基于传染病动态系统的混合型脉冲积分微分方程解法研究

IF 1.3 4区 数学 Q1 MATHEMATICS
Haiyan Li, Yuheng Guo, Min Wang
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引用次数: 0

摘要

自古以来,传染病一直是危害人类健康的重要根源。因此,科学家们在防治传染病的历史上建立了许多数学模型,研究传染规律,进而分析各种防治措施的实用性和有效性,为人类预防和研究传染病提供了科学依据。然而,由于许多疾病的传播机制和方式存在很大差异,传染病动态模型种类繁多,给研究带来了越来越大的难度。随着传染病研究技术的不断进步,人们采用了更多的方式来预防和干扰传染病的衍生和传播,这将使传染病系统的状态在瞬间发生变化。这种状态的突变可以用数学脉冲动力系统来描述,更加科学合理,使研究更具实用性。在此基础上,利用脉冲微分方程理论建立了脉冲效应下的传染病时延微分系统模型。研究了一类带积分边界条件的混合型脉冲积分微分方程的周期性边界值问题。利用比较定理、上下解法和单调迭代技术,得到了这些方程的周期解的存在性。最后,结合实际应用,将建立的时延微分系统模型应用于传染病动态系统稳定性和持续性的预测,进一步验证了结论的正确性。本研究为传染病的防治提供了一定的参考。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Study on the Solutions of Impulsive Integrodifferential Equations of Mixed Type Based on Infectious Disease Dynamical Systems
Since ancient times, infectious diseases have been a major source of harm to human health. Therefore, scientists have established many mathematical models in the history of fighting infectious diseases to study the law of infection and then analyzed the practicability and effectiveness of various prevention and control measures, providing a scientific basis for human prevention and research of infectious diseases. However, due to the great differences in the transmission mechanisms and modes of many diseases, there are many kinds of infectious disease dynamic models, which make the research more and more difficult. With the continuous progress of infectious disease research technology, people have adopted more ways to prevent and interfere with the derivation and spread of infectious disease, which will make the state of infectious disease system change in an instant. The mutation of this state can be described more scientifically and reasonably by the mathematical impulse dynamic system, which makes the research more practical. Based on this, a time-delay differential system model of infectious disease under impulse effect was established by means of impulse differential equation theory. A class of periodic boundary value problems for impulsive integrodifferential equations of mixed type with integral boundary conditions was studied. The existence of periodic solutions of these equations was obtained by using the comparison theorem, upper and lower solution methods, and the monotone iteration technique. Finally, combined with the practical application, the established time-delay differential system model was applied to the prediction of the stability and persistence of the infectious disease dynamic system, and the correctness of the conclusion was further verified. This study provides some reference for the prevention and treatment of infectious diseases.
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来源期刊
Journal of Mathematics
Journal of Mathematics Mathematics-General Mathematics
CiteScore
2.50
自引率
14.30%
发文量
0
期刊介绍: Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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