不同扩散策略下SI传染病模型的行波解

考虑具有标准发生率的不同扩散策略下SI传染病模型的行波解, 其中易感者采用随机扩散策略, 染病者采用非局部扩散策略. 利用上下解方法结合Schauder’s不动点定理, 证明当R₀>1, R_d>1, c>c*时系统行波解的存在性, 并应用两边夹定理、 Lyapunov泛函及Lebesgue控制收敛定理讨论该模型行波解的渐近行为.

Traveling Wave Solutions of SI Epidemic Model under Different Diffusion Strategies

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.