A free boundary problem for Aedes aegypti mosquito invasion

Canrong Tian, Shigui Ruan

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


An advection–reaction–diffusion model with free boundary is proposed to investigate the invasive process of Aedes aegypti mosquitoes. By analyzing the free boundary problem, we show that there are two main scenarios of invasive regime: vanishing regime or spreading regime, depending on a threshold in terms of model parameters. Once the mortality rate of the mosquito becomes large with a small specific rate of maturation, the invasive mosquito will go extinct. By introducing the definition of asymptotic spreading speed to describe the spreading front, we provide an estimate to show that the boundary moving speed cannot be faster than the minimal traveling wave speed. By numerical simulations, we consider that the mosquitoes invasive ability and wind driven advection effect on the boundary moving speed. The greater the mosquito invasive ability or advection, the larger the boundary moving speed. Our results indicate that the mosquitoes asymptotic spreading speed can be controlled by modulating the invasive ability of winged mosquitoes.

Original languageEnglish (US)
Pages (from-to)203-217
Number of pages15
JournalApplied Mathematical Modelling
StatePublished - Jun 2017


  • Advection–reaction–diffusion model
  • Free boundary
  • Mosquito invasion
  • Travelling wave

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics


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