Stability Analysis and Simulation of a Delayed Dengue Transmission Model with Logistic Growth and Nonlinear Incidence Rate

IF 1.9 4区数学 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS International Journal of Bifurcation and Chaos Pub Date : 2024-03-06 DOI:10.1142/s0218127424500287

Fangkai Guo, Xiaohong Tian

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Abstract

In this work, a dengue transmission model with logistic growth and time delay $(τ)$ is investigated. Through detailed mathematical analysis, the local stability of a disease-free equilibrium and an endemic equilibrium is discussed, the existence of Hopf bifurcation and stability switch is established, and it is proved that the system is permanent if the basic reproduction number is greater than 1. On the basis of Lyapunov functional and LaSalle’s invariance principle, sufficient conditions are derived for the global stability of the endemic equilibrium. The primary theoretical results are simulated numerically. In addition, when $τ = 0$ , relevant properties of the Hopf bifurcation are analyzed. Finally, sensitivity analysis is given and data fitting is carried out to predict the epidemic development trend of dengue fever in Singapore in 2020.

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具有逻辑增长和非线性发病率的延迟登革热传播模型的稳定性分析与模拟

本文研究了一个具有逻辑增长和时间延迟（τ）的登革热传播模型。通过详细的数学分析，讨论了无病平衡和流行平衡的局部稳定性，确定了霍普夫分岔和稳定性开关的存在，并证明了当基本繁殖数大于 1 时系统是永久的。对主要理论结果进行了数值模拟。此外，当 τ=0 时，还分析了霍普夫分岔的相关特性。最后，给出了敏感性分析并进行了数据拟合，以预测 2020 年登革热在新加坡的流行发展趋势。

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

International Journal of Bifurcation and Chaos 数学-数学跨学科应用

CiteScore

4.10

自引率

13.60%

发文量

237

审稿时长

2-4 weeks

期刊介绍： The International Journal of Bifurcation and Chaos is widely regarded as a leading journal in the exciting fields of chaos theory and nonlinear science. Represented by an international editorial board comprising top researchers from a wide variety of disciplines, it is setting high standards in scientific and production quality. The journal has been reputedly acclaimed by the scientific community around the world, and has featured many important papers by leading researchers from various areas of applied sciences and engineering. The discipline of chaos theory has created a universal paradigm, a scientific parlance, and a mathematical tool for grappling with complex dynamical phenomena. In every field of applied sciences (astronomy, atmospheric sciences, biology, chemistry, economics, geophysics, life and medical sciences, physics, social sciences, ecology, etc.) and engineering (aerospace, chemical, electronic, civil, computer, information, mechanical, software, telecommunication, etc.), the local and global manifestations of chaos and bifurcation have burst forth in an unprecedented universality, linking scientists heretofore unfamiliar with one another''s fields, and offering an opportunity to reshape our grasp of reality.