Skip to main content

2018 | OriginalPaper | Buchkapitel

The Burden of the Coinfection of HIV and TB in the Presence of Multi-drug Resistant Strains

verfasst von : Ana Carvalho, Carla M. A. Pinto

Erschienen in: Dynamical Systems in Theoretical Perspective

Verlag: Springer International Publishing

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

search-config
loading …

Abstract

We introduce a fractional-order model for the coinfection of the immunodeficiency virus and tuberculosis, in the presence of drug resistant tuberculosis strains and treatment for both diseases. We compute the reproduction number of the model. Numerical simulations show the different dynamics of the model for variation of relevant parameters. Moreover, the order of the fractional derivative plays an important role in the severity of the epidemics.

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 Madariaga, M.G., Lalloo, U.G., Swindells, S.: Extensively drug-resistant tuberculosis. Am. J. Med. 121(10), 835–844 (2008)CrossRef Madariaga, M.G., Lalloo, U.G., Swindells, S.: Extensively drug-resistant tuberculosis. Am. J. Med. 121(10), 835–844 (2008)CrossRef
2.
Zurück zum Zitat The World Health Organization (WHO): Global Tuberculosis Report (2016) The World Health Organization (WHO): Global Tuberculosis Report (2016)
3.
Zurück zum Zitat Gandhi, N.R., Nunn, P., Dheda, K., Schaaf, H.S., Zignol, M., Van Soolingen, D., Jensen, P., Bayona, J.: Multidrug-resistant and extensively drug-resistant tuberculosis: a threat to global control of tuberculosis. Lancet 375, 1830–1843 (2010)CrossRef Gandhi, N.R., Nunn, P., Dheda, K., Schaaf, H.S., Zignol, M., Van Soolingen, D., Jensen, P., Bayona, J.: Multidrug-resistant and extensively drug-resistant tuberculosis: a threat to global control of tuberculosis. Lancet 375, 1830–1843 (2010)CrossRef
4.
Zurück zum Zitat Agusto, F.B., Adekunle, A.I.: Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model. BioSystems 119, 20–44 (2014)CrossRef Agusto, F.B., Adekunle, A.I.: Optimal control of a two-strain tuberculosis-HIV/AIDS co-infection model. BioSystems 119, 20–44 (2014)CrossRef
5.
Zurück zum Zitat Bacaër, N.N., Ouifki, R., Pretorius, C., Wood, R., Williams, B.: Modeling the joint epidemics of TB and HIV in a South African township. J. Math. Biol. 57(4), 557–593 (2008)MathSciNetCrossRef Bacaër, N.N., Ouifki, R., Pretorius, C., Wood, R., Williams, B.: Modeling the joint epidemics of TB and HIV in a South African township. J. Math. Biol. 57(4), 557–593 (2008)MathSciNetCrossRef
6.
Zurück zum Zitat Bhunu, C.P., Garira, W., Mukandavire, Z.: Modeling HIV/AIDS and tuberculosis coinfection. Bull. Math. Biol. 71, 1745–1780 (2009)MathSciNetCrossRef Bhunu, C.P., Garira, W., Mukandavire, Z.: Modeling HIV/AIDS and tuberculosis coinfection. Bull. Math. Biol. 71, 1745–1780 (2009)MathSciNetCrossRef
7.
Zurück zum Zitat Castillo-Chavez, C., Feng, Z.: To treat or not to treat: the case of tuberculosis. J. Math. Biol. 35, 629–656 (1997)MathSciNetCrossRef Castillo-Chavez, C., Feng, Z.: To treat or not to treat: the case of tuberculosis. J. Math. Biol. 35, 629–656 (1997)MathSciNetCrossRef
8.
Zurück zum Zitat Denysiuk, R., Silva, C.J., Torres, D.F.M.: Multiobjective approach to optimal control for a tuberculosis model. Optim. Methods Softw. 30(5), (2015) Denysiuk, R., Silva, C.J., Torres, D.F.M.: Multiobjective approach to optimal control for a tuberculosis model. Optim. Methods Softw. 30(5), (2015)
9.
Zurück zum Zitat Sergeev, R., Colijn, C., Murray, M., Cohen, T.: Modeling the dynamic relationship between HIV and the risk of drug-resistant tuberculosis. Sci. Transl. Med. 4(135), 135–167 (2012)CrossRef Sergeev, R., Colijn, C., Murray, M., Cohen, T.: Modeling the dynamic relationship between HIV and the risk of drug-resistant tuberculosis. Sci. Transl. Med. 4(135), 135–167 (2012)CrossRef
10.
Zurück zum Zitat Silva, C.J., Torres, D.F.M.: A TB-HIV/AIDS coinfection model and optimal control treatment. Discrete Continuous Dyn. Syst. - A 35(9), 4639–4663 (2015)MathSciNetCrossRef Silva, C.J., Torres, D.F.M.: A TB-HIV/AIDS coinfection model and optimal control treatment. Discrete Continuous Dyn. Syst. - A 35(9), 4639–4663 (2015)MathSciNetCrossRef
11.
Zurück zum Zitat Ezz-Eldien, S.S., Doha, E.H., Bhrawy, A.H., El-Kalaawy, A.A., Machado, J.T.A.: A new operational approach for solving fractional variational problems depending on indefinite integrals. Commun. Nonlinear Sci. Numer. Simul. 57, 246–263 (2017)MathSciNetCrossRef Ezz-Eldien, S.S., Doha, E.H., Bhrawy, A.H., El-Kalaawy, A.A., Machado, J.T.A.: A new operational approach for solving fractional variational problems depending on indefinite integrals. Commun. Nonlinear Sci. Numer. Simul. 57, 246–263 (2017)MathSciNetCrossRef
12.
Zurück zum Zitat Nigmatullin, R.R., Zhang, W., Gubaidullin, I.: Accurate relationships between fractals and fractional integrals: new approaches and evaluations. Fractional Calc. Appl. Anal. 20(5), 1263–1280 (2017)MathSciNetMATH Nigmatullin, R.R., Zhang, W., Gubaidullin, I.: Accurate relationships between fractals and fractional integrals: new approaches and evaluations. Fractional Calc. Appl. Anal. 20(5), 1263–1280 (2017)MathSciNetMATH
13.
Zurück zum Zitat Carvalho, A.R.M., Pinto, C.M.A., Baleanu, D.: HIV/HCV coinfection model: a fractional-order perspective for the effect of the HIV viral load. Adv. Differ. Equ. 2018(1), 1–22 (2018)MathSciNetCrossRef Carvalho, A.R.M., Pinto, C.M.A., Baleanu, D.: HIV/HCV coinfection model: a fractional-order perspective for the effect of the HIV viral load. Adv. Differ. Equ. 2018(1), 1–22 (2018)MathSciNetCrossRef
14.
Zurück zum Zitat Copot, D., De Keyser, R., Derom, E., Ortigueira, M., Ionescu, C.M.: Reducing bias in fractional order impedance estimation for lung function evaluation. Biomed. Sig. Process. Control 39, 74–80 (2018)CrossRef Copot, D., De Keyser, R., Derom, E., Ortigueira, M., Ionescu, C.M.: Reducing bias in fractional order impedance estimation for lung function evaluation. Biomed. Sig. Process. Control 39, 74–80 (2018)CrossRef
15.
Zurück zum Zitat Oldham, K., Spanier, J.: The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order. Academic Press, New York, NY (1974)MATH Oldham, K., Spanier, J.: The Fractional Calculus: Theory and Application of Differentiation and Integration to Arbitrary Order. Academic Press, New York, NY (1974)MATH
16.
Zurück zum Zitat Samko, S., Kilbas, A., Marichev, O.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, London (1993)MATH Samko, S., Kilbas, A., Marichev, O.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach Science Publishers, London (1993)MATH
17.
Zurück zum Zitat Ventura, A., Tejado, I., Valério, D., Martins, J.: Fractional direct and inverse models of the dynamics of a human arm. J. Vibr. Control 22(9), 2240–2254 (2016)MathSciNetCrossRef Ventura, A., Tejado, I., Valério, D., Martins, J.: Fractional direct and inverse models of the dynamics of a human arm. J. Vibr. Control 22(9), 2240–2254 (2016)MathSciNetCrossRef
18.
Zurück zum Zitat Wu, G.C., Baleanu, D., Huang, L.L.: Novel Mittag-Leffler stability of linear fractional delay difference equations with impulse. Appl. Math. Lett. 82, 71–78 (2018)MathSciNetCrossRef Wu, G.C., Baleanu, D., Huang, L.L.: Novel Mittag-Leffler stability of linear fractional delay difference equations with impulse. Appl. Math. Lett. 82, 71–78 (2018)MathSciNetCrossRef
19.
Zurück zum Zitat Pinto, C.M.A., Carvalho, A.R.M.: New findings on the dynamics of HIV and TB coinfection models. Appl. Math. Comput. 242, 36–46 (2014)MathSciNetMATH Pinto, C.M.A., Carvalho, A.R.M.: New findings on the dynamics of HIV and TB coinfection models. Appl. Math. Comput. 242, 36–46 (2014)MathSciNetMATH
20.
Zurück zum Zitat Sardar, T., Rana, S., Bhattacharya, S., Al-Khaled, K., Chattopadhyay, J.: A generic model for a single strain mosquito-transmitted disease memory on the host and the vector. Math. Biosci. 263, 18–36 (2015)MathSciNetCrossRef Sardar, T., Rana, S., Bhattacharya, S., Al-Khaled, K., Chattopadhyay, J.: A generic model for a single strain mosquito-transmitted disease memory on the host and the vector. Math. Biosci. 263, 18–36 (2015)MathSciNetCrossRef
21.
Zurück zum Zitat Driessche, P., Watmough, P.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)MathSciNetCrossRef Driessche, P., Watmough, P.: Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission. Math. Biosci. 180, 29–48 (2002)MathSciNetCrossRef
Metadaten
Titel
The Burden of the Coinfection of HIV and TB in the Presence of Multi-drug Resistant Strains
verfasst von
Ana Carvalho
Carla M. A. Pinto
Copyright-Jahr
2018
DOI
https://doi.org/10.1007/978-3-319-96598-7_8

    Marktübersichten

    Die im Laufe eines Jahres in der „adhäsion“ veröffentlichten Marktübersichten helfen Anwendern verschiedenster Branchen, sich einen gezielten Überblick über Lieferantenangebote zu verschaffen.