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.
