On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China
Heterogeneity in sexual behavior is known to play an important role in the spread of HIV. In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. Assuming proportionate mixing, it was shown that the basic reprodu...
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| Language: | English |
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AIMS Press
2007-07-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.595 |
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| author | Nicolas Bacaër Xamxinur Abdurahman Jianli Ye Pierre Auger |
| author_facet | Nicolas Bacaër Xamxinur Abdurahman Jianli Ye Pierre Auger |
| author_sort | Nicolas Bacaër |
| collection | DOAJ |
| description | Heterogeneity in sexual behavior is known to play an important role in the spread of HIV. In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. Assuming proportionate mixing, it was shown that the basic reproduction number $R_0$ determining the epidemic threshold was proportional to $M+V/M$, where $M$ is the mean and $V$ the variance of the distribution. In the present paper, we notice that this theoretical distribution is different from the one obtained in behavioral surveys for the number of sexual partnerships over a period of length $\tau$. The latter is a ''mixed Poisson distribution'' whose mean $m$ and variance $v$ are such that $M=m/\tau$ and $V=(v-m)/\tau^2$. So $M+V/M=(m+v/m-1)/\tau$. This way, we improve the link between theory and data for sexual activity models of HIV/AIDS epidemics. As an example, we consider data concerning sex workers and their clients in Yunnan, China, and find an upper bound for the geometric mean of the transmission probabilities per partnership in this context. |
| format | Article |
| id | doaj-art-a497d2c7fb304f0ca0b9153a7e3983d7 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-07-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-a497d2c7fb304f0ca0b9153a7e3983d72025-01-24T01:54:07ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-07-014459560710.3934/mbe.2007.4.595On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, ChinaNicolas Bacaër0Xamxinur Abdurahman1Jianli Ye2Pierre Auger3Institut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedexInstitut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedexInstitut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedexInstitut de Recherche pour le Développement (I.R.D.), 32 avenue Henri Varagnat, 93143 Bondy cedexHeterogeneity in sexual behavior is known to play an important role in the spread of HIV. In 1986, a mathematical model based on ordinary differential equations was introduced to take into account the distribution of sexual activity. Assuming proportionate mixing, it was shown that the basic reproduction number $R_0$ determining the epidemic threshold was proportional to $M+V/M$, where $M$ is the mean and $V$ the variance of the distribution. In the present paper, we notice that this theoretical distribution is different from the one obtained in behavioral surveys for the number of sexual partnerships over a period of length $\tau$. The latter is a ''mixed Poisson distribution'' whose mean $m$ and variance $v$ are such that $M=m/\tau$ and $V=(v-m)/\tau^2$. So $M+V/M=(m+v/m-1)/\tau$. This way, we improve the link between theory and data for sexual activity models of HIV/AIDS epidemics. As an example, we consider data concerning sex workers and their clients in Yunnan, China, and find an upper bound for the geometric mean of the transmission probabilities per partnership in this context.https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.595basic reproduction numberhivmixed poisson distribution. |
| spellingShingle | Nicolas Bacaër Xamxinur Abdurahman Jianli Ye Pierre Auger On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China Mathematical Biosciences and Engineering basic reproduction number hiv mixed poisson distribution. |
| title | On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China |
| title_full | On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China |
| title_fullStr | On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China |
| title_full_unstemmed | On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China |
| title_short | On the basic reproduction number $R_0$ in sexual activity models for HIV/AIDS epidemics: Example from Yunnan, China |
| title_sort | on the basic reproduction number r 0 in sexual activity models for hiv aids epidemics example from yunnan china |
| topic | basic reproduction number hiv mixed poisson distribution. |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.595 |
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