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Zbl 1221.65201
González-Parra, Gilberto; Arenas, Abraham J.; Jódar, Lucas
Piecewise finite series solutions of seasonal diseases models using multistage Adomian method. (English)
[J] Commun. Nonlinear Sci. Numer. Simul. 14, No. 11, 3967-3977 (2009). ISSN 1007-5704

Summary: Our aim is to apply the multistage Adomian decomposition method (MADM) to solve systems of nonautonomous nonlinear differential equations that describe several epidemic models with periodic behavior. Here the concept of the MADM is introduced and then it is employed to obtain a piecewise finite series solution. The MADM is used here as a hybrid analytical-numerical technique for approximating the solutions of the epidemic models. In order to show the efficiency of the method, the obtained numerical results are compared with the fourth-order Runge-Kutta method solutions. Numerical comparisons show that the MADM is accurate, easy to apply and the calculated solutions preserve the periodic behavior of the continuous models. Moreover, the method has the advantage of giving a functional form of the solution for any time interval. Furthermore, it is shown that if the truncation order and the time step size are not properly chosen large computational work is required and inaccurate solutions may be obtained.

MSC 2000:: *65L99 Numerical methods for ODE
92D30 Epidemiology
34A45 Theoretical approximation of solutions of ODE

Keywords: piecewise finite series solution; Adomian decomposition method (ADM); nonautonomous ODEs; seasonal epidemic models

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Zentralblatt MATH Berlin [Germany]