A mathematical model of HPAI transmission between dairy cattle and wild birds with environmental effects

Highly pathogenic avian influenza (HPAI), particularly H5N1, poses an increasing threat at the wildlife–livestock–environment interface, with recent detections in dairy cattle motivating mechanistic models that capture multi-host transmission and environmental persistence. We develop and analyse a deterministic compartmental model for HPAI transmission among cattle, wild birds, and a shared contaminated environment. The model combines an SEIR structure for cattle with an SIR framework for wild birds and includes an environmental reservoir mediating indirect transmission. We establish positivity and boundedness, characterise disease-free and endemic equilibria, derive the basic reproduction number [Formula: see text], and analyse equilibrium stability. Numerical simulations explore threshold dynamics, robustness to initial conditions, time-to-peak patterns, and parameter-driven changes in disease trajectories. Global sensitivity analysis using Latin Hypercube Sampling and Partial Rank Correlation Coefficients identifies cattle–cattle transmission, cattle recovery, environmental transmission, and environmental viral decay as key determinants of [Formula: see text]. Response surfaces and PRCC-guided intervention scenarios show that reducing cattle transmission yields the greatest reduction in epidemic burden, while enhanced cattle recovery provides an additional effective control pathway. Environmental transmission acts primarily as an amplifier, suggesting that environmental management is most effective when combined with cattle-focused interventions. The proposed framework offers a mathematically tractable basis for analysing threshold behaviour, transmission pathways, and control mechanisms in multi-host HPAI systems, with natural extensions to spatial, stochastic, and movement-based formulations.