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

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