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In the present article, we implement the new iterative method proposed by Daftardar-Gejji and Jafari (NIM) [V.
Daftardar-Gejji, H. Jafari, An iterative method for solving nonlinear functional equations, J. Math. Anal. Appl.
316 (2006) 753-763] to solve two problems; the first one is the problem of spread of a non-fatal disease in a population
which is assumed to have constant size over the period of the epidemic, and the other one is the problem of the prey
and predator. The results demonstrate that the method has many merits such as being derivative-free, overcome
the difficulty arising in calculating Adomian polynomials to handle the nonlinear terms in Adomian Decomposition
Method (ADM), does not require to calculate Lagrange multiplier a
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