The Laplace Adomian decomposition method for solving a model for HIV infection of \(CD4^{+}T\) cells. (English) Zbl 1217.65164

Summary: The Laplace Adomian Decomposition Method is implemented to give an approximate solution of nonlinear ordinary differential equation systems, such as a model for HIV infection of \(CD4^{+}T\) cells. The technique is described and illustrated with numerical example. Some plots are presented to show the reliability and simplicity of the methods.


65L99 Numerical methods for ordinary differential equations
92D30 Epidemiology
Full Text: DOI


[1] Perelson, A. S.; Kirschner, D. E.; Boer, R. D., Dynamics of HIV infection \(C D 4^+ T\) cells, Math. Biosci., 114, 81-125 (1993) · Zbl 0796.92016
[2] Perelson, A. S.; Nelson, P. W., Mathematical analysis of HIV—I Dynamics in Vivo, SIAM Rev., 41, 1, 3-44 (1999) · Zbl 1078.92502
[3] Wang, L.; Li, M. Y., Mathematical analysis of the global dynamics of a model for HIV infection of \(C D 4^+ T\) cells, Math. Biosci., 200, 44-57 (2006) · Zbl 1086.92035
[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) · Zbl 1464.92061
[5] Nowak, M.; May, R., Mathematical biology of HIV infections: antigenic variation and diversity threshold, Math. Biosci., 106, 1-21 (1991) · Zbl 0738.92008
[6] Adomian, G., A review of the decomposition method and some recent results for nonlinear equations, Comput. Math. Appl., 21, 5, 101-127 (1991) · Zbl 0732.35003
[7] Adomian, G., Solving Frontier Problems of Physics: The Decomposition Method (1994), Kluwer: Kluwer Dordrecht · Zbl 0802.65122
[8] Bahuguna, D.; Ujlayan, A.; Pandeya, D. N., A comparative study of numerical methods for solving an integro-differential equation, Comput. Math. Appl., 57, 9, 1485-1493 (2009) · Zbl 1186.65158
[9] Momani, S.; Erturk, V. S., Solutions of non-linear oscillators by the modified differential transform method, Comput. Math. Appl., 55, 833-842 (2008) · Zbl 1142.65058
[10] Khuri, S. A., A new approach to Bratu’s problem, Appl. Math. Comput., 147, 131-136 (2004) · Zbl 1032.65084
[11] Kiymaz, O., An algorithm for solving initial value problems using Laplace Adomian Decomposition Method, Appl. Math. Sci., 3, 30, 1453-1459 (2009) · Zbl 1189.65138
[12] Babolian, E.; Biazar, J.; Vahidi, A. R., A new computational method for Laplace transforms by decomposition method, Appl. Math. Comput., 150, 841-846 (2004) · Zbl 1039.65094
[13] M. Merdan, Homotopy perturbation Method for solving a model for infection of \(C D 4^+ T\); M. Merdan, Homotopy perturbation Method for solving a model for infection of \(C D 4^+ T\)
[14] Yusufoglu (Agadjanov), E., Numerical solution of Duffing equation by the Laplace decomposition algorithm, Appl. Math. Comput., 177, 2, 572-580 (2006) · Zbl 1096.65067
[15] Abbasbandy, S., Application of He’s homotopy perturbation method for Laplace transform, Chaos Solitons Fractals, 30, 1206-1212 (2006) · Zbl 1142.65417
[16] Khuri, S. A., A Laplace decomposition algorithm applied to a class of nonlinear differential equations, J. Appl. Math., 1, 4, 141-155 (2001) · Zbl 0996.65068
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