Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay
We derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/742385 |
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| _version_ | 1832549528269488128 |
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| author | Xamxinur Abdurahman Ling Zhang Zhidong Teng |
| author_facet | Xamxinur Abdurahman Ling Zhang Zhidong Teng |
| author_sort | Xamxinur Abdurahman |
| collection | DOAJ |
| description | We derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction number R0<1, and the heroin-using is permanent when the basic reproduction number R0>1. |
| format | Article |
| id | doaj-art-948197a9a3bf45c4b2a2ec1f12d14a08 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-948197a9a3bf45c4b2a2ec1f12d14a082025-02-03T06:11:07ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/742385742385Global Dynamics of a Discretized Heroin Epidemic Model with Time DelayXamxinur Abdurahman0Ling Zhang1Zhidong Teng2College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaCollege of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, ChinaWe derive a discretized heroin epidemic model with delay by applying a nonstandard finite difference scheme. We obtain positivity of the solution and existence of the unique endemic equilibrium. We show that heroin-using free equilibrium is globally asymptotically stable when the basic reproduction number R0<1, and the heroin-using is permanent when the basic reproduction number R0>1.http://dx.doi.org/10.1155/2014/742385 |
| spellingShingle | Xamxinur Abdurahman Ling Zhang Zhidong Teng Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay Abstract and Applied Analysis |
| title | Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay |
| title_full | Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay |
| title_fullStr | Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay |
| title_full_unstemmed | Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay |
| title_short | Global Dynamics of a Discretized Heroin Epidemic Model with Time Delay |
| title_sort | global dynamics of a discretized heroin epidemic model with time delay |
| url | http://dx.doi.org/10.1155/2014/742385 |
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