{"title":"Stability, Hopf bifurcation and control of a fractional order delay cervical cancer model with HPV infection.","authors":"Ruiqing Shi, Chenning Zhao","doi":"10.1080/10255842.2025.2457601","DOIUrl":null,"url":null,"abstract":"<p><p>This paper presents a basic model for the therapeutic effect of two drugs on patients with early cervical cancer. Two cases are considered: with constant control and with optimal control. For case one, the system is proved to have a unique non-negativity solution if the initial values are positive; then the sufficient conditions for the existence and stability of the equilibriums are derived; and Hopf bifurcation is also considered. For case two, by using the Pontryagin's Maximum Principle, we get the optimal control solution. Some examples and numerical simulations are presented. Discussions and conclusions are listed at the end.</p>","PeriodicalId":50640,"journal":{"name":"Computer Methods in Biomechanics and Biomedical Engineering","volume":" ","pages":"1-25"},"PeriodicalIF":1.7000,"publicationDate":"2025-02-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computer Methods in Biomechanics and Biomedical Engineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1080/10255842.2025.2457601","RegionNum":4,"RegionCategory":"医学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper presents a basic model for the therapeutic effect of two drugs on patients with early cervical cancer. Two cases are considered: with constant control and with optimal control. For case one, the system is proved to have a unique non-negativity solution if the initial values are positive; then the sufficient conditions for the existence and stability of the equilibriums are derived; and Hopf bifurcation is also considered. For case two, by using the Pontryagin's Maximum Principle, we get the optimal control solution. Some examples and numerical simulations are presented. Discussions and conclusions are listed at the end.
期刊介绍：
The primary aims of Computer Methods in Biomechanics and Biomedical Engineering are to provide a means of communicating the advances being made in the areas of biomechanics and biomedical engineering and to stimulate interest in the continually emerging computer based technologies which are being applied in these multidisciplinary subjects. Computer Methods in Biomechanics and Biomedical Engineering will also provide a focus for the importance of integrating the disciplines of engineering with medical technology and clinical expertise. Such integration will have a major impact on health care in the future.
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