A two-strain TB model with multiplelatent stages
A two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically frie...
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| Format: | Article |
| Language: | English |
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AIMS Press
2016-04-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2016017 |
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| author | Azizeh Jabbari Carlos Castillo-Chavez Fereshteh Nazari Baojun Song Hossein Kheiri |
| author_facet | Azizeh Jabbari Carlos Castillo-Chavez Fereshteh Nazari Baojun Song Hossein Kheiri |
| author_sort | Azizeh Jabbari |
| collection | DOAJ |
| description | A two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically friendly gamma distributions, a reasonable alternative to the use of exponential distributed waiting periods or to integral equations involving ``arbitrary'' distributions. The model supports a globally-asymptotically stable disease-free equilibrium when the reproduction number is less than one and an endemic equilibriums, shown to be locally asymptotically stable, or l.a.s., whenever the basic reproduction number is greater than one. Conditions for the existence and maintenance of TB resistant strains are discussed. The possibility of exogenous re-infection is added and shown to be capable of supporting multiple equilibria; a situation that increases the challenges faced by public health experts. We show that exogenous re-infection may help established resilient communities of actively-TB infected individuals that cannot be eliminated using approaches based exclusively on the ability to bring the control reproductive number just below $1$. |
| format | Article |
| id | doaj-art-2bf93f3d1e6449de909a08c4956cac88 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2016-04-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-2bf93f3d1e6449de909a08c4956cac882025-01-24T02:36:34ZengAIMS PressMathematical Biosciences and Engineering1551-00182016-04-0113474178510.3934/mbe.2016017A two-strain TB model with multiplelatent stagesAzizeh Jabbari0Carlos Castillo-Chavez1Fereshteh Nazari2Baojun Song3Hossein Kheiri4Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, TabrizSimon A Levin Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287Simon A Levin Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287Department of Mathematical Sciences, Montclair State University, 1 Normal Avenue, Montclair, NJ 07043Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Tabriz, TabrizA two-strain tuberculosis (TB) transmission model incorporating antibiotic-generated TB resistant strains and long and variable waiting periods within the latently infected class is introduced. The mathematical analysis is carried out when the waiting periods are modeled via parametrically friendly gamma distributions, a reasonable alternative to the use of exponential distributed waiting periods or to integral equations involving ``arbitrary'' distributions. The model supports a globally-asymptotically stable disease-free equilibrium when the reproduction number is less than one and an endemic equilibriums, shown to be locally asymptotically stable, or l.a.s., whenever the basic reproduction number is greater than one. Conditions for the existence and maintenance of TB resistant strains are discussed. The possibility of exogenous re-infection is added and shown to be capable of supporting multiple equilibria; a situation that increases the challenges faced by public health experts. We show that exogenous re-infection may help established resilient communities of actively-TB infected individuals that cannot be eliminated using approaches based exclusively on the ability to bring the control reproductive number just below $1$.https://www.aimspress.com/article/doi/10.3934/mbe.2016017reproduction numberstabilityequilibriaresistant tuberculosistuberculosis models.gamma distributionepidemiological models |
| spellingShingle | Azizeh Jabbari Carlos Castillo-Chavez Fereshteh Nazari Baojun Song Hossein Kheiri A two-strain TB model with multiplelatent stages Mathematical Biosciences and Engineering reproduction number stability equilibria resistant tuberculosis tuberculosis models. gamma distribution epidemiological models |
| title | A two-strain TB model with multiplelatent stages |
| title_full | A two-strain TB model with multiplelatent stages |
| title_fullStr | A two-strain TB model with multiplelatent stages |
| title_full_unstemmed | A two-strain TB model with multiplelatent stages |
| title_short | A two-strain TB model with multiplelatent stages |
| title_sort | two strain tb model with multiplelatent stages |
| topic | reproduction number stability equilibria resistant tuberculosis tuberculosis models. gamma distribution epidemiological models |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2016017 |
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