一类具有非线性发生率与时滞的非局部扩散SIR模型的临界波的存在性

Existence of Critical Traveling Waves for Nonlocal Dispersal SIR Models With Delay and Nonlinear Incidence

研究了一类具有时滞的非局部扩散SIR传染病模型的行波解.首先,利用反证法证明了I是有界的,并根据I的有界性研究了波速c>c^*时行波解(波速大于最小波速的行波)的存在性.其次,利用c>c^*的行波的存在性结果证明了临界波(波速等于最小波速的行波)的存在性.最后,讨论了R0对临界波存在性的影响.

The existence of traveling wave solutions for nonlocal dispersal SIR epidemic models with delay was studied. Firstly, the boundedness of I was proved by contradiction. Then according to the boundedness of I, the existence of traveling waves with c>c^* was established. Secondly, through further analysis of traveling waves with super-critical speeds, the existence of traveling waves with the critical speed was derived. Finally, the influence of basic reproduction number R0 on the existence of c>c^* was discussed.