A Two-City, Two-Group SIR Model with Heterogeneous Risk-Perception Feedback and Group-Specific Mobility

We formulate and analyze a deterministic two-city, two-group susceptible–infected–recovered (SIR) model with heterogeneous behavioral adaptation and group-specific mobility. The model combines two mechanisms: (i) group-dependent contact reduction in response to local infection burden and (ii) symmetric inter-city diffusion with group-dependent mobility rates. Usinga next-generation matrix construction, we derive the invasion threshold and compute R0 under mobility coupling. Numerical experiments identify three robust dynamical regimes: weak coupling with delayed spillover, intermediate coupling with partial synchronization, and strong coupling with nearsynchronous outbreaks. Parameter sweeps over high-contact-group mobility and risk sensitivity show nonlinear mobility–behavior interactions affecting peak burden and final size. Across scenarios, interventions targeted at the high-contact group (increased risk sensitivity and/or reduced mobility) yield the largest burden reductions, and combined interventions dominate single-mechanism policies.