Study of immune response in a latent tuberculosis infection model

IF 3.4 2区数学 Q1 MATHEMATICS, APPLIED

Communications in Nonlinear Science and Numerical Simulation Pub Date : 2024-10-29 DOI:10.1016/j.cnsns.2024.108404

Hui Cao , Jianquan Li , Pei Yu

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Abstract

A simple mathematical model describing the immune response during the stage latent tuberculosis infection is established and analyzed. The main purpose of this study is to explore the sustained immune response of the immune system against invaded Mycobacterium tuberculosis in the stage of latent tuberculosis infection. First, the threshold

R_{0}

is defined to determine the occurrence of sustained immune response. Then, stability conditions are derived to show that the sustained immune response may converge to a constant or to a stable periodical oscillation, implying that the Mycobacterium tuberculosis, the infected macrophages, the activated uninfected macrophages, and the immune cells coexist to form the tuberculous granuloma structure. This structure may appear calcified if the system solution converges to a constant, or maintains a dynamic balance if the system solution undergoes a periodical oscillation. These findings well demonstrate the process of sustained immune response in the latent tuberculosis infection as the Mycobacterium tuberculosis is changing. Numerical examples are presented to illustrate the theoretical predictions.

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潜伏肺结核感染模型的免疫反应研究

建立并分析了一个描述结核病潜伏感染阶段免疫反应的简单数学模型。本研究的主要目的是探讨在结核病潜伏感染阶段免疫系统对入侵结核分枝杆菌的持续免疫反应。首先，定义了阈值 R0，以确定持续免疫反应的发生。然后，推导出稳定条件，表明持续免疫反应可能趋于恒定或稳定的周期振荡，这意味着结核分枝杆菌、受感染的巨噬细胞、活化的未感染巨噬细胞和免疫细胞共存，形成结核肉芽肿结构。如果系统溶液趋于恒定，这种结构就会出现钙化；如果系统溶液发生周期性振荡，这种结构就会保持动态平衡。这些发现很好地证明了在结核分枝杆菌不断变化的情况下，潜伏结核感染的持续免疫反应过程。本文还列举了一些数值实例来说明理论预测。

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

Communications in Nonlinear Science and Numerical Simulation MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

6.80

自引率

7.70%

发文量

378

审稿时长

78 days

期刊介绍： The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity. The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged. Topics of interest: Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity. No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.