Volume 42 Issue 12
Dec.  2021
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ZHANG Xiaoyan. Existence of Critical Traveling Wave Solutions for a Class of Discrete Diffusion SIR Models With Nonlinear Incidence and Time Delay[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1317-1326. doi: 10.21656/1000-0887.420111
Citation: ZHANG Xiaoyan. Existence of Critical Traveling Wave Solutions for a Class of Discrete Diffusion SIR Models With Nonlinear Incidence and Time Delay[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1317-1326. doi: 10.21656/1000-0887.420111

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

doi: 10.21656/1000-0887.420111
  • Received Date: 2021-04-28
  • Rev Recd Date: 2021-06-09
  • Available Online: 2021-12-31
  • 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.
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