REVIEW | doi:10.20944/preprints202007.0681.v1
Subject: Social Sciences, Government Keywords: asymptomatic disease; communicability; COVID-19; death rate; Ro; SARS-CoV-2; social distancing; transmission rate; infection rate; quarantine
Online: 28 July 2020 (11:57:26 CEST)
Decisions affecting the COVID-19 pandemic, by the individual and those with highest authority, are being made on the basis of unreliable data. Data about cases and deaths are collected daily but represent only a sample of reality. Statistics convert sample data into more reliable estimates. However, statistics have no magical powers; reliability requires dependable data. It is futile to rail against this darkness; COVID-19 is not a scientific experiment. However, we must do better both with data collection and data analysis. In this review, I focus on one element of the data, the asymptomatic case of COVID-19. Without reliable information about this number, decision makers are significantly blinded. By its nature, the asymptomatic case is hidden but contaminating to understanding COVID-19. The true case rate and death rate per case are unknowable without knowing the fraction of cases that are asymptomatic. The best estimate of asymptomatic cases is in the CDC document: COVID-19 Pandemic Planning Scenarios. For four different scenarios the estimates range from 10% to 70%, with the best estimate of 40% for asymptomatic cases. However, even the definition of the asymptomatic case is problematic. In simplest terms, two elements are required: an infection and no symptoms. How is “no symptoms” to be usefully defined? It appears to be analogous to pontificating about black swans from studying only white swans. It implies infection, but how is infection defined? Is it presence of the virus, replication of the virus, or presence of antibodies? Is asymptomatic disease an oxymoron? Without extensive, purposeful screening for specifically defined, essential symptoms and appropriate virus and antibody testing over time, the class of asymptomatic cases remains unknown. Current estimates range from <20% to ˃80%. If low, it can be ignored; if high, it dramatically and proportionately lowers the case rate and the death rate per case. Consequentially, the asymptomatic rate dramatically affects our societal and political responses. In this focused review, we assess the limitations of the published estimates, bring attention to the importance of obtaining accurate data, and exhort that high priority be given in the scientific community to understanding the issue, asymptomatic COVID-19 cases.
ARTICLE | doi:10.20944/preprints202302.0468.v1
Subject: Computer Science And Mathematics, Analysis Keywords: Modified Bessel functions; Communicability in graphs; Estrada index; Power-series; Fractional calculus; Caputo derivative; Riemann-Liouville integral; Paths; Cycles
Online: 27 February 2023 (09:39:57 CET)
Abstract The modified Bessel function (MBF) of the first kind is a fundamental special function in mathematics with applications in a large number of areas. When the order of this function is integer, it has an integral representation which includes the exponential of the cosine function. Here we generalize this MBF to include a fractional parameter, such that the exponential in the previously mentioned integral is replaced by a Mittag-Leffler function. The necessity for this generalization arises from a problem of communication in networks. We find the power series representation of the fractional MBF of the first kind, as well as some differential properties. We give some examples of its utility in graph/networks analysis and mention some fundamental open problems for further investigation.