Dynamics of delayed mosquitoes populations models with two different strategies of releasing sterile mosquitoes.

Liming Cai,Shangbing Ai,Guihong Fan

doi:10.3934/mbe.2018054

Abstract

To prevent the transmissions of mosquito-borne diseases (e.g., malaria, dengue fever), recent works have considered the problem of using the sterile insect technique to reduce or eradicate the wild mosquito population. It is important to consider how reproductive advantage of the wild mosquito population offsets the success of population replacement. In this work, we explore the interactive dynamics of the wild and sterile mosquitoes by incorporating the delay in terms of the growth stage of the wild mosquitoes. We analyze (both analytically and numerically) the role of time delay in two different ways of releasing sterile mosquitoes. Our results demonstrate that in the case of constant release rate, the delay does not affect the dynamics of the system and every solution of the system approaches to an equilibrium point; while in the case of the release rate proportional to the wild mosquito populations, the delay has a large effect on the dynamics of the system, namely, for some parameter ranges, when the delay is small, every solution of the system approaches to an equilibrium point; but as the delay increases, the solutions of the system exhibit oscillatory behavior via Hopf bifurcations. Numerical examples and bifurcation diagrams are also given to demonstrate rich dynamical features of the model in the latter release case.

Highlights

For more than a century, human beings have attempted to control blood-feeding mosquitoes
Despite some mosquito-borne diseases have been successfully controlled in many regions through vector-targeted intervention such as insecticide-treated bed nets (ITNs) and indoor residual sprays (IRS), massive and long time spraying of adulticide is not recommended
Our obtained results in Theorem 2.3 have shown that the growth time delay of the mosquito population has no destabilizing effect on the solution’s behavior in the constant release rate of sterile mosquitoes

Summary

Introduction

For more than a century, human beings have attempted to control blood-feeding mosquitoes. Vector control measures include the elimination or reduction of their nesting places by draining stagnant water deposits This measure has been very effective in places where the prevalence of the disease was not very high. Despite some mosquito-borne diseases have been successfully controlled in many regions through vector-targeted intervention such as insecticide-treated bed nets (ITNs) and indoor residual sprays (IRS), massive and long time spraying of adulticide is not recommended. Since they have commonly been chemically-based, the effectiveness of this measure has been hampered by the appearance of insecticide resistant vector strains [1, 2, 8]. The technique involves the massive release of male mosquitoes (sterilized through radiological or chemical means) into the environment to mate with wild mosquitoes that are present in the environment

Objectives

Conclusion