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Influence of the Effective Reproduction Number on the SIR Model with a Dynamic Transmission Rate

Author

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  • Fernando Córdova-Lepe

    (Facultad de Ciencias Básicas, Universidad Católica del Maule, Avenida San Miguel 3605, Talca 3480112, Chile
    These authors contributed equally to this work.)

  • Juan Pablo Gutiérrez-Jara

    (Centro de Investigación de Estudios Avanzados del Maule (CIEAM), Vicerrectoría de Investigación y Postgrado, Universidad Católica del Maule, Talca 3480112, Chile
    These authors contributed equally to this work.)

  • Gerardo Chowell

    (School of Public Health, Georgia State University, Atlanta, GA 30302, USA
    Department of Applied Mathematics, Kyung Hee University, Yongin 17104, Republic of Korea
    These authors contributed equally to this work.)

Abstract

In this paper, we examine the epidemiological model B -SIR, focusing on the dynamic law that governs the transmission rate B . We define this dynamic law by the differential equation B ′ / B = F ⊕ − F ⊖ , where F ⊖ represents a reaction factor reflecting the stress proportional to the active group’s percentage variation. Conversely, F ⊕ is a factor proportional to the deviation of B from its intrinsic value. We introduce the notion of contagion impulse f and explore its role within the model. Specifically, for the case where F ⊕ = 0 , we derive an autonomous differential system linking the effective reproductive number with f and subsequently analyze its dynamics. This analysis provides new insights into the model’s behavior and its implications for understanding disease transmission.

Suggested Citation

  • Fernando Córdova-Lepe & Juan Pablo Gutiérrez-Jara & Gerardo Chowell, 2024. "Influence of the Effective Reproduction Number on the SIR Model with a Dynamic Transmission Rate," Mathematics, MDPI, vol. 12(12), pages 1-10, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1793-:d:1411342
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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.
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