An advection-diffusion-reaction model for stress propagation between two interconnected zones

Abstract: In this work, we introduce a compartmental advection-diffusion network model to describe the propagation of stress in a population situated in two interconnected spatial zones during a disaster situation. The model accounts for interactions enabled by intrinsic transitions and imitations within each zone, as well as migrations between these zones. Using semigroup theory and abstract evolution equations, we prove the local existence, uniqueness, and regularity of the solutions. Additionally, we establish the positivity and $L^1$--boundedness of the solutions. Various numerical simulations are provided to illustrate different stress propagation scenarios, including the implementation of a local control strategy designed to minimize stress levels in a population facing a low-risk culture during a dangerous situation.