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

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 v...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-06, Vol.12 (12), p.1793
Main Authors: Córdova-Lepe, Fernando, Gutiérrez-Jara, Juan Pablo, Chowell, Gerardo
Format: Article
Language:English
Subjects:
Compliance
COVID-19
Differential equations
Disease transmission
Epidemics
Epidemiology
Health care industry
human behavior
infection disease
Infections
Mathematical models
mitigation policy
Pandemics
Restitution
SIR model
Vaccines
variable transmission rate
Variables
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12121793