An SEI–SI avian–human influenza model with diffusion and nonlocal delay

Abstract

An avian–human influenza epidemic model with diffusion and nonlocal delay is investigated. This model describes the transmission of avian influenza among birds and human; especially the asymptomatic individuals in the latent period have infectious force. By analyzing the corresponding characteristic equation, the local stability of uniform steady state of the bird system is discussed. Sufficient conditions are given for the global asymptotical stability of the disease-free equilibrium of the bird system by using the method of upper–lower solutions and its associated monotone iteration scheme. For the full system, the global stability of disease-free equilibrium is studied by the comparison arguments.