A statistical theory of the strength of epidemics: an application to the Italian COVID-19 case.

The proposed theory defines a relative index of epidemic lethality that compares any two configurations in different observation periods, preferably one in the acute and the other in a mild epidemic phase. Raw mortality data represent the input, with no need to recognize the cause of death. Data are categorized according to the victims' age, which must be renormalized because older people have a greater probability of developing a level of physical decay (human damage), favouring critical pathologies and co-morbidities. The probabilistic dependence of human damage on renormalized age is related to a death criterion considering a virus spread by contagion and our capacity to cure the disease. Remarkably, this is reminiscent of the Weibull theory of the strength of brittle structures containing a population of crack-like defects, in the correlation between the statistical distribution of cracks and the risk of fracture at a prescribed stress level. Age-of-death scaling laws are predicted in accordance with data collected in Italian regions and provinces during the first wave of COVID-19, taken as representative examples to validate the theory. For the prevention of spread and the management of the epidemic, the various parameters of the theory shall be informed on other existing epidemiological models.