Traveling Wave Solutions of a SIR Epidemic Model with Spatio-Temporal Delay  

作　　者：Zhihe Hou Zhihe Hou(School of Mathematics and Statistics, Shandong Normal University, Jinan, China)

机构地区：[1]School of Mathematics and Statistics, Shandong Normal University, Jinan, China

出　　处：《Journal of Applied Mathematics and Physics》2024年第10期3422-3438,共17页应用数学与应用物理（英文）

摘　　要：In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.In this paper, we studied the traveling wave solutions of a SIR epidemic model with spatial-temporal delay. We proved that this result is determined by the basic reproduction number R0and the minimum wave speed c*of the corresponding ordinary differential equations. The methods used in this paper are primarily the Schauder fixed point theorem and comparison principle. We have proved that when R0>1and c>c*, the model has a non-negative and non-trivial traveling wave solution. However, for R01and c≥0or R0>1and 0cc*, the model does not have a traveling wave solution.

关 键 词：Susceptible-Infected-Recovered Epidemic Model Traveling Wave Solutions Spatio-Temporal Delay Schauder Fixed Point Theorem 

分 类 号：O17[理学—数学]