Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment
We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'...
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AIMS Press
2013-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.599 |
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| author | Brandy Rapatski Juan Tolosa |
| author_facet | Brandy Rapatski Juan Tolosa |
| author_sort | Brandy Rapatski |
| collection | DOAJ |
| description | We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'' scenario model includingtesting and treatment in the SFCCC epidemic.We use compartmental, population-level models,described by systems ofordinary differential equations.We find the basic reproductive number $R_0$ for each system,and we prove that if $R_0<1 the="" system="" has="" only="" the="" disease-free="" equilibrium="" dfe="" which="" is="" locally="" and="" globally="" stable="" whereas="" if="" r_0="">1$, the DFE is unstable.In addition, when $R_0>1$, both systems have a unique endemic equilibrium (EE).We show that treatment alone would not have stopped the San Francisco MSM epidemic,but would have significantly reduced its impact. |
| format | Article |
| id | doaj-art-3c323e1b34dd49779777d66e256212c5 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-3c323e1b34dd49779777d66e256212c52025-01-24T02:28:12ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-12-0111359961910.3934/mbe.2014.11.599Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatmentBrandy Rapatski0Juan Tolosa1Department of Natural Sciences and Mathematics, Richard Stockton College of New Jersey, 101 Vera King Farris Drive, Galloway, NJ 08205-9441Department of Natural Sciences and Mathematics, Richard Stockton College of New Jersey, 101 Vera King Farris Drive, Galloway, NJ 08205-9441We investigate two HIV/AIDS epidemic models.The first model represents the early San Franciscomen having sex with men (MSM) epidemic.We use data from the San Francisco City Clinic Cohort Study (SFCCC), documentingthe onset of HIV in San Francisco (1978-1984).The second model is a ``what-if'' scenario model includingtesting and treatment in the SFCCC epidemic.We use compartmental, population-level models,described by systems ofordinary differential equations.We find the basic reproductive number $R_0$ for each system,and we prove that if $R_0<1 the="" system="" has="" only="" the="" disease-free="" equilibrium="" dfe="" which="" is="" locally="" and="" globally="" stable="" whereas="" if="" r_0="">1$, the DFE is unstable.In addition, when $R_0>1$, both systems have a unique endemic equilibrium (EE).We show that treatment alone would not have stopped the San Francisco MSM epidemic,but would have significantly reduced its impact.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.599mathematical modellyapunov function.reproduction numberstabilityhuman immunodeficiency virus (hiv) |
| spellingShingle | Brandy Rapatski Juan Tolosa Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment Mathematical Biosciences and Engineering mathematical model lyapunov function. reproduction number stability human immunodeficiency virus (hiv) |
| title | Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment |
| title_full | Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment |
| title_fullStr | Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment |
| title_full_unstemmed | Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment |
| title_short | Modeling and analysis of the San Francisco City Clinic Cohort (SFCCC) HIV-epidemic including treatment |
| title_sort | modeling and analysis of the san francisco city clinic cohort sfccc hiv epidemic including treatment |
| topic | mathematical model lyapunov function. reproduction number stability human immunodeficiency virus (hiv) |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.599 |
| work_keys_str_mv | AT brandyrapatski modelingandanalysisofthesanfranciscocitycliniccohortsfccchivepidemicincludingtreatment AT juantolosa modelingandanalysisofthesanfranciscocitycliniccohortsfccchivepidemicincludingtreatment |