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Solutions to the problem of prey and predator and the epidemic model via differential transform method. (English) Zbl 1180.49041
Summary: The purpose of this paper is to solve both the prey and predator problem and the problem of the spread of a non-fatal disease in a population which is assumed to have constant size over the period of the epidemic.
The Differential Transform Method (DTM) is employed to compute an approximation to the solutions of the systems of nonlinear ordinary differential equations of these problems.
Results obtained using the scheme presented here agree well with the results obtained by the Adomian decomposition and power series methods. Some plots are presented to show the reliability and simplicity of the method
This paper is believed to represent a new application for DTM on solving systems of nonlinear ordinary differential equations.

##### MSC:
 49N75 Pursuit and evasion games 91A24 Positional games (pursuit and evasion, etc.) 92D30 Epidemiology
##### Keywords:
cybernetics; differential equations; mathematical modelling
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##### References:
 [1] DOI: 10.1016/j.amc.2004.10.009 · Zbl 1090.65145 [2] DOI: 10.1016/S0096-3003(02)00794-4 · Zbl 1032.35011 [3] DOI: 10.1016/j.amc.2005.04.036 · Zbl 1087.92051 [4] DOI: 10.1016/j.amc.2004.05.001 · Zbl 1060.65612 [5] DOI: 10.1016/j.amc.2005.01.040 · Zbl 1084.65068 [6] DOI: 10.1016/j.amc.2005.02.037 · Zbl 1088.65085 [7] DOI: 10.1016/S0096-3003(98)10115-7 · Zbl 1028.35008 [8] DOI: 10.1016/j.amc.2006.11.075 · Zbl 1119.65066 [9] DOI: 10.1016/S0096-3003(03)00708-2 · Zbl 1054.65069 [10] DOI: 10.1016/S0096-3003(99)00137-X · Zbl 1023.65065 [11] DOI: 10.1016/S0096-3003(99)00293-3 · Zbl 1024.65093 [12] DOI: 10.1016/j.amc.2006.05.173 · Zbl 1115.65089 [13] DOI: 10.1108/eb005812 · Zbl 0697.65051
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