How relevant is the basic reproductive number computed during the coronavirus disease 2019 (COVID-19) pandemic, especially during lockdowns?

• Published in: Infection control and hospital epidemiology Vol. 43; no. 1; pp. 125 - 127
• Main Authors: Srinivasa Rao, Arni S R, Krantz, Steven G, Bonsall, Michael B, Kurien, Thomas, Byrareddy, Siddappa N, Swanson, David A, Bhat, Ramesh, Sudhakar, Kurapati
• Format: Journal Article
• Language: English
• Published: United States Cambridge University Press 01-01-2022
• Subjects: Basic Reproduction Number; Communicable Disease Control; Coronaviruses; COVID-19; Epidemics; Epidemiology; Humans; Infections; Letter to the Editor; Pandemics; SARS-CoV-2; Vitamin E
• ISSN: 0899-823X; 1559-6834
• DOI: 10.1017/ice.2020.1376

[...]in (b), the fourth secondary infection in (a), say, \({y_{24}}\) by primary infected \({y_2}\) becomes a primary infected that generates 3 secondary infections out of which only 2 were traced and diagnosed. [...]the mean number of secondary infections during (\({t_i}\), \({t_i+4}\)) is given by(2)\(\root 4 \of {\mathop \prod \limits_{k = 0}^3 \left( {1\, { + \, \gamma_{i + k}}\% } \right)}.\) Similarly, the trend in eq. Even if the testing numbers and testing patterns are constant over a period, the proportion of underreported cases may not be constant. [...]the estimation of \({R_0}\) is likely to be highly variable in any given situation. When the ratios \({Y_{i + k + 1}}{\rm{\;}}/{Y_{i + k}}\) for \(k = 0, 1, \ldots n\) are considered, then the geometric mean of these growth rates would be(4)\[\root n \of {\mathop \prod \limits_{k = 0}^n {{{Y_{i + k + 1}}} \over {{Y_{i + k}}} = \root n \of {{{Y_{i + n + 1}}} \over {{Y_i}}}.\] However, \[{\widehat R_0}\] or \[{\widehat R_t}\], (the estimated basic and time-varying reproductive numbers at the start or ongoing through an epidemic, respectively) may not be at all close to \({R_0}\) or \({R_t}\) even if the \({Y_i}\) values are generated from a mathematical model for a period \(i > 0\) that uses data on susceptible, exposed, infected, and recovered in which the underlying epidemiological processes are time varying.