Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity
In this paper, we investigated a new heroin–cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number [Formula: see text], which was defined by applying t...
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| Format: | Article |
| Language: | English |
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Taylor & Francis Group
2023-12-01
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| Series: | Journal of Biological Dynamics |
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| Online Access: | https://www.tandfonline.com/doi/10.1080/17513758.2023.2189026 |
| _version_ | 1797331584491192320 |
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| author | Jinhu Xu |
| author_facet | Jinhu Xu |
| author_sort | Jinhu Xu |
| collection | DOAJ |
| description | In this paper, we investigated a new heroin–cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number [Formula: see text], which was defined by applying the next-generation operator. The threshold type results shown that if [Formula: see text], then the drug-free steady state is globally asymptotically stable. If [Formula: see text], then heroin–cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of [Formula: see text] by analysing the local asymptotic stability and global attractivity. |
| first_indexed | 2024-03-08T07:36:35Z |
| format | Article |
| id | doaj.art-d354773b636147c9aa6e241dd4674ed8 |
| institution | Directory Open Access Journal |
| issn | 1751-3758 1751-3766 |
| language | English |
| last_indexed | 2024-03-08T07:36:35Z |
| publishDate | 2023-12-01 |
| publisher | Taylor & Francis Group |
| record_format | Article |
| series | Journal of Biological Dynamics |
| spelling | doaj.art-d354773b636147c9aa6e241dd4674ed82024-02-02T18:51:34ZengTaylor & Francis GroupJournal of Biological Dynamics1751-37581751-37662023-12-0117110.1080/17513758.2023.2189026Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneityJinhu Xu0School of Sciences, Xi'an University of Technology, Xi'an, People's Republic of ChinaIn this paper, we investigated a new heroin–cocaine epidemic model which incorporates spatial heterogeneity and nonlinear incidence rate. The main project of this paper is to explore the threshold dynamics in terms of the basic reproduction number [Formula: see text], which was defined by applying the next-generation operator. The threshold type results shown that if [Formula: see text], then the drug-free steady state is globally asymptotically stable. If [Formula: see text], then heroin–cocaine spread is uniformly persistent. Furthermore, the globally asymptotic stability of the drug-free steady state has been established for the critical case of [Formula: see text] by analysing the local asymptotic stability and global attractivity.https://www.tandfonline.com/doi/10.1080/17513758.2023.2189026Heroin–cocaine spreadspatial heterogeneitythe basic reproduction numberuniformly persistentglobal asymptotically stable |
| spellingShingle | Jinhu Xu Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity Journal of Biological Dynamics Heroin–cocaine spread spatial heterogeneity the basic reproduction number uniformly persistent global asymptotically stable |
| title | Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity |
| title_full | Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity |
| title_fullStr | Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity |
| title_full_unstemmed | Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity |
| title_short | Dynamical analysis of a heroin–cocaine epidemic model with nonlinear incidence and spatial heterogeneity |
| title_sort | dynamical analysis of a heroin cocaine epidemic model with nonlinear incidence and spatial heterogeneity |
| topic | Heroin–cocaine spread spatial heterogeneity the basic reproduction number uniformly persistent global asymptotically stable |
| url | https://www.tandfonline.com/doi/10.1080/17513758.2023.2189026 |
| work_keys_str_mv | AT jinhuxu dynamicalanalysisofaheroincocaineepidemicmodelwithnonlinearincidenceandspatialheterogeneity |