关键词: SI传染病模型, 行波解, 非局部扩散, 标准发生率

Abstract: The author considered the traveling wave solutions of the SI epidemic model under different diffusion strategies with standard incidence rates. The susceptible individuals adopted the random diffusion strategy, and the infected individuals adopted the non-local diffusion strategy. By means of the upper and lower solution method combined with Schauder’s the fixed point theorem, the existence of the traveling wave solutions of the system was proved when R₀>1, R_d>1 and c>c*. The asymptotic behavior of traveling wave solutions of the model was discussed by applying  squeeze theorem, Lyapunov functional and Lebesgue dominated convergence theorem.

Key words: SI epidemic model, traveling wave solution, non-local diffusion, standard incidence