Global Stability for a Binge Drinking Model with Two Stages
A more realistic two-stage model for binge drinking problem is introduced, where the youths with alcohol problems are divided into those who admit the problem and those who do not admit it. We also consider the direct transfer from the class of susceptible individuals towards the class of admitting...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2012/829386 |
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| _version_ | 1832564168881864704 |
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| author | Hai-Feng Huo Na-Na Song |
| author_facet | Hai-Feng Huo Na-Na Song |
| author_sort | Hai-Feng Huo |
| collection | DOAJ |
| description | A more realistic two-stage model for binge drinking problem is introduced, where the youths
with alcohol problems are divided into those who admit the problem and those who do not
admit it. We also consider the direct transfer from the class of susceptible individuals towards the
class of admitting drinkers. Mathematical analyses establish that the global dynamics of the model
are determined by the basic reproduction number, R0. The alcohol-free equilibrium is globally asymptotically stable, and the alcohol problems are eliminated from the population if R0<1. A unique
alcohol-present equilibrium is globally asymptotically stable if R0>1. Numerical simulations are also conducted in the analytic results. |
| format | Article |
| id | doaj-art-0db1535e43004ea68a69f6e95cc3d980 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-0db1535e43004ea68a69f6e95cc3d9802025-02-03T01:11:36ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2012-01-01201210.1155/2012/829386829386Global Stability for a Binge Drinking Model with Two StagesHai-Feng Huo0Na-Na Song1Department of Applied Mathematics, Lanzhou University of Technology, Gansu, Lanzhou 730050, ChinaDepartment of Applied Mathematics, Lanzhou University of Technology, Gansu, Lanzhou 730050, ChinaA more realistic two-stage model for binge drinking problem is introduced, where the youths with alcohol problems are divided into those who admit the problem and those who do not admit it. We also consider the direct transfer from the class of susceptible individuals towards the class of admitting drinkers. Mathematical analyses establish that the global dynamics of the model are determined by the basic reproduction number, R0. The alcohol-free equilibrium is globally asymptotically stable, and the alcohol problems are eliminated from the population if R0<1. A unique alcohol-present equilibrium is globally asymptotically stable if R0>1. Numerical simulations are also conducted in the analytic results.http://dx.doi.org/10.1155/2012/829386 |
| spellingShingle | Hai-Feng Huo Na-Na Song Global Stability for a Binge Drinking Model with Two Stages Discrete Dynamics in Nature and Society |
| title | Global Stability for a Binge Drinking Model with Two Stages |
| title_full | Global Stability for a Binge Drinking Model with Two Stages |
| title_fullStr | Global Stability for a Binge Drinking Model with Two Stages |
| title_full_unstemmed | Global Stability for a Binge Drinking Model with Two Stages |
| title_short | Global Stability for a Binge Drinking Model with Two Stages |
| title_sort | global stability for a binge drinking model with two stages |
| url | http://dx.doi.org/10.1155/2012/829386 |
| work_keys_str_mv | AT haifenghuo globalstabilityforabingedrinkingmodelwithtwostages AT nanasong globalstabilityforabingedrinkingmodelwithtwostages |