WAVE PROPAGATION FOR A DISCRETE DIFFUSIVE VACCINATION EPIDEMIC MODEL WITH BILINEAR INCIDENCE

Ran Zhang; Shengqiang Liu

doi:10.11948/20220040

2023 Volume 13 Issue 2

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Ran Zhang, Shengqiang Liu. WAVE PROPAGATION FOR A DISCRETE DIFFUSIVE VACCINATION EPIDEMIC MODEL WITH BILINEAR INCIDENCE[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 715-733. doi: 10.11948/20220040

Citation:

Ran Zhang, Shengqiang Liu. WAVE PROPAGATION FOR A DISCRETE DIFFUSIVE VACCINATION EPIDEMIC MODEL WITH BILINEAR INCIDENCE[J]. Journal of Applied Analysis & Computation, 2023, 13(2): 715-733. doi: 10.11948/20220040

WAVE PROPAGATION FOR A DISCRETE DIFFUSIVE VACCINATION EPIDEMIC MODEL WITH BILINEAR INCIDENCE

Ran Zhang¹,
Shengqiang Liu^2, ,

1.
School of Mathematical Science, Heilongjiang University, Harbin 150080, China
2.
School of Mathematical Science, Tiangong University, Tianjin 300387, China

Corresponding author: Email: sqliu@tiangong.edu.cn(S. Liu)
Fund Project: This research was supported by the National Natural Science Foundation of China (Nos.12271401, 12101309), the Natural Science Foundation of Tianjin, China (No.22JCYBJC00080), the Fundamental Research Funds for the Colleges and Universities in Heilongjiang Province (No.2022-KYYWF-1113) and the Heilongjiang Provincial Key Laboratory of the Theory and Computation of Complex Systems

Abstract

Abstract

The aim of the current paper is to study the existence of traveling wave solutions for a vaccination epidemic model with bilinear incidence. The existence result is determined by the basic reproduction number $ \Re_0 $. More specifically, the system admits nontrivial traveling wave solutions when $ \Re_0>1 $ and $ c \geq c^* $, where $ c^* $ is the critical wave speed. We also found that the traveling wave solution is connecting two different equilibria by constructing Lyapunov functional. Lastly, we give some biological explanations from the perspective of epidemiology.
- Traveling wave solution /
- vaccination model /
- lattice dynamical system /
- Schauder's fixed point theorem /
- Lyapunov functional
MSC: 92D30, 35C07, 35K57

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References

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