一类具有非线性发生率与时滞的离散扩散SIR模型临界行波解的存在性

研究了一类具有非线性发生率的离散扩散时滞SIR模型的临界行波解的存在性.在人口总数非恒定的条件下，首先,应用上下解法与Schauder不动点定理证明了解在有限闭区间上的存在性；其次，通过极限讨论了临界行波解在整个实数域上存在;最后，通过反证法与波动引理得到了行波解在无穷远处的渐近行为.

Existence of Critical Traveling Wave Solutions for a Class of Discrete Diffusion SIR Models With Nonlinear Incidence and Time Delay

The existence of critical traveling wave solutions for a class of discrete diffusion SIR models with nonlinear incidence and time delay were studied. Under the condition that the total population is not a constant, the upper and lower solutions method and the Schauder fixed point theorem were used to prove the existence of the solution on a finite interval. Furthermore, the existence of critical traveling wave solutions was proved on the real number field through limit arguments. Finally, with the fluctuation lemma and the proof by contradiction, the asymptotic boundary of the critical traveling wave was obtained.