IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i2p287-d726937.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/2/287/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/2/287/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. 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.
    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).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Aldo Carranza & Marcel Goic & Eduardo Lara & Marcelo Olivares & Gabriel Y. Weintraub & Julio Covarrubia & Cristian Escobedo & Natalia Jara & Leonardo J. Basso, 2022. "The Social Divide of Social Distancing: Shelter-in-Place Behavior in Santiago During the Covid-19 Pandemic," Management Science, INFORMS, vol. 68(3), pages 2016-2027, March.
    2. Elisabeth K Brockhaus & Daniel Wolffram & Tanja Stadler & Michael Osthege & Tanmay Mitra & Jonas M Littek & Ekaterina Krymova & Anna J Klesen & Jana S Huisman & Stefan Heyder & Laura M Helleckes & Mat, 2023. "Why are different estimates of the effective reproductive number so different? A case study on COVID-19 in Germany," PLOS Computational Biology, Public Library of Science, vol. 19(11), pages 1-27, November.
    3. Reese Richardson & Emile Jorgensen & Philip Arevalo & Tobias M. Holden & Katelyn M. Gostic & Massimo Pacilli & Isaac Ghinai & Shannon Lightner & Sarah Cobey & Jaline Gerardin, 2022. "Tracking changes in SARS-CoV-2 transmission with a novel outpatient sentinel surveillance system in Chicago, USA," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    4. Maria Bekker‐Nielsen Dunbar & Felix Hofmann & Leonhard Held & the SUSPend modelling consortium, 2022. "Assessing the effect of school closures on the spread of COVID‐19 in Zurich," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S1), pages 131-142, November.
    5. James, Nick & Menzies, Max, 2023. "Collective infectivity of the pandemic over time and association with vaccine coverage and economic development," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    6. Palatella, Luigi & Vanni, Fabio & Lambert, David, 2021. "A phenomenological estimate of the true scale of CoViD-19 from primary data," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    7. Jonas E. Arias & Jesús Fernández-Villaverde & Juan F. Rubio-Ramirez & Minchul Shin, 2021. "Bayesian Estimation of Epidemiological Models: Methods, Causality, and Policy Trade-Offs," Working Papers 21-18, Federal Reserve Bank of Philadelphia.
    8. Diana Rose E. Ranoa & Robin L. Holland & Fadi G. Alnaji & Kelsie J. Green & Leyi Wang & Richard L. Fredrickson & Tong Wang & George N. Wong & Johnny Uelmen & Sergei Maslov & Zachary J. Weiner & Alexei, 2022. "Mitigation of SARS-CoV-2 transmission at a large public university," Nature Communications, Nature, vol. 13(1), pages 1-16, December.
    9. Bradley S Price & Maryam Khodaverdi & Adam Halasz & Brian Hendricks & Wesley Kimble & Gordon S Smith & Sally L Hodder, 2021. "Predicting increases in COVID-19 incidence to identify locations for targeted testing in West Virginia: A machine learning enhanced approach," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-16, November.
    10. Dominic P. Brass & Christina A. Cobbold & Bethan V. Purse & David A. Ewing & Amanda Callaghan & Steven M. White, 2024. "Role of vector phenotypic plasticity in disease transmission as illustrated by the spread of dengue virus by Aedes albopictus," Nature Communications, Nature, vol. 15(1), pages 1-22, December.
    11. Massimo Bilancia & Domenico Vitale & Fabio Manca & Paola Perchinunno & Luigi Santacroce, 2024. "A dynamic causal modeling of the second outbreak of COVID-19 in Italy," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 108(1), pages 1-30, March.
    12. Wang, Xiangrong & Hou, Hongru & Lu, Dan & Wu, Zongze & Moreno, Yamir, 2024. "Unveiling the reproduction number scaling in characterizing social contagion coverage," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    13. Sabah Bushaj & Xuecheng Yin & Arjeta Beqiri & Donald Andrews & İ. Esra Büyüktahtakın, 2023. "A simulation-deep reinforcement learning (SiRL) approach for epidemic control optimization," Annals of Operations Research, Springer, vol. 328(1), pages 245-277, September.
    14. Mohammad Reza Davahli & Krzysztof Fiok & Waldemar Karwowski & Awad M. Aljuaid & Redha Taiar, 2021. "Predicting the Dynamics of the COVID-19 Pandemic in the United States Using Graph Theory-Based Neural Networks," IJERPH, MDPI, vol. 18(7), pages 1-12, April.
    15. Yee Whye Teh & Bryn Elesedy & Bobby He & Michael Hutchinson & Sheheryar Zaidi & Avishkar Bhoopchand & Ulrich Paquet & Nenad Tomasev & Jonathan Read & Peter J. Diggle, 2022. "Efficient Bayesian inference of instantaneous reproduction numbers at fine spatial scales, with an application to mapping and nowcasting the Covid‐19 epidemic in British local authorities," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(S1), pages 65-85, November.
    16. Yun Lin & Bingyi Yang & Sarah Cobey & Eric H. Y. Lau & Dillon C. Adam & Jessica Y. Wong & Helen S. Bond & Justin K. Cheung & Faith Ho & Huizhi Gao & Sheikh Taslim Ali & Nancy H. L. Leung & Tim K. Tsan, 2022. "Incorporating temporal distribution of population-level viral load enables real-time estimation of COVID-19 transmission," Nature Communications, Nature, vol. 13(1), pages 1-8, December.
    17. Adrian Lison & Sam Abbott & Jana Huisman & Tanja Stadler, 2024. "Generative Bayesian modeling to nowcast the effective reproduction number from line list data with missing symptom onset dates," PLOS Computational Biology, Public Library of Science, vol. 20(4), pages 1-32, April.
    18. Daniel Henrik Nevermann & Claudius Gros, 2025. "How oscillations in SIRS epidemic models are affected by the distribution of immunity times," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 98(2), pages 1-10, February.
    19. Amanda C. Perofsky & Chelsea L. Hansen & Roy Burstein & Shanda Boyle & Robin Prentice & Cooper Marshall & David Reinhart & Ben Capodanno & Melissa Truong & Kristen Schwabe-Fry & Kayla Kuchta & Brian P, 2024. "Impacts of human mobility on the citywide transmission dynamics of 18 respiratory viruses in pre- and post-COVID-19 pandemic years," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    20. Hyukpyo Hong & Eunjin Eom & Hyojung Lee & Sunhwa Choi & Boseung Choi & Jae Kyoung Kim, 2024. "Overcoming bias in estimating epidemiological parameters with realistic history-dependent disease spread dynamics," Nature Communications, Nature, vol. 15(1), pages 1-13, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:2:p:287-:d:726937. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.