Modeling the heterogeneous susceptibility and infectivity: A nonlocal state-structured SIR epidemic model

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation Pub Date : 2025-09-30 DOI:10.1016/j.matcom.2025.09.030

Kailong Zhao, Zhijun Liu, Lianwen Wang

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引用次数: 0

Abstract

This work develops and analytically investigate a nonlocal state-structured SIR epidemic model governed by integro-differential equations, which characterizes heterogeneous host susceptibility and variable infectivity of infected individuals. Constructing appropriate Lyapunov functionals, we show that the basic reproduction number exclusively determines global stability of both disease-free and endemic steady states. Numerical simulations corroborate our theoretical findings and demonstrate the substantial impact of nonlocal kernels on disease transmission dynamics, besides, some significantly effective strategies are identified, including immunization of susceptible populations, contact-reduction measures, mitigation of pathogen-specific infectivity and retardation of disease progression. Furthermore, we apply an SVELITR model derived by discretizing the nonlocal state-structured model to project tuberculosis prevalence trends in China, providing quantitative insights into the efficacy of several interventions.

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异质易感性和传染性建模：非局部状态结构SIR流行病模型

本研究开发并分析研究了一个由积分微分方程控制的非局部状态结构SIR流行病模型，该模型表征了被感染个体的异质宿主易感性和可变感染性。构造适当的Lyapunov泛函，我们证明了基本繁殖数唯一地决定了无病和地方性稳定状态的全局稳定性。数值模拟证实了我们的理论发现，并证明了非局部核对疾病传播动力学的实质性影响，此外，还确定了一些非常有效的策略，包括易感人群的免疫接种、减少接触措施、减轻病原体特异性传染性和延缓疾病进展。此外，我们应用非局部状态结构模型离散化得到的SVELITR模型来预测中国结核病流行趋势，为几种干预措施的有效性提供定量见解。

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

Mathematics and Computers in Simulation 数学-计算机：跨学科应用

CiteScore

8.90

自引率

4.30%

发文量

335

审稿时长

54 days

期刊介绍： The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles. Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO. Topics covered by the journal include mathematical tools in: •The foundations of systems modelling •Numerical analysis and the development of algorithms for simulation They also include considerations about computer hardware for simulation and about special software and compilers. The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research. The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.