Stability analysis of Toxoplasma gondii propagation model
Toxoplasma gondii as a typical zoonotic disease, because there is no suitable vaccine, its control is important in prevention, so it has been the subject of research by all scholars. in order to study the critical value of controlling its transmission and carry out relevant theoretical analysis, Thi...
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| Format: | Article |
| Language: | zho |
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Hebei University of Science and Technology
2018-12-01
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| Series: | Journal of Hebei University of Science and Technology |
| Subjects: | |
| Online Access: | http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201806005&flag=1&journal_ |
| _version_ | 1811268778267246592 |
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| author | Lixia REN Yakui XUE |
| author_facet | Lixia REN Yakui XUE |
| author_sort | Lixia REN |
| collection | DOAJ |
| description | Toxoplasma gondii as a typical zoonotic disease, because there is no suitable vaccine, its control is important in prevention, so it has been the subject of research by all scholars. in order to study the critical value of controlling its transmission and carry out relevant theoretical analysis, This paper establishes a mathematical model based on the life history and transmission route of Toxoplasma gondii, and analyzes the basic regeneration number that determines whether the disease continues to exist. When the basic reproduction number is less than 1, the disease died out finally. When the basic reproduction number is greater than 1, the model had a unique endemic equilibrium point, and the disease uniformly persisted. In addition, the sufficient conditions for the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium are given by establishing a suitable Lyapunov function. In this paper, a systematic and complete stability study of the established mathematical model can be provided to provide advice for controlling the spread of disease. |
| first_indexed | 2024-04-12T21:29:04Z |
| format | Article |
| id | doaj.art-53525c147e7c4da99c60eeceb8bbcf58 |
| institution | Directory Open Access Journal |
| issn | 1008-1542 |
| language | zho |
| last_indexed | 2024-04-12T21:29:04Z |
| publishDate | 2018-12-01 |
| publisher | Hebei University of Science and Technology |
| record_format | Article |
| series | Journal of Hebei University of Science and Technology |
| spelling | doaj.art-53525c147e7c4da99c60eeceb8bbcf582022-12-22T03:16:05ZzhoHebei University of Science and TechnologyJournal of Hebei University of Science and Technology1008-15422018-12-0139651151710.7535/hbkd.2018yx06005b201806005Stability analysis of Toxoplasma gondii propagation modelLixia REN0Yakui XUE1School of Science, North University of China, Taiyuan, Shanxi 030051,ChinaSchool of Science, North University of China, Taiyuan, Shanxi 030051,ChinaToxoplasma gondii as a typical zoonotic disease, because there is no suitable vaccine, its control is important in prevention, so it has been the subject of research by all scholars. in order to study the critical value of controlling its transmission and carry out relevant theoretical analysis, This paper establishes a mathematical model based on the life history and transmission route of Toxoplasma gondii, and analyzes the basic regeneration number that determines whether the disease continues to exist. When the basic reproduction number is less than 1, the disease died out finally. When the basic reproduction number is greater than 1, the model had a unique endemic equilibrium point, and the disease uniformly persisted. In addition, the sufficient conditions for the global asymptotic stability of the disease-free equilibrium and the endemic equilibrium are given by establishing a suitable Lyapunov function. In this paper, a systematic and complete stability study of the established mathematical model can be provided to provide advice for controlling the spread of disease.http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201806005&flag=1&journal_theory of stabilityToxoplasma gondiifinal hostbasic reproduction numberglobal stabilityLyapunov function |
| spellingShingle | Lixia REN Yakui XUE Stability analysis of Toxoplasma gondii propagation model Journal of Hebei University of Science and Technology theory of stability Toxoplasma gondii final host basic reproduction number global stability Lyapunov function |
| title | Stability analysis of Toxoplasma gondii propagation model |
| title_full | Stability analysis of Toxoplasma gondii propagation model |
| title_fullStr | Stability analysis of Toxoplasma gondii propagation model |
| title_full_unstemmed | Stability analysis of Toxoplasma gondii propagation model |
| title_short | Stability analysis of Toxoplasma gondii propagation model |
| title_sort | stability analysis of toxoplasma gondii propagation model |
| topic | theory of stability Toxoplasma gondii final host basic reproduction number global stability Lyapunov function |
| url | http://xuebao.hebust.edu.cn/hbkjdx/ch/reader/create_pdf.aspx?file_no=b201806005&flag=1&journal_ |
| work_keys_str_mv | AT lixiaren stabilityanalysisoftoxoplasmagondiipropagationmodel AT yakuixue stabilityanalysisoftoxoplasmagondiipropagationmodel |