Solution of a nonlinear time-delay model in biology via semi-analytical approaches

The delay logistic equations have been extensively used as models in biology and other sciences, with particular emphasis on population dynamics. In this work, the variational iteration and Adomian decomposition methods are applied to solve the delay logistic equation. The variational iteration method is based on the incorporation of a general Lagrange multiplier in the construction of correction functional for the equation. On the other hand, the Adomian decomposition method approximates the solution as an infinite series and usually converges to the accurate solution. Moreover, these techniques reduce the volume of calculations because they have no need of discretization of the variables, linearization or small perturbations. Illustrative examples are included to demonstrate the validity and applicability of the presented methods.