Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic
Since the discovery of HIV/AIDS there have been numerous mathematical modelsproposed to explain the epidemic of the disease and to evaluate possiblecontrol measures. In particular, several recent studies have looked at thepotential impact of condom usage on the epidemic[1, 2, 3, 4]. We develop a si...
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AIMS Press
2009-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.363 |
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| author | Jeff Musgrave James Watmough |
| author_facet | Jeff Musgrave James Watmough |
| author_sort | Jeff Musgrave |
| collection | DOAJ |
| description | Since the discovery of HIV/AIDS there have been numerous mathematical modelsproposed to explain the epidemic of the disease and to evaluate possiblecontrol measures. In particular, several recent studies have looked at thepotential impact of condom usage on the epidemic[1, 2, 3, 4]. We develop a simplemodel for HIV/AIDS, and investigate the effectiveness of condoms as apossible control strategy. We show that condoms can greatly reduce the numberof outbreaks and the size of the epidemic. However, the necessary condom usagelevels are much higher than the current estimates. We conclude that condomsalone will not be sufficient to halt the epidemic in most populationsunless current estimates of the transmission probabilities are high.Our model has only five independentparameters, which allows for a complete analysis. We show that the assumptionsof mass action and standard incidence provide similar results, which impliesthat the results of the simpler mass action model can be used as a good firstapproximation to the peak of the epidemic. |
| format | Article |
| id | doaj-art-252619929a2448128e5895ec3df97734 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-252619929a2448128e5895ec3df977342025-01-24T01:59:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-02-016236337610.3934/mbe.2009.6.363Examination of a simple model of condom usage and individual withdrawal for the HIV epidemicJeff Musgrave0James Watmough1Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3Since the discovery of HIV/AIDS there have been numerous mathematical modelsproposed to explain the epidemic of the disease and to evaluate possiblecontrol measures. In particular, several recent studies have looked at thepotential impact of condom usage on the epidemic[1, 2, 3, 4]. We develop a simplemodel for HIV/AIDS, and investigate the effectiveness of condoms as apossible control strategy. We show that condoms can greatly reduce the numberof outbreaks and the size of the epidemic. However, the necessary condom usagelevels are much higher than the current estimates. We conclude that condomsalone will not be sufficient to halt the epidemic in most populationsunless current estimates of the transmission probabilities are high.Our model has only five independentparameters, which allows for a complete analysis. We show that the assumptionsof mass action and standard incidence provide similar results, which impliesthat the results of the simpler mass action model can be used as a good firstapproximation to the peak of the epidemic.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.363disease transmission modelcontrol reproduction number.epidemiology |
| spellingShingle | Jeff Musgrave James Watmough Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic Mathematical Biosciences and Engineering disease transmission model control reproduction number. epidemiology |
| title | Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic |
| title_full | Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic |
| title_fullStr | Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic |
| title_full_unstemmed | Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic |
| title_short | Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic |
| title_sort | examination of a simple model of condom usage and individual withdrawal for the hiv epidemic |
| topic | disease transmission model control reproduction number. epidemiology |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.363 |
| work_keys_str_mv | AT jeffmusgrave examinationofasimplemodelofcondomusageandindividualwithdrawalforthehivepidemic AT jameswatmough examinationofasimplemodelofcondomusageandindividualwithdrawalforthehivepidemic |