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Global Dynamics of Tuberculosis Models with Density Dependent Demography

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Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory

Part of the book series: The IMA Volumes in Mathematics and its Applications ((IMA,volume 126))

Abstract

Mathematical models for Tuberculosis with linear and logistic growth rates are considered. The global dynamic structure for the logistic recruitment model is analyzed with the help of a strong version of the Poincaré-Bendixson Theorem. The nature of the global dynamics of the same model with a linear recruitment rate is established with the use of explicit threshold quantities controlling the absolute and relative spread of the disease and the likelihood of extinction or persistence of the total population. The classification of planar quadratic systems helps rule out the existence of closed orbits (limit cycles).

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Author information

Authors and Affiliations

  1. Department of Biometrics, Cornell University, Ithaca, NY, 14853, USA

    Baojun Song & Carlos Castillo-Chavez

  2. Universidad de Belgrano-CONICET, Zabala 1851, piso 12, 1428, Buenos Aires, Argentina

    Juan P. Aparicio

Authors
  1. Baojun Song
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  2. Carlos Castillo-Chavez
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  3. Juan P. Aparicio
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Editor information

Editors and Affiliations

  1. Mathematical and Theoretical Biology Institute and member, Departments of Biometrics, Statistics and Theoretical and Applied Mechanics, Cornell University, 14853-7801, Ithaca, NY, USA

    Carlos Castillo-Chavez

  2. Department of Biomathematics, UCLA School of Medicine, 90095-1766, Los Angeles, CA, USA

    Sally Blower

  3. Department of Math and Stats, University of Victoria, V8W 3P4, Victoria, British Columbia, Canada

    Pauline van den Driessche

  4. Dept. of Microbiology and Immunology, University of Michigan Medical School, 48109-0620, Ann Arbor, MI, USA

    Denise Kirschner

  5. Department of Mathematics Howard, Howard University, 20059, Washington, DC, USA

    Abdul-Aziz Yakubu

  6. Biometrics Department, Cornell University, USA

    Abdul-Aziz Yakubu

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© 2002 Springer Science+Business Media New York

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Song, B., Castillo-Chavez, C., Aparicio, J.P. (2002). Global Dynamics of Tuberculosis Models with Density Dependent Demography. In: Castillo-Chavez, C., Blower, S., van den Driessche, P., Kirschner, D., Yakubu, AA. (eds) Mathematical Approaches for Emerging and Reemerging Infectious Diseases: Models, Methods, and Theory. The IMA Volumes in Mathematics and its Applications, vol 126. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0065-6_16

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  • DOI: https://doi.org/10.1007/978-1-4613-0065-6_16

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-6550-4

  • Online ISBN: 978-1-4613-0065-6

  • eBook Packages: Springer Book Archive

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