通过经典和 ABC 分式算子分析疟疾传播动态的年龄结构数学模型

4区 工程技术 Q1 Mathematics Mathematical Problems in Engineering Pub Date : 2024-01-25 DOI:10.1155/2024/3855146
Ademe Kebede Gizaw, Chernet Tuge Deressa
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引用次数: 0

摘要

疟疾是一种复杂的疾病,影响传播动态的因素很多,其中包括年龄。本研究利用经典整数阶和 Atangana-Baleanu-Caputo 分数算子建立了一个年龄结构数学模型,从而分析了疟疾的传播动态。对模型的分析主要集中在几个重要方面。根据一些定点定理,如 Banach 和 Krasnoselski,探讨了分数阶解的存在性和唯一性。还研究了解的正定性和有界性。此外,通过数学分析技术,我们分析了不同类型的稳定性结果,结果表明,如果基本繁殖数小于 1,模型的无病平衡点被证明是局部和全局渐近稳定的;而如果基本繁殖数大于 1,模型的地方病平衡点是局部和全局渐近稳定的。敏感性分析结果表明,对控制或消除疟疾至关重要的最敏感参数是蚊虫叮咬率、依赖密度的自然死亡率、临床康复率和蚊虫招募率。此外,还进行了数值模拟,以检查模型在不同分数阶α值下的行为,结果显示,随着α值从 1 开始减小,疟疾流行的扩散速度会减慢。通过结合这些发现,本研究有助于阐明疟疾的动态变化,并为如何制定有效的控制措施提供信息。
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Analysis of Age-Structured Mathematical Model of Malaria Transmission Dynamics via Classical and ABC Fractional Operators
Malaria is a complex disease with many factors influencing the transmission dynamics, including age. This research analyzes the transmission dynamics of malaria by developing an age-structured mathematical model using the classical integer order and Atangana–Baleanu–Caputo fractional operators. The analysis of the model focused on several important aspects. The existence and uniqueness of solutions of fractional order were explored based on some fixed-point theorems,such as Banach and Krasnoselski. The Positivity and boundedness of the solutions were also investigated. Furthermore, through mathematical analysis techniques, we analyzed different types of stability results, and the results showed that the disease-free equilibrium point of the model is proved to be both locally and globally asymptotically stable if the basic reproduction number is less than one, whereas the endemic equilibrium point of the model is both locally and globally asymptotically stable if the basic reproduction number is greater than one. The findings from the sensitivity analysis revealed that the most sensitive parameters, essential for controlling or eliminating malaria are mosquito biting rate, density-dependent natural mortality rate, clinical recovery rate, and recruitment rate for mosquitoes. Numerical simulations are also performed to examine the behavior of the model for different values of the fractional-order alpha,and the result revealed that as the value α reduces from 1, the spread of the endemic grows slower. By incorporating these findings, this research helps to clarify the dynamics of malaria and provides information on how to create efficient control measures.
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来源期刊
Mathematical Problems in Engineering
Mathematical Problems in Engineering 工程技术-工程:综合
CiteScore
4.00
自引率
0.00%
发文量
2853
审稿时长
4.2 months
期刊介绍: Mathematical Problems in Engineering is a broad-based journal which publishes articles of interest in all engineering disciplines. Mathematical Problems in Engineering publishes results of rigorous engineering research carried out using mathematical tools. Contributions containing formulations or results related to applications are also encouraged. The primary aim of Mathematical Problems in Engineering is rapid publication and dissemination of important mathematical work which has relevance to engineering. All areas of engineering are within the scope of the journal. In particular, aerospace engineering, bioengineering, chemical engineering, computer engineering, electrical engineering, industrial engineering and manufacturing systems, and mechanical engineering are of interest. Mathematical work of interest includes, but is not limited to, ordinary and partial differential equations, stochastic processes, calculus of variations, and nonlinear analysis.
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