SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1493-1519, January 2020.
Diapause, a period of arrested development driven by adverse environmental conditions, plays an important role in the establishment and invasion of insects and other invertebrate organisms in temperate and subtropical areas. In order to describe the spatial dynamics of diapausing species, we propose a novel model involving (a) seasonal succession to distinguish the normal growth period, diapause period, and postdiapause period; (b) a diffusion term to represent the random movement of species; and (c) a maturation delay term to describe the developmental duration of species. We first study the model in a bounded domain for the survival and establishment of a species. The extinction and persistence of the species can be predicted by the basic reproduction ratio $\mathcal {R}_0$. Then we investigate the model in an unbounded domain for the spreading of the species. Our results show that the minimal wave speed for a periodic traveling wave is equal to the spreading speed. Numerical simulations are performed to validate theoretical results and in particular to compare the effects of two diapausing strategies: diapausing in the adult stage and in the immature stage.

中文翻译：

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滞育对种群增长影响的具有扩散的延迟继承模型

SIAM应用数学杂志，第80卷，第3期，第1493-1519页，2020年1月。
滞育期是在不利的环境条件下导致的发育停滞期，在温带和亚热带地区昆虫和其他无脊椎动物的建立和入侵中起着重要作用。为了描述滞育物种的空间动态，我们提出了一个新颖的模型，该模型包括：（a）季节演替，以区分正常生长期，滞育期和滞育后时期；（b）扩散项，表示物种的随机运动；（c）成熟延迟术语，用以描述物种的发育持续时间。我们首先在有界域中研究模型的生存和建立。物种的灭绝和持久性可以通过基本繁殖率$ \ mathcal {R} _0 $来预测。然后，我们在无界域中研究该模型的传播。我们的结果表明，周期性行波的最小波速等于扩展速度。进行数值模拟以验证理论结果，尤其是比较两种滞育策略的效果：成年期和未成熟期的滞育。