Skip to main content
SpringerLink
Log in

Comparison Between Protein-Protein Interaction Networks CD4\(^+\)T and CD8\(^+\)T and a Numerical Approach for Fractional HIV Infection of CD4\(^{+}\)T Cells

  • Conference paper
  • First Online:
Computational Science and Its Applications – ICCSA 2021 (ICCSA 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12949))

Included in the following conference series:

Abstract

This research examines and compares the construction of protein-protein interaction (PPI) networks of CD4\(^{+}\) and CD8\(^{+}\)T cells and investigates why studying these cells is critical after HIV infection. This study also examines a mathematical model of fractional HIV infection of CD4\(^{+}\)T cells and proposes a new numerical procedure for this model that focuses on a recent kind of orthogonal polynomials called discrete Chebyshev polynomials. The proposed scheme consists of reducing the problem by extending the approximated solutions and by using unknown coefficients to nonlinear algebraic equations. For calculating unknown coefficients, fractional operational matrices for orthogonal polynomials are obtained. Finally, there is an example to show the effectiveness of the recommended method. All calculations were performed using the Maple 17 computer code.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ali, N., Ahmad, S., Aziz, S., Zaman, G.: The adomian decomposition method for solving HIV infection model of latently infected cells. Matrix Sci. Math. 3, 5–8 (2019)

    Article  Google Scholar 

  2. Anastasio, T.J.: The fractional-order dynamics of bainstem vestibulo-oculomotor neurons. Biol. Cybern. 72, 69–79 (1994)

    Article  Google Scholar 

  3. Angulo, J., Cuesta, T., Menezes, E., Pedroso, C., Brites, C.: A systematic review on the influence of HLA-B polymorphisms on HIV-1 mother to child transmission. Braz. J. Infec. Dis. 23, 53–9 (2019)

    Article  Google Scholar 

  4. Asquith, B., Bangham, C.R.M.: The dynamics of T-cell fratricide: application of a robust approach to mathematical modelling in immunology. J. Theoret. Biol. 222, 53–69 (2003)

    Article  MathSciNet  Google Scholar 

  5. Attaullah, Sohaib, M.: Mathematical modeling and numerical simulation of HIV infection model. Results Appl. Math. 7, 100–118 (2020)

    Google Scholar 

  6. Conte, D., Farsimadan, E., Moradi, L., Palmieri, F., Paternoster, B.: Time-Delay Fractional Optimal Control Problems: A Survey Based on Methodology. In: Proceedings of the 8th International Conference on Fracture, Fatigue and Wear, Belgium, pp. 325–337 (2021)

    Google Scholar 

  7. Djordjević, V.D., Jarić, J., Fabry, B., Fredberg, J.J., Stamenović, D.: Fractional derivatives embody essential features of cell rheological behavior. Ann. Biomed. Eng. 31, 692–699 (2003)

    Article  Google Scholar 

  8. Duro, R., Pereira, N., Figueiredo, C., Pineiro, C., Caldas, C., Serrao, R.: Routine CD4 monitoring in HIV patients with viral suppression: is it really necessary? A Portuguese cohort. J. Microbiol. Immunol. Infect. 51, 593–7 (2018)

    Article  Google Scholar 

  9. Gogin, N., Hirvensalo, M.: On the generating function of discrete Chebyshev polynomials. J. Math. Sci. 2, 224 (2017)

    MathSciNet  MATH  Google Scholar 

  10. Kirschner, D.E.: Using mathematics to understand HIV immune dynamics. Not. Am. Math. Soc. 43, 191–202 (1996)

    MathSciNet  MATH  Google Scholar 

  11. Hallbergc, D., Kimariob, T., Mtuyab, C., Msuyab, M., Bjorlingc, G.: Factors affecting HIV disclosure among partners in morongo. tanzania. Int J Afr Nurs Sci 10, 49–54 (2019)

    Google Scholar 

  12. Jesus, I.S., Machado, J.A.T., Cunha, J.B.: Fractional electrical impedances in botanical elements. J. Vib. Control 14, 1389–1402 (2008)

    Article  Google Scholar 

  13. Li, Q., Xiao, Y.: Global dynamics of a virus immune system with virus guided therapy and saturation growth of virus. Math. Probl. Eng. 1–18 (2018)

    Google Scholar 

  14. Merdan, M., Gökdǒgan, A., Yildirim, A.: On the numerical solution of the model for HIV infection of CD4+T-cells. Comput. Math. Appl. 62, 118–123 (2011)

    Article  MathSciNet  Google Scholar 

  15. Moradi, L., Mohammadi, F.: A comparative approach for time-delay fractional optimal control problems: discrete versus continuous Chebyshev polynomials. Asian J. Control 21(6), 1–13 (2019)

    MathSciNet  Google Scholar 

  16. Nelson, P.W., Perelson, A.S.: Mathematical analysis of delay differential equation models of HIV-1 infection. Math. Biosci. 179, 73–94 (2002)

    Article  MathSciNet  Google Scholar 

  17. Nigmatullin, R.R., Nelson, S.O.: Recognition of the fractional kinetics in complex systems: dielectric properties of fresh fruits and vegetables form 0.01 to 1.8 GHz. Signal Process. 86, 2744–2759 (2006)

    Google Scholar 

  18. Nikiforov, A.F., Suslov, S.K., Uvarov, V.B.: Classical Orthogonal Polynomials of a Discrete Variable. Springer Series in Computational Physics, Springer, Heidelberg (1991). https://doi.org/10.1007/978-3-642-74748-9_2

    Book  MATH  Google Scholar 

  19. Nowak, M., May, R.: Mathematical biology of HIV infections: antigenic variation and diversity threshold. Math. Biosci. 106, 1–21 (1991)

    Article  Google Scholar 

  20. Oldham, K.B., Spanier, J.: The Fractional Calculus. Academic Press, New York (1974)

    MATH  Google Scholar 

  21. Omondi, E., Mbogo, W., Luboobi, L.: A mathematical modeling study of HIV infection in two heterosexual age groups in Kenya. Infec. Dis. Modell. 4, 83–98 (2019)

    Article  Google Scholar 

  22. Ongun, M.: The Laplace adomian decomposition method for solving a model for HIV infection of CD4+T-cells. Math. Comput. Modell. 63, 597–603 (2011)

    Article  MathSciNet  Google Scholar 

  23. Perelson, A.S., Kirschner, D.E., Boer, R.D.: Dynamics of HIV infection CD4\(^+\)T cells. Math. Biosci. 114, 81–125 (1993)

    Article  Google Scholar 

  24. Perelson, A.S., Nelson, P.W.: Mathematical analysis of HIV-I dynamics in vivo. SIAM Rev. 41(1), 3–44 (1999)

    Article  MathSciNet  Google Scholar 

  25. Petrovic, L.M., Spasic, D.T., Atanackovic, T.M.: On a mathematical model of a human root dentin. Dent. Mater. 21, 125–128 (2005)

    Article  Google Scholar 

  26. Ransome, Y., Thurber, K., Swen, M., Crawford, N., Germane, D., Dean, L.: Social capital and HIV/AIDS in the United States: knowledge, gaps, and future directions. SSM Popul. Health 5, 73–85 (2018)

    Article  Google Scholar 

  27. Riordan, J.: An Introduction to Combinatorial Analysis. Wiley, New York (1980)

    Book  Google Scholar 

  28. Samko, S.G., Kilbas, A.A., Marichev, O.I.: Fractional Integrals and Derivatives: Theory and Applications. Gordon and Breach, Langhorne (1993)

    MATH  Google Scholar 

  29. Theys, K., Libin, P., Pena, A.C.P., Nowe, A., Vandamme, A.M., Abecasis, A.B.: The impact of HIV-1 within host evolution on transmission dynamics. Curr. Opin. Virol. 28, 92–101 (2018)

    Article  Google Scholar 

  30. Wang, L., Li, M.Y.: Mathematical analysis of the global dynamics of a model for HIV infection of CD4+T cells. Math. Biosci. 200, 44–57 (2006)

    Article  MathSciNet  Google Scholar 

  31. Yddotuzbasi, S., Karacayir, M.: An exponential Galerkin method for solution of HIV infected model of CD4+t-cells. Comput. Biol. Chem. 67, 205–12 (2017)

    Article  MathSciNet  Google Scholar 

  32. Yüzbas, S.: A numerical approach to solve the model for HIV infection of CD4+T-cells. Appl. Math. Model. 36, 5876–5890 (2012)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. University of Salerno, 84084, Fisciano, Italy

    Eslam Farsimadan, Leila Moradi, Dajana Conte, Beatrice Paternoster & Francesco Palmieri

Authors
  1. Eslam Farsimadan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Leila Moradi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Dajana Conte
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Beatrice Paternoster
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Francesco Palmieri
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eslam Farsimadan .

Editor information

Editors and Affiliations

  1. University of Perugia, Perugia, Italy

    Osvaldo Gervasi

  2. University of Basilicata, Potenza, Potenza, Italy

    Beniamino Murgante

  3. Covenant University, Ota, Nigeria

    Sanjay Misra

  4. University of Cagliari, Cagliari, Italy

    Chiara Garau

  5. University of Cagliari, Cagliari, Italy

    Ivan Blečić

  6. Monash University, Clayton, VIC, Australia

    David Taniar

  7. Kyushu Sangyo University, Fukuoka, Japan

    Bernady O. Apduhan

  8. University of Minho, Braga, Portugal

    Ana Maria A. C. Rocha

  9. Polytechnic University of Bari, Bari, Italy

    Eufemia Tarantino

  10. Polytechnic University of Bari, Bari, Italy

    Carmelo Maria Torre

Rights and permissions

Reprints and permissions

Copyright information

© 2021 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Farsimadan, E., Moradi, L., Conte, D., Paternoster, B., Palmieri, F. (2021). Comparison Between Protein-Protein Interaction Networks CD4\(^+\)T and CD8\(^+\)T and a Numerical Approach for Fractional HIV Infection of CD4\(^{+}\)T Cells. In: Gervasi, O., et al. Computational Science and Its Applications – ICCSA 2021. ICCSA 2021. Lecture Notes in Computer Science(), vol 12949. Springer, Cham. https://doi.org/10.1007/978-3-030-86653-2_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-86653-2_6

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-86652-5

  • Online ISBN: 978-3-030-86653-2

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation