Stochastic Modelling and Analysis of Within-Farm Highly Pathogenic Avian Influenza Dynamics in Dairy Cattle

Abstract: Highly pathogenic avian influenza (HPAI) has expanded its host range with recent detections in dairy cattle, raising critical concerns regarding within-herd persistence and cross-species spillover. This study develops a stochastic $SEI_sI_aR-B$ compartmental model to analyse HPAI transmission, explicitly accounting for environmental pathogen reservoirs and noise intensities through Wiener processes. The positivity and boundedness of solutions are established, and the disease-free and endemic equilibria are analytically derived. The basic reproduction number is determined using the next-generation matrix method. Numerical simulations confirm that the model dynamics are consistent with theoretical analysis and illustrate how stochastic fluctuations significantly influence disease persistence. Furthermore, sensitivity analysis using Latin Hypercube Sampling (LHS) and Partial Rank Correlation Coefficients (PRCC) identifies the transmission rate from asymptomatic infectious cattle ($β_a$) as the primary driver of transmission. The model effectively captures the dynamics of environmental variability affecting HPAI spread, suggesting that effective control strategies must prioritise the early detection and isolation of asymptomatic carriers alongside environmental management.