2. COVID 19 patients lie awake as if preys unwillingly waiting for their predators.

Some ideas are presented about a geometric motivation of the apparent capacity of generalized logistic equations to describe the outbreak of quite many epidemics, possibly including that of the COVID-19 infection. This interpretation pivots on the complex, possibly fractal, structure of the locus describing the “contagion event set”, and on what can be learnt from the models of trophic webs with “herd behaviour”.

Under the hypothesis that the total number of cases, as a function of time, is fitted by a solution of the Generalized Richards Model, it is argued that the exponents appearing in that differential equation, usually determined empirically, represent the geometric signature of the non-space filling, network-like locus on which contagious contacts take place.

Keywords: COVID-19 outbreak, Generalized Richards Model, Herd behaviour, Population dynamics, Fractal dimension

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1. Introduction

In these days of worldwide mourning for the human tragedy due to the COVID-19 pandemic, while experiencing a heavy lockdown, and the fear of a possible forthcoming economical and social crisis, I think every scientist is reasoning about how to be of help, in terms of ideas and technical culture. Besides humbly admitting this to be, first of all, the work of doctors, nurses, virologists, biologists and epidemiologists, not to mention the engineers who design medical and life-saving devices, each of us wonders what technical tools among ours might either help the fight, or at least teach something about how the pandemic appears to work. I wrote down these thoug be interpreted in two equivalent ways: on the one hand, one may say that the effectiveness of the limiting process depends on the population itself as

Δeff(C)=rKp+δCδ,

(12)

so that the larger the population is, the more destructive the self-limitation turns out to be among the individuals in Eact; on the other hand, one might as well state that there is aC-localeffective carrying capacity K eff(C) decreasing with C

infected people is really in contact with susceptible ones, being able to “produce new infectious people”. Once this Eact is identified, its “size” should be expressed as a function of the “size” of the whole E, so to be able to write the expression C act(C): provided things work as in the herd behaviour of TWT, i.e. provided Eact is a non-space-filling subset of E, hence with a

Explanation: