This paper deals with a general age-structured model with diffusion. The existence and uniqueness of solutions of the equivalent integral equation are obtained in light of the contraction mapping theorem. By taking the mosquito population growth as a motivating example, we derive a periodic stage-structured model with diffusion, intra-specific competition and periodic delay. Next, we show that the solution is globally bounded for the setup we chose. Then, the basic reproduction number $R_0$ for this model is introduced to establish the threshold dynamics on mosquito extinction and persistence in terms of $R_0$. In the case where intra-specific competition among immature individuals is ignored, the adult equation is decoupled from the full equations, and the global stability of the positive periodic solution is then obtained by introducing a suitable phase space on which the periodic semiflow is eventually strongly monotone and strictly subhomogeneous.

本文讨论具有扩散的一般年龄结构模型。根据压缩映射定理，得到了等价积分方程解的存在性和唯一性。通过以蚊子种群增长为例，我们得出了具有扩散，种内竞争和周期性延迟的周期性阶段结构模型。接下来，我们显示该解决方案对于我们选择的设置是全局范围内的。然后，基本再现数${\mathrm{[R}}_0$ 引入该模型以建立关于蚊子灭绝和持久性的阈值动态 ${\mathrm{[R}}_0$。在忽略未成熟个体之间的种内竞争的情况下，将成人方程与完整方程解耦，然后通过引入合适的相空间来获得正周期解的全局稳定性，在该相空间上最终将强周期半流动单调且严格亚同质。