This paper introduces a stochastic SEIR-based modeling framework for studying the propagation and recovery of disruptions across transport logistics networks. The framework adapts the classic Susceptible–Exposed–Infected–Recovered (SEIR) compartmental structure to a logistics framework, where each operational entity (e.g., warehouse, terminal, distribution center) can transition between four states according to its level of susceptibility to disruption and its subsequent recovery. Disruption propagation is determined by non-monotonic incidence functions that capture nonlinear escalation effects and saturation effects within cascading failures. Structural and organizational constraints are introduced in the form of restrictions on which flows can transmit disruptions, capturing realistic logistics dependencies. Further, the model is formulated as a stochastic process to capture operational uncertainty. The proposed framework supports two broad aims. First, it characterizes how random shocks and uncertainty influence network performance over time. Second, it provides a systematic opportunity to assess robustness and resilience to disruptions, via analyses of how fast and how effective the logistics network can absorb a disruption and restore service. Illustrative scenario-based analyses are conducted to develop expectations of the anticipated dynamic behaviour of the model, based on different disruption scenarios. These qualitative outcomes are intended to inform the design of transport logistics systems that can provide service continuity in a stressful situation. A thorough quantitative simulation and empirical validation is planned for the extension of this work.