Oscillation threshold for a mosquito population suppression model with time delay

Hui, Yuan; Lin, Geng Hong; Sun, Qi

doi:10.3934/mbe.2019367

Cited by 5 publications

(8 citation statements)

References 24 publications

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“…Mathematical models have been formulated to study the interactive dynamics of wild and sterile mosquito populations or the control of mosquitoes [6,7,9,11,13,14,15,16,17,18,19,23,24,34,35,36,38,39], among which the models in [6,23] involve three different strategies in the releases of sterile mosquitoes with constant release rate, the rate proportional to the wild mosquitoes, and the rate proportional to wild mosquitoes with saturation. It is assumed in [6] that the mosquito population follows the logistic growth in the absence of interactions, and considered homogeneous mosquito populations without distinguishing the four distinct stage of development during a lifetime: egg, pupa, larva, and adult.…”

Section: Introduction Sterile Insect Technique (Sit) Is a Promising mentioning

confidence: 99%

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A delayed differential equation model for mosquito population suppression with sterile mosquitoes

Yang¹,

Lin²,

Yu³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - B

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The technique of sterile mosquitoes plays an important role in the control of mosquito-borne diseases such as malaria, dengue, yellow fever, west Nile, and Zika. To explore the interactive dynamics between the wild and sterile mosquitoes, we formulate a delayed mosquito population suppression model with constant releases of sterile mosquitoes. Through the analysis of global dynamics of solutions of the model, we determine a threshold value of the release rate such that if the release threshold is exceeded, then the wild mosquito population will be eventually suppressed, whereas when the release rate is less than the threshold, the wild and sterile mosquitoes coexist and the model exhibits a complicated feature. We also obtain theoretical results including a sufficient and necessary condition for the global asymptotic stability of the zero solution. We provide numerical examples to demonstrate our results and give brief discussions about our findings.

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Section: Introduction Sterile Insect Technique (Sit) Is a Promising mentioning

confidence: 99%

“…In fact, if (19) does not hold, then there exists t 7 > t 0 such that S ν (t 7 ) = ε and 0 < S ν (t) < ε for all t ∈ [t 0 −τ, t 7 ). Hence S ν (t 7 ) ≥ 0.…”

mentioning

confidence: 99%

A delayed differential equation model for mosquito population suppression with sterile mosquitoes

Yang¹,

Lin²,

Yu³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - B

Self Cite

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“…In recent years, mathematical models have been developed to understand the interplays between wild and sterile mosquitoes [4,5,7,11,15,16,18,19,21,25,31,32], or Wolbachiainfected mosquitoes [8][9][10][12][13][14]30,33,[35][36][37], and thus to provide feasible releasing policies in mosquito control. Among these works, an ordinary differential equation model for the competition of wild and sterile mosquitoes was proposed in [4]…”

Section: Introductionmentioning

confidence: 99%

Stability analysis in a mosquito population suppression model

Lin

Yang

2020

Journal of Biological Dynamics

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In this work, we study a non-autonomous differential equation model for the interaction of wild and sterile mosquitoes. Suppose that the number of sterile mosquitoes released in the field is a given nonnegative continuous function. We determine a threshold s * g for the number of sterile mosquitoes and provide a sufficient condition for the origin s 0 to be globally asymptotically stable based on the threshold s * g. For the case when the number of sterile mosquitoes keeps at a constant level, we find that the origin s 0 is globally asymptotically stable if and only if the constant number s g of sterile mosquitoes released in the field is above s * g .

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“…Also, the study of releases of sterile mosquitoes has been investigated in [4], with a Beverton-Holt type model for survivability, as well as in [5]. It is well-known that Beverton-Holt type models are very popular to study the evolution of species that reproduce by eggs, [4,[6][7][8][9][10][11][12] such as birds, insects, or fish. More general difference equations which generalize those kinds of problems are studied in detail in [13,14].…”

Section: Introductionmentioning

confidence: 99%

Stage-Dependent Structured Discrete-Time Models for Mosquito Population Evolution with Survivability: Solution Properties, Equilibrium Points, Oscillations, and Population Feedback Controls

2019

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This paper relied on the investigation of the properties of the stage-structured model of coupled larvae and adult mosquito populations’ evolution when parameterized, in general, by time-varying (or stage-dependent) sequences. In particular, the investigated properties were the non-negativity of the solution under non-negative initial conditions, the boundedness of the sequence solutions under any finite non-negative initial conditions, the equilibrium points, and the convergence conditions to them in the event that the parameterizing sequences converge to finite limits. Some further properties that were investigated relied on deriving the oscillation conditions of the solutions under certain conditions of the parameterizations. The use of feedback controls to decrease the foreseen numbers of alive mosquitoes in future evolution stages is also proposed. The proposed control actions are exerted on the birth rate and/or the maximum progression rate sequences. Some illustrative examples are also given.

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Oscillation threshold for a mosquito population suppression model with time delay

Cited by 5 publications

References 24 publications

A delayed differential equation model for mosquito population suppression with sterile mosquitoes

A delayed differential equation model for mosquito population suppression with sterile mosquitoes

Stability analysis in a mosquito population suppression model

Stage-Dependent Structured Discrete-Time Models for Mosquito Population Evolution with Survivability: Solution Properties, Equilibrium Points, Oscillations, and Population Feedback Controls

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