Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme
In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the con...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/4272914 |
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| _version_ | 1832561353674457088 |
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| author | Zhaofeng An Suxia Zhang Jinhu Xu |
| author_facet | Zhaofeng An Suxia Zhang Jinhu Xu |
| author_sort | Zhaofeng An |
| collection | DOAJ |
| description | In this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. Threshold dynamics of the continuous model are performed by constructing Lyapunov functions. The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model. In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations. |
| format | Article |
| id | doaj-art-50e4643cdb1a4cfc885fc3ad2181cf61 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-50e4643cdb1a4cfc885fc3ad2181cf612025-02-03T01:25:17ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/42729144272914Stability Analysis of an Alcoholism Model with Public Health Education and NSFD SchemeZhaofeng An0Suxia Zhang1Jinhu Xu2School of Science, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Science, Xi’an University of Technology, Xi’an 710048, ChinaSchool of Science, Xi’an University of Technology, Xi’an 710048, ChinaIn this paper, an alcoholism model of SEAR type with different susceptibilities due to public health education is investigated, with the form of continuous differential equations as well as discrete differential equations by applying the Mickens nonstandard finite difference (NSFD) scheme to the continuous equations. Threshold dynamics of the continuous model are performed by constructing Lyapunov functions. The analysis of a discrete model indicates that the alcohol-free equilibrium is globally asymptotically stable if the basic reproductive number R0<1, and conversely, the alcohol-present equilibrium is globally asymptotically stable if R0>1, revealing the consistency and efficiency of the discrete model to preserve the dynamical properties of the corresponding continuous model. In addition, stability preserving and the impact of the parameters related with public health education are conducted by numerical simulations.http://dx.doi.org/10.1155/2020/4272914 |
| spellingShingle | Zhaofeng An Suxia Zhang Jinhu Xu Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme Discrete Dynamics in Nature and Society |
| title | Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme |
| title_full | Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme |
| title_fullStr | Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme |
| title_full_unstemmed | Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme |
| title_short | Stability Analysis of an Alcoholism Model with Public Health Education and NSFD Scheme |
| title_sort | stability analysis of an alcoholism model with public health education and nsfd scheme |
| url | http://dx.doi.org/10.1155/2020/4272914 |
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