Transmission Dynamics and Control of a Deterministic Bird-Human Avian Influenza Model

This paper develops a deterministic model to analyze the transmission dynamics and control measures of avian influenza, with a specific emphasis on bird-to-human transmission. The model innovatively integrates key intervention measures, including vaccination, treatment, and quarantine, while categorizing the human population into seven distinct classes and the bird population into four. A dynamic analysis is conducted to elucidate the epidemiological characteristics and potential control measures for avian influenza outbreaks. The qualitative properties of the model are rigorously assessed using the Jacobian matrix, and the basic reproductive ratios are calculated utilizing the next-generation matrix approach. A stability analysis of the equilibrium states is performed through the trace and determinant of the Jacobian matrix, revealing the existence of two key equilibria: the disease-free equilibrium and an endemic equilibrium. Simulation experiments show that the synergistic application of all three control measures significantly reduces infection rates compared to the implementation of individual or paired strategies. Furthermore, a sensitivity analysis highlights the most influential parameters affecting control outcomes, enhancing the understanding of effective management strategies. This research provides valuable insights into managing avian influenza transmission, contributing to the broader discourse on infectious disease control in avian and human populations.