Beyond the Poisson renewal process: A tutorial survey

AbstractAfter sketching the basic principles of renewal theory and recalling the classical Poisson process, we discuss two renewal processes characterized by waiting time laws with the same power asymptotics defined by special functions of Mittag–Leffler and of Wright type. We compare these three processes with each other

Seroprevalence Survey of Anti-SARS-CoV-2 Antibodies in a Population of Emilia-Romagna Region, Northern Italy

taly was the first Western European country to be severely hit by the COVID-19 pandemic. Variations in seroprevalence rates were reported according to geographical and temporal differences of previous surveys, as well as depending on demographic and occupational factors. In this cross-sectional study, we evaluated the prevalence of anti-SARS-CoV-2 antibodies in a population of the Emilia-Romagna region in Northern Italy after the first wave in the period from 26 September 2020–26 March 2021. We included 5128 subjects who voluntarily underwent serological tests to determine anti-SARS-CoV-2 antibody positivity, including both self-referred individuals (24.2%) and workers adhering to company screening programs (76.8%). Overall, seroprevalence was 11.3%, higher in self-referred (13.8%) than employed-referred (10.5%) individuals. A slightly higher seroprevalence emerged in women compared to men (12.3% and 10.7%), as well as in the extreme age categories (18.6% for 60–69 years, 18.0% for ≥70 years, and 17.1% for <20 years compared to 7.6% for 20–39 years). Healthcare professionals showed the highest prevalence of seropositivity (22.9%), followed by workers in direct contact with customers, such as the communication, finance, and tourism sectors (15.7%). Overall subgroups seroprevalence increased compared to the first wave data but the trends agreed between the first and subsequent waves, except for an increase in the younger age group and in the sector in direct contact with customers. Among the occupational categories, our study confirms that healthcare workers and workers in the sports sector were at high risk of exposure to SARS-CoV-2

Continuous time random walk and parametric subordination in fractional diffusion

The well-scaled transition to the diffusion limit in the framework of the theory of continuous-time random walk (CTRW)is presented starting from its representation as an infinite series that points out the subordinated character of the CTRW itself. We treat the CTRW as a combination of a random walk on the axis of physical time with a random walk in space, both walks happening in discrete operational time. In the continuum limit we obtain a generally non-Markovian diffusion process governed by a space-time fractional diffusion equation. The essential assumption is that the probabilities for waiting times and jump-widths behave asymptotically like powers with negative exponents related to the orders of the fractional derivatives. By what we call parametric subordination, applied to a combination of a Markov process with a positively oriented L\'evy process, we generate and display sample paths for some special cases.Comment: 28 pages, 18 figures. Workshop 'In Search of a Theory of Complexity'. Denton, Texas, August 200