Abstract
An SEIR epidemic model with distributed and infinite delay is investigated. This model describes the transmission of disease such as tuberculosis and HIV/AIDS. The behavior of positive solution to a reaction–diffusion system with homogenous Neumann boundary conditions are investigated. Sufficient conditions for the local and global asymptotical stability are given by spectral analysis and comparison arguments. Our result shows that the disease-free equilibrium is global asymptotically stable if the contact rate is small.
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