Some fractal thoughts about the COVID-19 infection outbreak. (December 2019) - Materassi, Massimo
Highlights: Criticism on the "Mass Hypothesis" in models of epidemic spreading. Review of the Generalized Richards Model of epidemic outbreaks. Review of the form of segregation named "herd behaviour" in the Trophic Web Theory. Adaptation of "herd behaviour" to epidemic outbreak description, as a motivation to the Generalized Richards Model. Interpretation of the exponents p and α of the Generalized Richards Model with particular reference to the COVID-19 case. Abstract: 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.