Farm-level transmission dynamics and risk assessment of H5 Avian Influenza

Highly Pathogenic Avian Influenza (HPAI), especially the H5 subtype, remains a persistent global threat to poultry production systems and public health. This study develops a stochastic model to characterize the spread dynamics of Avian Influenza in large-scale farms, explicitly incorporating both direct contact and environmental transmission pathways. Through theoretical analysis, we derive key epidemiological thresholds, including the basic reproduction number (R0), a additional threshold (R1) and outbreak probability, and establish rigorous risk classification criteria in farm level. In addition, we give mathematical expressions for several risk measures: between-farm transmission risk, infection risk for single susceptible individual, and transmission risk from a single infected individual. Moreover, we discovered that the stochastic model reveals significant outcome variability under identical initial conditions, demonstrating the inherent unpredictability of disease spread that deterministic approaches fail to capture. Simulations of a standardized farm housing 10,000 chickens show that H5 avian influenza can cause medium-to-high-risk outbreaks despite 82.44% vaccination and weekly disinfection, with environmental risk from a single infection peaking at 150 days. Furthermore, inter-farm transmission risk increases nonlinearly with trade volume, reaching 30% within three months after the introduction of an infected individual when 1000 chickens are transferred. Most critically, sustaining a vaccination efficacy exceeding 86% is essential to maintain a low-risk status.