A Hybrid Identification Method for Mathematical Models for Zika Virus

IF 1.8 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2025-07-05 DOI:10.1002/mma.11176

S. Buitrago, R. Escalante, M. Villasana

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引用次数: 0

Abstract

This paper studies some deterministic mathematical models that seek to explain the expansion of Zika virus, as a viral epidemic, using published data for Brazil. Three SIR type models considering several aspects in the spread of the disease are considered with 3, 6, and 10 unknown parameters, respectively. The parameter identification is carried through a search algorithm based on a combination of a stochastic domain exploration and a heuristic calculation of a descent direction, in order to avoid stopping the algorithm at a local optimum. The models are validated using the epidemic data found. Finally, it was confirmed that the basic reproductive ratio $ℜ_{0}$ is consistent with those previously reported in the literature. We conclude that the proposed optimization method improves computation time with respect to a genetic algorithm or an exhaustive search in the parameter space.

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寨卡病毒数学模型的混合识别方法

本文研究了一些确定性数学模型，这些模型试图解释寨卡病毒作为一种病毒性流行病的扩张，使用了巴西的已发表数据。考虑疾病传播的几个方面的三种SIR型模型分别具有3、6和10个未知参数。为了避免算法在局部最优处停止，采用了一种基于随机域探索和启发式下降方向计算相结合的搜索算法进行参数辨识。利用发现的流行病数据对模型进行了验证。最后，确定了基本繁殖比为0 $$ {\mathfrak{\Re}}_0 $$ 与先前文献报道一致。我们的结论是，相对于遗传算法或在参数空间中的穷举搜索，所提出的优化方法提高了计算时间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.