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Modelling diapause in mosquito population growth

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Abstract

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 \({\mathcal {R}}\) 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.

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Acknowledgements

The work of Y. L. and K. L. was supported in part by the Research Grants Council (PolyU 153277/16P) of Hong Kong. D. G. was supported by NSFC (11601336), Program for Professor of Special Appointment (Eastern Scholar) at Shanghai Institutions of Higher Learning (TP2015050), and Shanghai Gaofeng Project for University Academic Development Program. S. R. was supported by National Science Foundation (DMS-1853622) and Centre for Disease Control and Prevention “Southeastern Regional Centre of Excellence in Vector-Borne Diseases: The Gateway Program” (U01CK000510). The authors would like to thank Dr. Hongying Shu for helpful discussions on this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

    Yijun Lou, Kaihui Liu & Daihai He

  2. Mathematics and Science College, Shanghai Normal University, Shanghai, 200234, China

    Daozhou Gao

  3. Department of Mathematics, University of Miami, Coral Gables, FL, 33146, USA

    Shigui Ruan

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  1. Yijun Lou
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Correspondence to Yijun Lou.

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Lou, Y., Liu, K., He, D. et al. Modelling diapause in mosquito population growth. J. Math. Biol. 78, 2259–2288 (2019). https://doi.org/10.1007/s00285-019-01343-6

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