Numerical approximation and convergence to steady state solutions of a model for the dynamics of the sexual phase of Monogonont rotifera

Abstract

We consider the numerical approximation of the asymptotic behavior of an age-structured compartmental population model for the dynamics of the sexual phase of Monogonont rotifera. To cope with the difficulties of the infinite lifespan in long-time simulations, the main approach introduces a second order numerical discretization of a reformulation of the model problem in terms of a new computational size variable that evolves with age. The main contribution is to establish second order of convergence of the steady-state solutions of the discrete equations to the theoretical steady states of the continuous age-structured population model. Moreover, we report numerical evidence of a threshold for the male–female encounter rate parameter in the model after which the steady solution becomes unstable and a stable limit cycle appears in the dynamics. Finally, we confirm the effectiveness of the numerical technique we propose, when considering long-time integration of age-structured population models with infinite lifespan.