Dynamic analysis and optimal control of HIV/AIDS model considering the first 95% target

IF 2.1 3区数学 Q1 MATHEMATICS, APPLIED

Mathematical Methods in the Applied Sciences Pub Date : 2024-11-04 DOI:10.1002/mma.10563

Wenhui Hao, Juping Zhang, Zhen Jin

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引用次数: 0

Abstract

Based on the level of awareness of the population, an HIV/AIDS model is developed, which focused on the first 95% plan developed by UNAIDS. The threshold $R_{0}$ of model and the expressions of the disease-free equilibrium and the endemic equilibrium are calculated, proving the existence of backward bifurcation. Backward bifurcation is caused by the imperfect protection rate of susceptible population due to education. Using China's actual data for parameter fitting, it is found that new HIV infections are on an upward trend. In response to this phenomenon, publicity and education, condoms, screening, and treatment of infected populations are considered as control measures. It is concluded that publicity and education is the primary strategy. This measure can not only effectively reduce the number of infected populations but also effectively increase the awareness rate of HIV-infected populations. It is recommended to use condoms and have fewer sexual partners during sexual contact. Numerical simulation verifies that early stage publicity and education are much more important than post-infection screening and treatment measures.

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来源期刊

Mathematical Methods in the Applied Sciences 数学-应用数学

CiteScore

4.90

自引率

6.90%

发文量

798

审稿时长

6 months

期刊介绍： Mathematical Methods in the Applied Sciences publishes papers dealing with new mathematical methods for the consideration of linear and non-linear, direct and inverse problems for physical relevant processes over time- and space- varying media under certain initial, boundary, transition conditions etc. Papers dealing with biomathematical content, population dynamics and network problems are most welcome. Mathematical Methods in the Applied Sciences is an interdisciplinary journal: therefore, all manuscripts must be written to be accessible to a broad scientific but mathematically advanced audience. All papers must contain carefully written introduction and conclusion sections, which should include a clear exposition of the underlying scientific problem, a summary of the mathematical results and the tools used in deriving the results. Furthermore, the scientific importance of the manuscript and its conclusions should be made clear. Papers dealing with numerical processes or which contain only the application of well established methods will not be accepted. Because of the broad scope of the journal, authors should minimize the use of technical jargon from their subfield in order to increase the accessibility of their paper and appeal to a wider readership. If technical terms are necessary, authors should define them clearly so that the main ideas are understandable also to readers not working in the same subfield.