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.