The numerical algorithm for stochastic age-dependent population system with Lévy noise in a polluted environment

Abstract

Environmental pollution has significant effects on population systems worldwide. In this study, we established a numerical algorithm for modelling stochastic age-dependent population systems driven by Lévy noise in a polluted environment. A modified explicit Euler–Maruyama (EM) discretization scheme was employed for ensuring the positiveness of the numerical solution used for modelling the stochastic age-dependent population hybrid system with Lévy noise in a polluted environment. The convergence of the numerical solution was confirmed by It's formula and a projection operator under the condition that the drift coefficient satisfies the local Lipschitz and global one-sided Lipschitz conditions. The theoretical results were finally verified with a numerical example.