Ecological dynamics of a sexed and staged population model

Sexual reproduction is a special feature of some animals, but their ecological dynamics are rarely studied mathematically. Here we present a theoretical framework via delay differential equations to fill the knowledge gap. This new model takes into account the sex difference and age stage structure of the population. Using eigenvalue analysis, comparison method and iterative principle, we first derive the conditions which guarantee the global stability of the boundary and positive equilibria, and then propose a pest management strategy by controlling the adult female subpopulation. We finally clarify the effects of sex and stage structure on the dynamics by numerical analysis. The results indicated that (1) the dynamic of females and juvenile stage play an important role in the population duration process; (2) the length of juvenile stage can induce periodic fluctuation of the model solutions; and (3) reducing the adult females can effectively control the whole population.