Dynamical Models of Tuberculosis and Their Applications
The reemergence of tuberculosis (TB) from the 1980s to the early1990s instigated extensive researches on the mechanisms behind thetransmission dynamics of TB epidemics. This article provides adetailed review of the work on the dynamics and control of TB. Theearliest mathematical models describing t...
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| Format: | Article |
| Language: | English |
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AIMS Press
2004-06-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.361 |
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| author | Carlos Castillo-Chavez Baojun Song |
| author_facet | Carlos Castillo-Chavez Baojun Song |
| author_sort | Carlos Castillo-Chavez |
| collection | DOAJ |
| description | The reemergence of tuberculosis (TB) from the 1980s to the early1990s instigated extensive researches on the mechanisms behind thetransmission dynamics of TB epidemics. This article provides adetailed review of the work on the dynamics and control of TB. Theearliest mathematical models describing the TB dynamics appeared inthe 1960s and focused on the prediction and control strategies usingsimulation approaches. Most recently developed models not only payattention to simulations but also take care of dynamical analysisusing modern knowledge of dynamical systems. Questions addressed bythese models mainly concentrate on TB control strategies, optimalvaccination policies, approaches toward the elimination of TB in theU.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responsesof the immune system, impacts of demography, the role of publictransportation systems, and the impact of contact patterns. Modelformulations involve a variety of mathematical areas, such as ODEs(Ordinary Differential Equations) (both autonomous andnon-autonomous systems), PDEs (Partial Differential Equations),system of difference equations, system of integro-differentialequations, Markov chain model, and simulation models. |
| format | Article |
| id | doaj-art-5b0a0f62f9884e16941d2f8ba12f99ec |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5b0a0f62f9884e16941d2f8ba12f99ec2025-01-24T01:46:54ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-06-011236140410.3934/mbe.2004.1.361Dynamical Models of Tuberculosis and Their ApplicationsCarlos Castillo-Chavez0Baojun Song1Mathematics, Computational and Modeling Sciences Center, Arizona State University, PO Box 871904, Tempe, AZ 85287Department of Mathematical Sciences, Montclair State University, Upper Montclair, NJ 07043The reemergence of tuberculosis (TB) from the 1980s to the early1990s instigated extensive researches on the mechanisms behind thetransmission dynamics of TB epidemics. This article provides adetailed review of the work on the dynamics and control of TB. Theearliest mathematical models describing the TB dynamics appeared inthe 1960s and focused on the prediction and control strategies usingsimulation approaches. Most recently developed models not only payattention to simulations but also take care of dynamical analysisusing modern knowledge of dynamical systems. Questions addressed bythese models mainly concentrate on TB control strategies, optimalvaccination policies, approaches toward the elimination of TB in theU.S.A., TB co-infection with HIV/AIDS, drug-resistant TB, responsesof the immune system, impacts of demography, the role of publictransportation systems, and the impact of contact patterns. Modelformulations involve a variety of mathematical areas, such as ODEs(Ordinary Differential Equations) (both autonomous andnon-autonomous systems), PDEs (Partial Differential Equations),system of difference equations, system of integro-differentialequations, Markov chain model, and simulation models.https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.361hivdynamical modelstuberculosisdisease emergence and reemergence.bifurcationprevention and controlglobal dynamics |
| spellingShingle | Carlos Castillo-Chavez Baojun Song Dynamical Models of Tuberculosis and Their Applications Mathematical Biosciences and Engineering hiv dynamical models tuberculosis disease emergence and reemergence. bifurcation prevention and control global dynamics |
| title | Dynamical Models of Tuberculosis and Their Applications |
| title_full | Dynamical Models of Tuberculosis and Their Applications |
| title_fullStr | Dynamical Models of Tuberculosis and Their Applications |
| title_full_unstemmed | Dynamical Models of Tuberculosis and Their Applications |
| title_short | Dynamical Models of Tuberculosis and Their Applications |
| title_sort | dynamical models of tuberculosis and their applications |
| topic | hiv dynamical models tuberculosis disease emergence and reemergence. bifurcation prevention and control global dynamics |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.361 |
| work_keys_str_mv | AT carloscastillochavez dynamicalmodelsoftuberculosisandtheirapplications AT baojunsong dynamicalmodelsoftuberculosisandtheirapplications |