The Volterra-Kostitzin Integro-differential model of population dynamics solved by the decomposition method (Adomian)

摘要

The Volterra-Kostitzin model is derived from the Malthus and Verhulst models with the addition of an integral term, which represents a reinforcing or degrading factor (e.g. synergy or environment poisoning by the individuals of a population). Considering populations in a wide sense (e.g. molecules, cells or individuals), we argue that a certain number of published experimental results described under a logistic dynamic should be taken up again using the Volterra-Kostitzin model, which would reflect a better understanding of the stages involved in population growth. The fact that the solution of the integro-differential equation which describes the Volterra-Kostitzin model is expressed in parametric form and that one of the equations can only be given approximately, results in a high degree of mathematical difficulty and requires the use of numeric methods. In this paper, we present a new numeric decomposition method (Adomian) to solve the Volterra-Kostitzin model. We analyse the convenience of the new method and we compare it with another method previously applied (Miladie).