| Abstract: |
| Each species is subject to various biotic and abiotic factors during growth. This talk presents a deterministic model with the consideration of various factors regulating population growth such as age-dependent birth and death rates, spatial movements, seasonal variations, intra-specific competition and time-varying maturation simultaneously. The model takes the form of two coupled reaction-diffusion equations with time-dependent delays, which bring novel challenges to the theoretical analysis. The well-posedness of the system is established. Then the model is analyzed when competition among immatures is negligible, in which situation one equation for the adult population density is decoupled. The basic reproduction number is defined and shown to determine the global attractivity of either the zero equilibrium or a positive periodic solution by using the dynamical system approach on an appropriate phase space. When the competition is included, the model consisting of two coupled equations is neither cooperative (where the comparison principle holds) nor reducible to a single equation. In this case, the threshold dynamics about the population extinction and uniform persistence are established by using the basic reproduction number as a threshold index. |
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