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

Fernando Córdova-Lepe (), Juan Pablo Gutiérrez-Jara () and Gerardo Chowell
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Fernando Córdova-Lepe: Facultad de Ciencias Básicas, Universidad Católica del Maule, Avenida San Miguel 3605, Talca 3480112, Chile
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
Gerardo Chowell: School of Public Health, Georgia State University, Atlanta, GA 30302, USA

Mathematics, 2024, vol. 12, issue 12, 1-10

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.

Keywords: infection disease; SIR model; variable transmission rate; COVID-19; mitigation policy; human behavior (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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