Mathematical Modeling of Avian Influenza Transmission with Neural Network-Based Simulation

Avian influenza (AI) remains a serious threat to poultry and public health worldwide due to its zoonotic nature and pandemic potential. This paper develops and analyzes a coupled system of nonlinear ordinary differential equations and an SEIR-SEIR model that describes the transmission dynamics of avian influenza in both human and bird populations. The model incorporates multiple transmission routes (bird-to-bird, bird-to-human, human-to-human), exposed/latent compartments in both hosts, disease-induced mortality, and demographic processes. From a mathematical perspective, we present a rigorous analysis of this eight-dimensional dynamical system. We prove positivity and boundedness of solutions in R+8, characterize the equilibrium points, and derive the basic reproduction numbers R0b and R0h using the next-generation matrix method. Local asymptotic stability of the disease-free equilibrium is established via the Routh–Hurwitz criterion. A composite Lyapunov function is constructed to prove global asymptotic stability when both reproduction numbers are less than unity—a result that exploits the cascade structure of the system and provides a template for analyzing similar multi-host models. Sensitivity analysis using normalized forward sensitivity indices identifies critical parameters. In addition, we use neural network models to validate both models and provide error analysis. These results emphasize the crucial role of controlling cross-species transmission and improving recovery efforts, which have significant implications for the design of effective intervention and surveillance programs in the context of the One Health framework.