A double age-structured model of the co-infection of tuberculosis and HIV
After decades on the decline, it is believed that the emergence of HIV is responsible for an increase in the tuberculosis prevalence. The leading infectious disease in the world, tuberculosis is also the leading cause of death among HIV-positive individuals. Each disease progresses through several s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2014-11-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.23 |
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| _version_ | 1832590120684879872 |
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| author | Georgi Kapitanov |
| author_facet | Georgi Kapitanov |
| author_sort | Georgi Kapitanov |
| collection | DOAJ |
| description | After decades on the decline, it is believed that the emergence of HIV is responsible for an increase in the tuberculosis prevalence. The leading infectious disease in the world, tuberculosis is also the leading cause of death among HIV-positive individuals. Each disease progresses through several stages. The current model suggests modeling these stages through a time-since-infection tracking transmission rate function, which, when considering co-infection, introduces a double-age structure in the PDE system. The basic and invasion reproduction numbers for each disease are calculated and the basic ones established as threshold for the disease progression. Numerical results confirm the calculations and a simple treatment scenario suggests the importance of time-since-infection when introducing disease control and treatment in the model. |
| format | Article |
| id | doaj-art-692004dc4511452ca2791585a7f6e118 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2014-11-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-692004dc4511452ca2791585a7f6e1182025-01-24T02:31:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182014-11-01121234010.3934/mbe.2015.12.23A double age-structured model of the co-infection of tuberculosis and HIVGeorgi Kapitanov0Mathematics Department, Purdue University, 150 N. University Street, West Lafayette, IN 47907-2067After decades on the decline, it is believed that the emergence of HIV is responsible for an increase in the tuberculosis prevalence. The leading infectious disease in the world, tuberculosis is also the leading cause of death among HIV-positive individuals. Each disease progresses through several stages. The current model suggests modeling these stages through a time-since-infection tracking transmission rate function, which, when considering co-infection, introduces a double-age structure in the PDE system. The basic and invasion reproduction numbers for each disease are calculated and the basic ones established as threshold for the disease progression. Numerical results confirm the calculations and a simple treatment scenario suggests the importance of time-since-infection when introducing disease control and treatment in the model.https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.23partial differential equationstuberculosisbasic reproduction numberco-infectioninvasion reproduction numberage-structure.hivpopulation dynamicsmathematical epidemiology |
| spellingShingle | Georgi Kapitanov A double age-structured model of the co-infection of tuberculosis and HIV Mathematical Biosciences and Engineering partial differential equations tuberculosis basic reproduction number co-infection invasion reproduction number age-structure. hiv population dynamics mathematical epidemiology |
| title | A double age-structured model of the co-infection of tuberculosis and HIV |
| title_full | A double age-structured model of the co-infection of tuberculosis and HIV |
| title_fullStr | A double age-structured model of the co-infection of tuberculosis and HIV |
| title_full_unstemmed | A double age-structured model of the co-infection of tuberculosis and HIV |
| title_short | A double age-structured model of the co-infection of tuberculosis and HIV |
| title_sort | double age structured model of the co infection of tuberculosis and hiv |
| topic | partial differential equations tuberculosis basic reproduction number co-infection invasion reproduction number age-structure. hiv population dynamics mathematical epidemiology |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015.12.23 |
| work_keys_str_mv | AT georgikapitanov adoubleagestructuredmodelofthecoinfectionoftuberculosisandhiv AT georgikapitanov doubleagestructuredmodelofthecoinfectionoftuberculosisandhiv |