{"title":"带有间接环境传播和优化控制的结核病模型分析","authors":"Xianyi Zhao, Hui Cao, Danfeng Pang","doi":"10.1007/s10867-024-09667-1","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper, the dynamic behaviors of tuberculosis in the context of indirect environmental transmission are discussed by establishing the SEIRB epidemic model. The basic reproduction number is computed by employing the next-generation matrix approach. The global stability of disease-free equilibrium and endemic equilibrium is proved by constructing the Lyapunov function and the application of LaSalle’s invariance principle. It shows that when the basic reproduction number is greater than 1, tuberculosis will spread among the population. When the basic reproduction number is less than 1, tuberculosis will disappear. Finally, an optimal control problem is constructed by using the extended model, which reveals the spread of tuberculosis can be effectively controlled by eliminating <i>Mycobacterium tuberculosis</i> in the environment and controlling tuberculosis patients at the same time. Numerical example results show the effectiveness of the optimization strategies.</p></div>","PeriodicalId":612,"journal":{"name":"Journal of Biological Physics","volume":"51 1","pages":""},"PeriodicalIF":1.8000,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of tuberculosis model with indirect environmental transmission and optimal control\",\"authors\":\"Xianyi Zhao, Hui Cao, Danfeng Pang\",\"doi\":\"10.1007/s10867-024-09667-1\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this paper, the dynamic behaviors of tuberculosis in the context of indirect environmental transmission are discussed by establishing the SEIRB epidemic model. The basic reproduction number is computed by employing the next-generation matrix approach. The global stability of disease-free equilibrium and endemic equilibrium is proved by constructing the Lyapunov function and the application of LaSalle’s invariance principle. It shows that when the basic reproduction number is greater than 1, tuberculosis will spread among the population. When the basic reproduction number is less than 1, tuberculosis will disappear. Finally, an optimal control problem is constructed by using the extended model, which reveals the spread of tuberculosis can be effectively controlled by eliminating <i>Mycobacterium tuberculosis</i> in the environment and controlling tuberculosis patients at the same time. Numerical example results show the effectiveness of the optimization strategies.</p></div>\",\"PeriodicalId\":612,\"journal\":{\"name\":\"Journal of Biological Physics\",\"volume\":\"51 1\",\"pages\":\"\"},\"PeriodicalIF\":1.8000,\"publicationDate\":\"2024-11-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Biological Physics\",\"FirstCategoryId\":\"99\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10867-024-09667-1\",\"RegionNum\":4,\"RegionCategory\":\"生物学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"BIOPHYSICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Biological Physics","FirstCategoryId":"99","ListUrlMain":"https://link.springer.com/article/10.1007/s10867-024-09667-1","RegionNum":4,"RegionCategory":"生物学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"BIOPHYSICS","Score":null,"Total":0}
Analysis of tuberculosis model with indirect environmental transmission and optimal control
In this paper, the dynamic behaviors of tuberculosis in the context of indirect environmental transmission are discussed by establishing the SEIRB epidemic model. The basic reproduction number is computed by employing the next-generation matrix approach. The global stability of disease-free equilibrium and endemic equilibrium is proved by constructing the Lyapunov function and the application of LaSalle’s invariance principle. It shows that when the basic reproduction number is greater than 1, tuberculosis will spread among the population. When the basic reproduction number is less than 1, tuberculosis will disappear. Finally, an optimal control problem is constructed by using the extended model, which reveals the spread of tuberculosis can be effectively controlled by eliminating Mycobacterium tuberculosis in the environment and controlling tuberculosis patients at the same time. Numerical example results show the effectiveness of the optimization strategies.
期刊介绍：
Many physicists are turning their attention to domains that were not traditionally part of physics and are applying the sophisticated tools of theoretical, computational and experimental physics to investigate biological processes, systems and materials.
The Journal of Biological Physics provides a medium where this growing community of scientists can publish its results and discuss its aims and methods. It welcomes papers which use the tools of physics in an innovative way to study biological problems, as well as research aimed at providing a better understanding of the physical principles underlying biological processes.
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