Propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED Mathematical Methods in the Applied Sciences Pub Date : 2024-09-09 DOI:10.1002/mma.10466

Juan He, Guo-Bao Zhang

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Abstract

In this paper, we are interested in propagation dynamics of a nonlocal dispersal Zika transmission model with general incidence. When the threshold $R$ is greater than one, we prove that there is a wave speed $c^{*} > 0$ such that the model has a traveling wave solution with speed $c > c^{*}$ , and there is no traveling wave solution with speed less than $c^{*}$ . When the threshold $R$ is less than or equal to one, we show that there is no nontrivial traveling wave solution. The approaches we use here are Schauder's fixed point theorem with an explicit construction of a pair of upper and lower solutions, the contradictory approach, and the two-sided Laplace transform.

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具有一般发病率的非本地分散寨卡传播模型的传播动力学

在本文中，我们关注的是具有一般发生率的非局部扩散寨卡病毒传播模型的传播动力学。当阈值大于 1 时，我们证明存在一个波速，使得模型有一个速度为、的行波解，并且不存在速度小于、的行波解。当阈值小于或等于 1 时，我们证明不存在非小的行波解。我们在此使用的方法有：明确构造一对上解和下解的 Schauder 定点定理、矛盾方法和双面拉普拉斯变换。

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.