Stage-structured wild and sterile mosquito population models and their dynamics

ABSTRACT

To study the impact of the sterile insect technique and effects of the mosquitoes' metamorphic stage structure on the transmission dynamics of mosquito-borne diseases, we formulate stage-structured continuous-time mathematical models, based on systems of differential equations, for the interactive dynamics of the wild and sterile mosquitoes. We incorporate different strategies for the releases of sterile mosquitoes in the models and investigate the model dynamics, including the existence of positive equilibria and their stability. Numerical examples are provided to demonstrate the dynamical features of the models.

KEYWORDS:

• Allee effects
• stability
• stage structure
• sterile mosquito releases
• vector-bornediseases

AMS SUBJECT CLASSIFICATIONS:

• 34D20
• 92D25
• 92D30
• 92D40

Acknowledgments

The authors thank two anonymous reviewers for their careful reading and valuable comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported partially by U.S. National Science Foundation [DMS-1118150], the National Natural Science Foundation of China [11371305], China Scholarship Council [201308410212] and Nanhu Scholars Program for Young Scholars XYNU. A part of the work was performed while Liming Cai was visiting the University of Alabama in Huntsville.