Estimation of the Instantaneous Reproduction Number and Its Confidence Interval for Modeling the COVID-19 Pandemic

Publio Darío Cortés-Carvajal, Mitzi Cubilla-Montilla and David Ricardo González-Cortés
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Publio Darío Cortés-Carvajal: Independent Researcher, Panama City 0824, Panama
Mitzi Cubilla-Montilla: Departamento de Estadística, Universidad de Panamá, Panama City 0824, Panama
David Ricardo González-Cortés: Tetrapack Panamá, Panama City 0819, Panama

Mathematics, 2022, vol. 10, issue 2, 1-30

Abstract: In this paper, we derive an optimal model for calculating the instantaneous reproduction number, which is an important metric to help in controlling the evolution of epidemics. Our approach, within a frequentist framework , gave us the opportunity to calculate a more realistic confidence interval , a fundamental tool for a safe interpretation of the instantaneous reproduction number value, so that health and governmental people pay more attention to it. Our reasoning begins by decoupling the incidence data in mean and Gaussian noise by using practical series analysis techniques; then, we continue with a likely relationship between the present and past incidence data. Monte Carlo simulations and numerical integrations were conducted to complement the analytical proofs, and illustrations are provided for each stage of analysis to validate the analytical results. Finally, a real case study is discussed with the incidence data of the Republic of Panama regarding the COVID-19 pandemic. We have shown that, for the calculation of the confidence interval of the instantaneous reproduction number, it is essential to include all sources of variability, not only the Poissonian processes of the incidences. This proposal is delivered with analysis tools developed with Microsoft Excel.

Keywords: Bayesian framework; COVID-19; generation time; Monte Carlo simulation; Poissonian variation; serial interval; time-since-infection models (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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