Global asymptotic stability of an SEIRS model and its solutions by nonstandard finite difference schemes

IF 1.1 Q1 MATHEMATICS

Journal of Nonlinear Functional Analysis Pub Date : 2020-01-01 DOI:10.23952/jnfa.2020.34

M. T. Hoang, O. Egbelowo

引用次数: 0

Abstract

. In this paper, we present a mathematically rigorous analysis for the global asymptotic stability of a recognized SEIRS model with nonlinear incidence and vertical transmission. Our main objective is to re-establish the local asymptotic stability of the disease endemic equilibrium point without the assumption proposed in [L. Qi, J. Cui, The stability of an SEIRS model with nonlinear incidence, vertical transmission and time delay, Appl. Math. Comput. 221 (2013), 360-366] and prove that this equilibrium point is not only locally asymptotically stable but also globally asymptotically stable if it exists. Therefore, the global stability of the model is established rigorously. Additionally, we design nonstandard ﬁnite difference (NSFD) schemes that preserve essential properties of the SEIRS model using the Mickens methodology. A set of numerical experiments are performed to support the validity of the theoretical results as well as to show advantages and efﬁciency of the NSFD schemes over the standard ﬁnite difference schemes.

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一类SEIRS模型的全局渐近稳定性及其非标准有限差分格式解

．本文对一类具有非线性入射和垂直传输的公认SEIRS模型的全局渐近稳定性进行了严密的数学分析。我们的主要目标是在不采用[L]中提出的假设的情况下，重新建立疾病地方性平衡点的局部渐近稳定性。齐军，崔军，具有非线性入射、垂直传输和时间延迟的SEIRS模型的稳定性，应用科学。数学。计算[j] . 221(2013)， 360-366]，证明该平衡点存在时不仅局部渐近稳定，而且全局渐近稳定。因此，严格地建立了模型的全局稳定性。此外，我们设计了非标准有限差分(NSFD)方案，使用Mickens方法保留了SEIRS模型的基本属性。通过一组数值实验验证了理论结果的有效性，并证明了NSFD格式相对于标准有限差分格式的优势和效率。

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

Journal of Nonlinear Functional Analysis Multiple-

CiteScore

2.40

自引率

0.00%

发文量

期刊介绍： Journal of Nonlinear Functional Analysis focuses on important developments in nonlinear functional analysis and its applications with a particular emphasis on topics include, but are not limited to: Approximation theory; Asymptotic behavior; Banach space geometric constant and its applications; Complementarity problems; Control theory; Dynamic systems; Fixed point theory and methods of computing fixed points; Fluid dynamics; Functional differential equations; Iteration theory, iterative and composite equations; Mathematical biology and ecology; Miscellaneous applications of nonlinear analysis; Multilinear algebra and tensor computation; Nonlinear eigenvalue problems and nonlinear spectral theory; Nonsmooth analysis, variational analysis, convex analysis and their applications; Numerical analysis; Optimal control; Optimization theory; Ordinary differential equations; Partial differential equations; Positive operator inequality and its applications in operator equation spectrum theory and so forth; Semidefinite programming polynomial optimization; Variational and other types of inequalities involving nonlinear mappings; Variational inequalities.