On Volterra's Population Growth Models

Abstract

A class of population growth problems is considered. We consider the case when the problems employ delay kernels reflecting the presence of some instantaneous effect on growth rate response, with delayed maximum effect. Under appropriate assumptions on the data of the problems, we construct an analytical solution with the help of an optimal homotopy analysis approach. This optimal approach contains a convergence-control parameter which can be estimated by minimizing the square residual error. Finally, numerical examples are presented that illustrate the approach efficiency