Lou Yijun, Liu Kaihui, He Daihai, Gao Daozhou, Ruan Shigui
Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong.
Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China.
J Math Biol. 2019 Jun;78(7):2259-2288. doi: 10.1007/s00285-019-01343-6. Epub 2019 Mar 1.
Diapause, a period of arrested development caused by adverse environmental conditions, serves as a key survival mechanism for insects and other invertebrate organisms in temperate and subtropical areas. In this paper, a novel modelling framework, motivated by mosquito species, is proposed to investigate the effects of diapause on seasonal population growth, where the diapause period is taken as an independent growth process, during which the population dynamics are completely different from that in the normal developmental and post-diapause periods. More specifically, the annual growth period is divided into three intervals, and the population dynamics during each interval are described by different sets of equations. We formulate two models of delay differential equations (DDE) to explicitly describe mosquito population growth with a single diapausing stage, either immature or adult. These two models can be further unified into one DDE model, on which the well-posedness of the solutions and the global stability of the trivial and positive periodic solutions in terms of an index [Formula: see text] are analysed. The seasonal population abundances of two temperate mosquito species with different diapausing stages are simulated to identify the essential role on population persistence that diapause plays and predict that killing mosquitoes during the diapause period can lower but fail to prevent the occurrence of peak abundance in the following season. Instead, culling mosquitoes during the normal growth period is much more efficient to decrease the outbreak size. Our modelling framework may shed light on the diapause-induced variations in spatiotemporal distributions of different mosquito species.
滞育是由不利环境条件导致的发育停滞期,是温带和亚热带地区昆虫及其他无脊椎动物的关键生存机制。本文提出了一种受蚊虫物种启发的新型建模框架,以研究滞育对季节性种群增长的影响,其中滞育期被视为一个独立的增长过程,在此期间种群动态与正常发育和滞育后时期完全不同。更具体地说,将年生长周期分为三个区间,每个区间的种群动态由不同的方程组描述。我们构建了两个延迟微分方程(DDE)模型,以明确描述具有单个滞育阶段(未成熟或成虫)的蚊虫种群增长。这两个模型可进一步统一为一个DDE模型,并分析该模型解的适定性以及平凡解和正周期解关于一个指标[公式:见正文]的全局稳定性。模拟了两种具有不同滞育阶段的温带蚊虫物种的季节性种群丰度,以确定滞育在种群持续存在方面所起的关键作用,并预测在滞育期杀灭蚊虫可降低但无法防止下一季出现丰度峰值。相反,在正常生长期间捕杀蚊虫对减小爆发规模更有效。我们的建模框架可能有助于揭示滞育引起的不同蚊虫物种时空分布变化。