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

Author

Listed:
  • Publio Darío Cortés-Carvajal

    (Independent Researcher, Panama City 0824, Panama)

  • Mitzi Cubilla-Montilla

    (Departamento de Estadística, Universidad de Panamá, Panama City 0824, Panama
    Investigadora del Sistema Nacional de Investigación de la Secretaría Nacional de Ciencia, Tecnología e Innovación (SENACYT), Panama City 0824, Panama)

  • David Ricardo González-Cortés

    (Tetrapack Panamá, Panama City 0819, Panama)

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.

Suggested Citation

  • Publio Darío Cortés-Carvajal & Mitzi Cubilla-Montilla & David Ricardo González-Cortés, 2022. "Estimation of the Instantaneous Reproduction Number and Its Confidence Interval for Modeling the COVID-19 Pandemic," Mathematics, MDPI, vol. 10(2), pages 1-30, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:287-:d:726937
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    References listed on IDEAS

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    1. Katelyn M Gostic & Lauren McGough & Edward B Baskerville & Sam Abbott & Keya Joshi & Christine Tedijanto & Rebecca Kahn & Rene Niehus & James A Hay & Pablo M De Salazar & Joel Hellewell & Sophie Meaki, 2020. "Practical considerations for measuring the effective reproductive number, Rt," PLOS Computational Biology, Public Library of Science, vol. 16(12), pages 1-21, December.
    2. Florin Avram & Rim Adenane & David I. Ketcheson, 2021. "A Review of Matrix SIR Arino Epidemic Models," Mathematics, MDPI, vol. 9(13), pages 1-14, June.
    3. Shah Hussain & Elissa Nadia Madi & Hasib Khan & Sina Etemad & Shahram Rezapour & Thanin Sitthiwirattham & Nichaphat Patanarapeelert, 2021. "Investigation of the Stochastic Modeling of COVID-19 with Environmental Noise from the Analytical and Numerical Point of View," Mathematics, MDPI, vol. 9(23), pages 1-20, December.
    4. Na, Jiaming & Tibebu, Haileleol & De Silva, Varuna & Kondoz, Ahmet & Caine, Michael, 2020. "Probabilistic approximation of effective reproduction number of COVID-19 using daily death statistics," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
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    Cited by:

    1. Raydonal Ospina & João A. M. Gondim & Víctor Leiva & Cecilia Castro, 2023. "An Overview of Forecast Analysis with ARIMA Models during the COVID-19 Pandemic: Methodology and Case Study in Brazil," Mathematics, MDPI, vol. 11(14), pages 1-18, July.
    2. Amin Ullah & Khalid Mahmood Malik & Abdul Khader Jilani Saudagar & Muhammad Badruddin Khan & Mozaherul Hoque Abul Hasanat & Abdullah AlTameem & Mohammed AlKhathami & Muhammad Sajjad, 2022. "COVID-19 Genome Sequence Analysis for New Variant Prediction and Generation," Mathematics, MDPI, vol. 10(22), pages 1-16, November.

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