Asymptotic behavior of an SEI epidemic model with diffusion

Authors:
Kwang Ik Kim;Zhigui Lin
Affiliations:
Department of Mathematics, Pohang University of Science and Technology, Pohang, 790-784, Republic of Korea;School of Mathematical Science, Yangzhou University, Yangzhou 225002, PR China
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

Citing 3
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Abstract

An SEI epidemic model with constant recruitment and infectious force in the latent period is investigated. This model describes the transmission of diseases such as SARS. The behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions are investigated. Sufficient conditions for the local and global asymptotical stability are given by linearization and by the method of upper and lower solutions and its associated monotone iterations. Our result shows that the disease-free equilibrium is globally asymptotically stable if the contact rate is small.