Networked infrastructures are essential for modern society but are vulnerable to various threats that can lead to significant disruptions. Traditional models often fail to capture the complex dynamics of these systems. To address this issue, we propose a novel framework based on coupled logistic dynamics, where each unit is represented as a node in a coupled logistic system. In this model, damage growth within individual nodes follows logistic patterns and propagates through interdependent units via coupling mechanisms. Our analysis demonstrates that degradation spreads radially across the network, with delays in damage that scale logarithmically with respect to the coupling strength and the distance from the initial failure. We conclude with numerical results that support our theoretical findings, offering insights into the resilience and vulnerability of networked infrastructures.