Abstract
In this paper, a numerical solution of population dynamics of human immunodeficiency type 1 virus (HIV-1) model is considered by using Legendre spectral-collocation method. The computed results given here are compared with previous works to show efficiency of the proposed method.
Similar content being viewed by others
References
CDC.: Pneumocystis pneumonia—Los Angeles. MMWR. 30:250–2 (1981)
WHO: Global health sector response to HIV, 2000–2015: focus on innovations in Africa. http://www.who.int/hiv/pub/progressreports/2015-progress-report/en/. Accessed 1 Dec 2015
Perelson, A.S.: Modelling the interaction of the immune system with HIV. In: Castillo-Chavez, C. (ed.) Mathematical and Statistical Approaches to AIDS Epidemiology, p. 350. Springer, Berlin (1989)
Perelson, A.S., Kirschner, D.E., Boer, R.D.: Dynamics of HIV infection CD4+ T cells. Math. Biosci. 114, 81–125 (1993)
Culshaw, R.V., Ruan, S.: A delay-differential equation model of HIV infection of CD4+ T-cells. Math. Biosci. 165, 27–39 (2000)
Merdan, M.: Homotopy perturbation method for solving a model for HIV infection of CD4+ T-cells. Istanbul Ticaret Üniversitesi Fen Bilimleri Dergisi Yil: 6 Sayi: 12 Güz 2007/2 s. pp. 39–52
Ongun, M.Y.: The Laplace Adomian decomposition method for solving a model for HIV infection of CD4+ T cells. Math. Comput. Model. 53, 597–603 (2011)
Merdan, M., Gökdoğan, A., Yildirim, A.: On the numerical solution of the model for HIV infection of CD4+ T cells. Comput. Math. Appl. 62(1), 118–123 (2011)
Ghoreishi, M., Ismail, AIBMd, Alomari, A.K.: Application of the homotopy analysis method for solving a model for HIV infection of CD4+ T-cells. Math. Comput. Model. 54(11–12), 3007–3015 (2011)
Yüzbaşı, Ş.: A numerical approach to solve the model for HIV infection of CD4+ T cells. Appl. Math. Model. 36(12), 5876–5890 (2012)
Srivastava, V.K., Awasthi, M.K., Kumar, S.: Numerical approximation for HIV infection of CD4+ T cells mathematical model. Ain Shams Eng. J. 5, 625–629 (2014)
Tang, T.: On spectral methods for volterra integral equations and the convergence analysis. J. Comput. Math. 26(6), 825–837 (2008)
Szegö, G.: Orthogonal Polynomials, 5th edn. AMS, Providence (1975)
Costa, B., Don, W.S.: On the computation of high order pseudospectral derivatives. Appl. Numer. Math. 33, 151–159 (2000)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
El-Baghdady, G.I., Abbas, M.M., El-Azab, M.S. et al. The Spectral Collocation Method for Solving (HIV-1) via Legendre Polynomials. Int. J. Appl. Comput. Math 3, 3333–3340 (2017). https://doi.org/10.1007/s40819-016-0299-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40819-016-0299-8