Stochastic Dynamics of Urban Predator-Prey Systems: Integrating Human Disturbance and Functional Responses

Urban ecosystems exhibit complex predator-prey dynamics increasingly disrupted by anthropogenic disturbances (e.g., noise, habitat fragmentation). Classical Lotka-Volterra (LV) models fail to capture these human-induced stressors, and integrated frameworks incorporating functional responses, stochasticity, and spatial dynamics remain scarce. We develop a comprehensive stochastic model to quantify how human disturbance reshapes predator-prey interactions in urban landscapes, using rat-cat systems as a case study. Our framework extends the LV model to incorporate: (i) human disturbance as an external mortality factor, (ii) Holling Type III functional responses to model predation saturation and prey refugia, (iii) multiplicative noise and periodic forcing to capture stochastic disturbance regimes, and (iv) spatial diffusion across fragmented habitats. We non-dimensionalize the system to generalize dynamics and analyze stability, bifurcations, and noise-induced transitions. Numerical simulations (MATLAB) reveal three key outcomes: (1) Human disturbance disrupts classical oscillations, inducing quasi-periodic cycles and elevating extinction risks; (2) Stochasticity lowers collapse thresholds by 25% compared to deterministic predictions; (3) Spatial diffusion drives pattern formation (e.g., disturbance shadows, prey hotspots) through habitat coupling. Results highlight the extreme vulnerability of urban wildlife to anthropogenic pressures, demonstrating how disturbance intensity (μ) governs system stability (μ>0.7 triggers irreversible collapse). The model provides a predictive framework for conservation strategies, emphasizing refuge enhancement (ϕ>0.005) and phased interventions synchronized with population cycles.