Variational Iteration Method for Solving HIV/AIDS Epidemic Model

Okperhie E. P., Oguntolu F. A., Akinduko O. B., Ajisope M. O., Faniyi O. E.

Abstract


In this paper, a deterministic model on the transmission dynamics of Hiv/Aids was presented. Variational Iteration Method Method (VIM) was employed to attempt the series solution of the model. The validity of the VIM in solving the model was established by using the computer in-built classical fourth-order Runge-Kutta method. The comparism between Variational Iteration Method solution and Runge-Kutta (RK4) were performed which were found to be efficient, accurate and rapidly convergence.


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Abbasbandy, E & Shivanian, E. (2009). Application of the variational iteration method for system of nonlinear Volterra’s integro-differential equations, Mathematical and Comp. Applic., 14(2), 147-158.

Abdou, M . A & Soliman, A . A (2005). New application of Variational iteration method, Physica D211 (1-2):1-8

Abdou, M . A & Soliman, A . A (2005). Variational iteration method for solving Burger’s and coupled Burger’s equation,J.Comp.Appl.Math 181(2):245-251

Akinboro, F. S., Alao, S., & Akinpelu, F. O. (2014). Numerical solution of SIR model using differential transformation method and variational iteration method. General Mathematics Notes, 22(2), 82-92.

Arazoza, H. D., and Lounes, R. (2002), A Non-linear model for a sexually transmitted disease with contact tracing, IMA J Math. Appl. Med. Biol., 19: 221-234.

Aytaç Arıkoğlu, İbrahim Özkol (2006), Solution of difference equations by using differential transform method. Applied Mathematics and Computation, 174 (2): 1216-1228.

Batiha, B, Noorani, M. S. M, and Hashim, I (2007). Application of Variational Iteration Method to a General Riccati Equation. International Mathematical Forum, 2 (56) 2759 - 2770

Chavez, C (2004), Dynamical models of tuberculosis and their applications. Math. Bioscience, 1: 361-404.

Darania, P Ali Ebadian (2007), A method for the numerical solution of the integro-differential equations. Applied Mathematics and Computation, 188(1): 657-668.

Lawi G. O., Mugisha J.Y., Omolo N. O. (2011), Mathematical Model for Malaria and Meningitis Co-infection among Children. Applied Mathematics Sciences, 47(5): 2337-2359.

Ming–Jyi Jang, Chieh–Li Chen, Yung–Chin Liy (2000), On solving the initial-value problems using the differential transformation method. Applied Mathematics and Computation, 115 (2-3): 145-160

Peter, O. J., O. A. Afolabi, F. A. Oguntolu, C. Y. Ishola, and A. A. Victor. 2019. “Semi analytic Method for Solving Infectious Disease modelâ€. Science World Journal. 14(1): 64-68.

Peter O. J and Akinduko O. B. (2018). Semi Analytic Method for Solving HIV/AIDS Epidemic Model. Int. J. Modern Biol .Med, 9(1): 1-8

Sarah, A. (2011), Stability analysis of an HIV/AIDS Epidemic Model with Screening. International Mathematical Forum, 66(6): 3251-3273.

Srinivasa Rao, A.S.R. (2003), Mathematical modeling of AIDS epidemic in India, Curr. Sci., 84: 1192-1197

Udoy S. B, Bimal K. D, Prodip K. G. (2015), Mathematical Analysis of an HIV/AIDS Epidemic Model. American Journal of Mathematics and Statistics, 5(5), (2015): 253-258.

Zhou, J. K. (1986), Differential Transformation and Its Applications for Electrical Circuits, Huazhong University Press, Wuhan, China, (in Chinese).


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