractal time scale. A Burr-XII shaped solution of the fractal-like equation is obtained. The model is tested using data from several countries, showing that a single function is able to describe very different shapes of the outbreak. The diverse behavior of the outbreak on those countries is presented and discussed. Moreover, a criterion to determine the existence of the pandemic peak and a expression to find the time to reach herd immunity are also obtained.