EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVES IN A HOST-VECTOR EPIDEMIC MODEL

Xijun Deng; Aiyong Chen

doi:10.11948/20180197

2021 Volume 11 Issue 2

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Xijun Deng, Aiyong Chen. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVES IN A HOST-VECTOR EPIDEMIC MODEL[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 602-613. doi: 10.11948/20180197

Citation:

Xijun Deng, Aiyong Chen. EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVES IN A HOST-VECTOR EPIDEMIC MODEL[J]. Journal of Applied Analysis & Computation, 2021, 11(2): 602-613. doi: 10.11948/20180197

EXISTENCE AND ASYMPTOTIC BEHAVIOR OF TRAVELING WAVES IN A HOST-VECTOR EPIDEMIC MODEL

Xijun Deng¹,
Aiyong Chen^2,3, ,

1.
Department of Mathematics and Computing Science, Hunan University of Arts and Science, 415000 Changde, China
2.
Department of Mathematics, Hunan First Normal University, Changsha, 410205, China
3.
School of Mathematics and Computing Science, Guilin University of Electronic Technology, Guilin, 541004, China

Corresponding author: Email address: aiyongchen@163.com(A. Chen)
Fund Project: The first author was partially supported by Natural Science Foundation of Hunan Province (No. 2018JJ2272), by the Scientific Research Fund of Hunan Provincial Education Department (No.18C0721), and Doctoral Research Fund of Hunan University of Arts and Science (No.16BSQD04). The second author was supported by National Natural Science Foundation of China (Nos. 11671107, 11971163)

Abstract

Abstract

In this paper, we are concerned with a diffusive host-vector epidemic model with a nonlocal spatiotemporal interaction. When the delay kernel takes some special form, by employing linear chain techniques and geometric singular perturbation theory, we establish the existence of travelling front solutions connecting the two spatially uniform steady states for sufficiently small delays. Furthermore, by employing standard asymptotic theory, we also obtain the asymptotic behavior of traveling wave fronts of this model.
- Host-vector epidemic model /
- traveling waves /
- linear chain technique /
- geometric singular perturbation theory
MSC: 34E15, 34D15, 35Q53, 35C07

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References

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