Skip to main content

2019 | OriginalPaper | Buchkapitel

7. Models for Tuberculosis

verfasst von : Fred Brauer, Carlos Castillo-Chavez, Zhilan Feng

Erschienen in: Mathematical Models in Epidemiology

Verlag: Springer New York

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

In this chapter we describe several models for tuberculosis (TB). The disease is endemic in many areas of the world. The models in this chapter will be extensions of the standard SIR or SEIR type of endemic models presented in Chap. 3. Depending on the typical characteristics of a specific disease, various modifications of the standard models will be considered.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literatur
1.
Zurück zum Zitat Aparicio, J. P., and C. Castillo-Chavez (2009) Mathematical modelling of tuberculosis epidemics, Math. Biosc. Eng. 6: 209–237.MathSciNetCrossRef Aparicio, J. P., and C. Castillo-Chavez (2009) Mathematical modelling of tuberculosis epidemics, Math. Biosc. Eng. 6: 209–237.MathSciNetCrossRef
2.
Zurück zum Zitat Blower, S. M., and T. Chou (2004) Modeling the emergence of the ‘hot zones’: tuberculosis and the amplification dynamics of drug resistance, Nature Medicine 10: 1111–1116.CrossRef Blower, S. M., and T. Chou (2004) Modeling the emergence of the ‘hot zones’: tuberculosis and the amplification dynamics of drug resistance, Nature Medicine 10: 1111–1116.CrossRef
3.
Zurück zum Zitat Blower, S. M., P.M. Small, and P.C. Hopewell (1996) Control strategies for tuberculosis epidemics: new models for old problems, Science 273: 497–500.CrossRef Blower, S. M., P.M. Small, and P.C. Hopewell (1996) Control strategies for tuberculosis epidemics: new models for old problems, Science 273: 497–500.CrossRef
4.
Zurück zum Zitat Castillo-Chavez, C., and Z. Feng (1997) To treat or not to treat: the case of tuberculosis. J. Math. Biol. 35: 629–656.MathSciNetCrossRef Castillo-Chavez, C., and Z. Feng (1997) To treat or not to treat: the case of tuberculosis. J. Math. Biol. 35: 629–656.MathSciNetCrossRef
5.
Zurück zum Zitat Castillo-Chavez, C., and Z. Feng (1998) Global stability of an age-structure model for TB and its applications to optimal vaccination strategies, Math.Biosc. 151: 135–154.CrossRef Castillo-Chavez, C., and Z. Feng (1998) Global stability of an age-structure model for TB and its applications to optimal vaccination strategies, Math.Biosc. 151: 135–154.CrossRef
7.
Zurück zum Zitat Cohen, T., and M. Murray (2004) Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness Nature Medicine 10: 1117–1121.CrossRef Cohen, T., and M. Murray (2004) Modeling epidemics of multidrug-resistant M. tuberculosis of heterogeneous fitness Nature Medicine 10: 1117–1121.CrossRef
8.
Zurück zum Zitat Dye, C., and B.G. Williams (2000) Criteria for the control of drug-resistant tuberculosis, Proc. Nat. Acad. Sci. 97: 8180–8185.CrossRef Dye, C., and B.G. Williams (2000) Criteria for the control of drug-resistant tuberculosis, Proc. Nat. Acad. Sci. 97: 8180–8185.CrossRef
9.
Zurück zum Zitat Feng, Z., C. Castillo-Chavez, and A.F. Capurro (2000) A model for tuberculosis with exogenous reinfection, Theor. Pop. Biol. 57: 235–247.CrossRef Feng, Z., C. Castillo-Chavez, and A.F. Capurro (2000) A model for tuberculosis with exogenous reinfection, Theor. Pop. Biol. 57: 235–247.CrossRef
10.
Zurück zum Zitat Feng, Z., W. Huang, and C. Castillo-Chavez (2001) On the role of variable latent periods in mathematical models for tuberculosis, J. Dyn. Diff. Eq. 13: 435–452.MathSciNetCrossRef Feng, Z., W. Huang, and C. Castillo-Chavez (2001) On the role of variable latent periods in mathematical models for tuberculosis, J. Dyn. Diff. Eq. 13: 435–452.MathSciNetCrossRef
11.
Zurück zum Zitat Feng, Z., M. Iannelli, and F.A. Milner (2002) A two-strain tuberculosis model with age of infection, SIAM J. Appl. Math. 62: 1634–1656.MathSciNetMATH Feng, Z., M. Iannelli, and F.A. Milner (2002) A two-strain tuberculosis model with age of infection, SIAM J. Appl. Math. 62: 1634–1656.MathSciNetMATH
12.
Zurück zum Zitat Fister, K. R., S. Lenhart, and J.S. McNally (1998) Optimizing chemotherapy in an HIV model, Electronic J. Diff. Eq. 32: 1–12.MATH Fister, K. R., S. Lenhart, and J.S. McNally (1998) Optimizing chemotherapy in an HIV model, Electronic J. Diff. Eq. 32: 1–12.MATH
13.
Zurück zum Zitat Fleming, W., and R. Rishel (1975) Deterministic and Stochastic Optimal Control, Springer. Fleming, W., and R. Rishel (1975) Deterministic and Stochastic Optimal Control, Springer.
14.
Zurück zum Zitat Jung, E., S. Lenhart, and Z. Feng (2002) Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems Series B 2: 473–482.MathSciNetCrossRef Jung, E., S. Lenhart, and Z. Feng (2002) Optimal control of treatments in a two-strain tuberculosis model, Discrete and Continuous Dynamical Systems Series B 2: 473–482.MathSciNetCrossRef
15.
Zurück zum Zitat Kirschner, D., S. Lenhart, and S. Serbin (1997) Optimal control of the chemotherapy of HIV J. Math. Biol. 35: 775–792.MathSciNetCrossRef Kirschner, D., S. Lenhart, and S. Serbin (1997) Optimal control of the chemotherapy of HIV J. Math. Biol. 35: 775–792.MathSciNetCrossRef
16.
Zurück zum Zitat Levin, S. and D. Pimentel (1981) Selection of intermediate rates of increase in parasite-host systems, Am. Naturalist 117: 308–315.MathSciNetCrossRef Levin, S. and D. Pimentel (1981) Selection of intermediate rates of increase in parasite-host systems, Am. Naturalist 117: 308–315.MathSciNetCrossRef
17.
Zurück zum Zitat Murphy, B. M., B.H. Singer, and D. Kirschner (2003) On treatment of tuberculosis in heterogeneous populations, J. Theor. Biol. 223: 391–404.CrossRef Murphy, B. M., B.H. Singer, and D. Kirschner (2003) On treatment of tuberculosis in heterogeneous populations, J. Theor. Biol. 223: 391–404.CrossRef
18.
Zurück zum Zitat Nowak, M.A., and R.M. May (1994) Superinfection and the evolution of parasite virulence, Proc. Roy. Soc. London, Series B: Biological Sciences 255: 81–89. Nowak, M.A., and R.M. May (1994) Superinfection and the evolution of parasite virulence, Proc. Roy. Soc. London, Series B: Biological Sciences 255: 81–89.
19.
Zurück zum Zitat Pontryagin, L.S. (1987) Mathematical Theory of Optimal Processes, CRC Press. Pontryagin, L.S. (1987) Mathematical Theory of Optimal Processes, CRC Press.
20.
Zurück zum Zitat Porco, T.C., P.M. Small, and S.M. Blower (2001) Amplification dynamics: predicting the effect of HIV on tuberculosis outbreaks, J. Acquired Immune Deficiency Syndromes 28: 437–444.CrossRef Porco, T.C., P.M. Small, and S.M. Blower (2001) Amplification dynamics: predicting the effect of HIV on tuberculosis outbreaks, J. Acquired Immune Deficiency Syndromes 28: 437–444.CrossRef
21.
Zurück zum Zitat Rodrigues, P., M.G.M. Gomes, and C. Rebelo (2007) Drug resistance in tuberculosis, a reinfection model, Theor. Pop. Biol. 71: 196–212.CrossRef Rodrigues, P., M.G.M. Gomes, and C. Rebelo (2007) Drug resistance in tuberculosis, a reinfection model, Theor. Pop. Biol. 71: 196–212.CrossRef
22.
Zurück zum Zitat Roeger, L-I.W., Z. Feng, and C. Castillo-Chavez (2009) Modeling TB and HIV co-infections Math. Biosc. Eng. 6: 815–837.CrossRef Roeger, L-I.W., Z. Feng, and C. Castillo-Chavez (2009) Modeling TB and HIV co-infections Math. Biosc. Eng. 6: 815–837.CrossRef
23.
Zurück zum Zitat Singer, B.H., and D.E. Kirschner (2004) Influence of backward bifurcation on interpretation of \({\mathcal R}_0\) in a model of epidemic tuberculosis with reinfection, Math. Biosc. Eng. 1: 81–93.CrossRef Singer, B.H., and D.E. Kirschner (2004) Influence of backward bifurcation on interpretation of \({\mathcal R}_0\) in a model of epidemic tuberculosis with reinfection, Math. Biosc. Eng. 1: 81–93.CrossRef
24.
Zurück zum Zitat Styblo, K. (1991) Selected papers. vol. 24, Epidemiology of tuberculosis, Hague, The Netherlands: Royal Netherlands Tuberculosis Association. Styblo, K. (1991) Selected papers. vol. 24, Epidemiology of tuberculosis, Hague, The Netherlands: Royal Netherlands Tuberculosis Association.
Metadaten
Titel
Models for Tuberculosis
verfasst von
Fred Brauer
Carlos Castillo-Chavez
Zhilan Feng
Copyright-Jahr
2019
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4939-9828-9_7