Calculus of Variations and Geometric Measure Theory
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G. Pisano - G. Royer Carfagni

A statistical theory of the strength of epidemics. The Italian Covid-19 case

created by royercarfagni on 18 May 2020

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Preprint

Inserted: 18 may 2020
Last Updated: 18 may 2020

Year: 2020

Abstract:

We propose a theory of the lethality of epidemics which conforms to the classical Weibull model of the statistical strength of brittle structures which contain a population of crack-like defects. A relation between the probability of developing a critical pathology and the risk of death is adopted in the same manner that the mechanical strength model correlates the statistical spatial distribution of crack size to the risk of fracture at a prescribed stress level. The fracture toughness criterion that determines the onset of catastrophic crack propagation in the structure suggests a death criterion that considers the health system's capability of treating the disease. Our theory relies upon a renormalization of the life-time that assigns the elderly a higher probability of developing a critical pathology. The theory predicts scaling laws for the age of death which are in agreement with the data collected in the Italian regions and provinces before and after the spread of COVID-19. A "strength index" of the epidemic is defined and calculated by categorizing the mortality data, according to the victims' age, from comparable periods of observation in both pre-epidemic and epidemic conditions.


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