Stability Analysis of Influenza Virus Spread Model in Bird Population with Reaction-Diffusion

Abstract

The avian influenza virus is a pathogen that predominantly infects wild birds but can also affect domestic poultry. This study established an epidemiological model, $SEIZ$, which incorporates infection factors from contaminated environments and transmission resulting from contact among avian species. The model was mathematically analyzed to identify two equilibrium points: a disease-free equilibrium point that is locally asymptotically stable when $\mathcal{R}_0<1$, indicating potential extinction of the bird, and an endemic equilibrium point that is locally asymptotically stable when $\mathcal{R}_0>1$, leading to disease persistence within the population. The model was subsequently transformed into a reaction-diffusion model featuring Gaussian initial conditions and Neumann boundary conditions. The developed reaction-diffusion model was subsequently solved numerically employing the finite volume method, utilizing parameters derived from empirical data. Simulation results indicated that an increase in the basic reproduction number can expedite viral infection. Moreover, augmenting the diffusion coefficient accelerates the propagation of infection into regions with the highest density of susceptible individuals and broadens the geographical extent. Virus concentrations in the environment exhibit longer persistence than those in infected populations, thereby increasing the probability of serving as a source of future infections. This study's findings suggest that control strategies for avian influenza virus should account for both direct and indirect infections, as well as the spatial movement of avian hosts, since such movement substantially affects virus spread and the efficacy of control measures.