Received: 10-09-2016
Revised: 18-12-2016
Accepted: 25-02-2017
Published in Issue 27-07-2025
Copyright (c) 2025 Hossein Pourbashash, Hossein Kheiri (Author)

This work is licensed under a Creative Commons Attribution 4.0 International License.
Abstract
The sinc method is known as an ecient numerical method for solving ordinary or par-tial dierential equations but the system of dierential equations has not been solved by this method which is the focus of this paper. We have shown that the proposed version of sinc is able to solve sti system while Runge-kutta method can not able to solve. Moreover, Due to the great attention to mathematical models in disease, the detailed stability analyses and numerical experiments are given on the standard within-host virus infections model.
Keywords
- Stability,
- Sinc method,
- dynamical systems,
- the within-host virus model
References
- [1] K. Al-Khaled, Numerical approximations for population growth models, Appl. Math. Comput, 160
- (2005) 865{873.
- [2] R. Bock, L. Jackson, A. de Vos, W. Jorgensen, Babesiosis of cattle. Parasitology, 129 (2004) 247{269.H. Pourbashash & H. Kheiri/ IJM2C, 7 - 1 (2017) 27-37. 37
- [3] P. De Leenheer, H. L. Smith, Virus dynamics: A global analysis, SIAM J. Appl. Math, 63 (4) (2003)
- 1313{1327.
- [4] A. Estrada-Pena, Forecasting habitat suitability for ticks and prevention of tick-borne diseases, Vet.
- Parasitol, 98 (2001) 111{132.
- [5] D. Ganem and A. M. Prince, Hepatitis B virus infectionnatural history and clinical consequences,
- New Engl. J. Med, 350 (2004) 1118{1129.
- [6] M. Y. Li and J. S. Muldowney, A geometric approach to the global-stability problems, SIAM J.
- Math. Anal, 27 (4) (1996) 1070{1083.
- [7] I. Marcelino, AM. de Almeida, M. Ventosa, L. Pruneau, DF. Meyer, D. Martinez ,T Lefranois , N.
- Vachiry and AV. Coelho, Tick-borne diseases in cattle: applications of proteomics to develop new
- generation vaccines, J Proteomics, 75 (14) (2012) 4232{4250.
- [8] R. H. Martin, Logarithmic norms and projections applied to linear differential systems, J. math.
- Anal. Appl, 45 (1974) 432{454.
- [9] J. Mosqueda, A. Olvera-Ramrez, G. Aguilar-Tipacam and G. J. Cant, Current Advances in Detection
- and Treatment of Babesiosis, Curr Med Chem, 19 (10) (2012) 1504{1518.
- [10] S. Narasimhan, K. Chen and F. Stenger, A Harmonic sinc solution of the Laplace equation for
- problems with singularities and semi-infinite domains, Numer. Heat Transfer B, 33 (4) (1998) 33{
- 450.
- [11] M. A. Nowak and R. M. May, Virus dynamics, New york: oxford University press, (2000).
- [12] A. S. Perelson and P. W. Nelson, Mathematical analysis of HIV-1 dynamics in vivo. SIAM Rev, 41
- (1999) 3{44.
- [13] D. D. Richman, Human Immunodeficiency Virus. International Medical Press, London, (2004).
- [14] L. Rong, Z. Feng and A. S. Perelson, Emergence of HIV-1 drug resistance during antiretroviral
- treatment. Bull. Math. Biol, 69 (2007) 2027{2060.
- [15] R. Smith and K. Bowers, Sinc-Galerkin estimation of diffusivity in parabolic problems, Inverse
- Problems, 9 (1993) 113{135.
- [16] F. Stenger and M.J. OReilly, Computing solutions to medical problems via sinc convolution, IEEE
- Trans. Automat. Control, 43 (6) (1998) 843{848.
- [17] F. Stenger, Handbook of Sinc Numerical Methods, CRC Press, (2011).
- [18] F. Stenger, Numerical Methods Based on Sinc and Analytic Functions, Springer, NewYork, (1993).
- [19] L. Wang and M. Y. Li, Mathematical analysis of the global dynamics of a model for HIV infection
- of CD4+ T cells, Math. Biosci, 200 (2006) 44{57.
- [20] D. F. Winnter, K. L. Bowers and J. Lund, Wind-Driven currents in a sea with variable Eddy viscosity
- calculated via a sincGalerkin technique, Internat. J. Numer. Meth. Fluids, 33 (2000) 1041{1073.
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