A time-delayed epidemic model for control of highly pathogenic avian influenza (HPAI H5Nx) with vaccination, compliance, and non-pharmaceutical interventions.

Introduction: Highly pathogenic avian influenza poses an ongoing zoonotic risk with the potential for severe human outbreaks. Existing epidemic models often assume immediate vaccine effectiveness and homogeneous populations, which may overestimate the impact of vaccination during the early phase of an outbreak. This study develops a time-delayed epidemic model to examine how vaccination timing, delayed immune protection, behavioral heterogeneity, and non-pharmaceutical interventions jointly shape the transmission dynamics of a hypothetical human outbreak of highly pathogenic avian influenza H5Nx. Methods: A time-delayed epidemic model was developed that incorporates incubation delay, vaccine deployment delay, and vaccine-to-protection delay. The population was stratified into vaccine-accepting and vaccine-hesitant groups to represent behavioral heterogeneity in vaccine uptake. The model was analyzed through reproduction number and stability analyses, and numerical simulations were performed to evaluate the effects of delays on peak infectious burden, cumulative infections, epidemic timing, and intervention effectiveness. Results: The results showed that delays in vaccine deployment and immune protection substantially reduced the effectiveness of vaccination in limiting peak infection burden. Earlier vaccine deployment reduced transmission during the initial growth phase, whereas delayed deployment shifted the impact of vaccination to later stages of the epidemic. Higher vaccination acceptance reduced both peak burden and cumulative infections, while vaccine-hesitant individuals consistently experienced higher attack rates. Non-pharmaceutical interventions reduced transmission immediately and exerted the strongest influence during the early phase of the epidemic. The incubation delay altered epidemic timing and transient dynamics without changing the invasion threshold. Discussion: The findings demonstrate that epidemic outcomes depend strongly on intervention timing, the rate at which immune protection develops, and population behavior. Delays associated with vaccine availability and immune response can substantially diminish the short-term benefits of vaccination, particularly when outbreak growth is rapid. Incorporating behavioral heterogeneity and multiple delay mechanisms provides a more realistic basis for evaluating intervention strategies and strengthening preparedness for future human outbreaks of highly pathogenic avian influenza.