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Title of article :
Dynamical analysis of the transmission of seasonal diseases using the differential transformation method
Author/Authors :
Arenas، نويسنده , , Abraham J. and Gonzلlez-Parra، نويسنده , , Gilberto and Chen-Charpentier، نويسنده , , Benito M.، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2009
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Abstract :
The aim of this paper is to apply the differential transformation method ( D T M ) to solve systems of nonautonomous nonlinear differential equations that describe several epidemic models where the solutions exhibit periodic behavior due to the seasonal transmission rate. These models describe the dynamics of the different classes of the populations. Here the concept of D T M is introduced and then it is employed to derive a set of difference equations for this kind of epidemic models. The D T M is used here as an algorithm for approximating the solutions of the epidemic models in a sequence of time intervals. 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 D T M is accurate, easy to apply and the calculated solutions preserve the properties of the continuous models, such as the periodic behavior. Furthermore, it is showed that the D T M avoids large computational work and symbolic computation.
Keywords :
Differential transformation method ( D T M ) , Nonautonomous ODEs , Numerical solution , Seasonal epidemic models
Journal title :
Mathematical and Computer Modelling
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