Periodic Traveling Wave Solutions of Time-Periodic SIR Epidemic Models With External Supplies

SONG Xue; YANG Yunrui; YANG Lu

doi:10.21656/1000-0887.430108

Volume 43 Issue 10

Oct. 2022

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SONG Xue, YANG Yunrui, YANG Lu. Periodic Traveling Wave Solutions of Time-Periodic SIR Epidemic Models With External Supplies[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1164-1176. doi: 10.21656/1000-0887.430108

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Periodic Traveling Wave Solutions of Time-Periodic SIR Epidemic Models With External Supplies

doi: 10.21656/1000-0887.430108

School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, P.R.China

Received Date: 2022-03-30
Accepted Date: 2022-06-24
Rev Recd Date: 2022-06-24

Available Online: 2022-08-31

Publish Date: 2022-10-31

Abstract

Abstract

The existence and non-existence of periodic traveling wave solutions of a class of time-periodic SIR epidemic models with external supplies were considered. Firstly, the appropriate upper and lower solutions of the auxiliary system were built and a closed convex cone was defined, the existence of periodic traveling waves was transformed into a fixed-point problem of the non-monotonic operator defined on the closed convex cone. The existence of periodic solutions of the auxiliary system was established under the Schauder fixed-point theorem, and the Arzela-Ascoli theorem was used to prove the existence of periodic traveling waves for the original model. Secondly, the non-existence of periodic traveling waves was obtained by analytic techniques.
- periodic traveling wave solution,
- existence,
- auxiliary system,
- fixed-point theorem

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References(22)

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