Qualitative analysis for a Wolbachia infection model with diffusion

Huang, Mu Gen; Yu, Jing; Hu, Lin; Zheng, Baodong

doi:10.1007/s11425-016-5149-y

Cited by 55 publications

(19 citation statements)

References 30 publications

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“…ey gave a precise threshold for the infection frequency, and their numerical simulation is well fitting with the experimental data; then, Huang et al proposed the corresponding reaction diffusion equations with homogeneous Neumann boundary condition and obtained similar results [11,12]. In 2019, Zheng et al have carried out a mathematical model to study combining incompatible and sterile insect techniques (IIT-SIT) to eliminate the population of Aedes mosquitoes in the wild, and they proved the feasibility of regional control of mosquito vector population by combining IIT-SIT through field experiments [13].…”

Section: Introductionmentioning

confidence: 70%

ModelingWolbachiaDiffusion in Mosquito Populations by Discrete Competition Model

Guo

Xing

2020

Discrete Dynamics in Nature and Society

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Dengue fever is caused by dengue virus and transmitted by Aedes mosquitoes. A promising avenue to control this disease is to infect the wild Aedes population with the bacterium Wolbachia driven by cytoplasmic incompatibility (CI). To study the invasion of Wolbachia into wild mosquito population, we formulate a discrete competition model and analyze the competition between released mosquitoes and wild mosquitoes. We show the global asymptotic properties of the trivial equilibrium, boundary equilibrium, and positive equilibrium and give the conditions for the successful invasion of Wolbachia. Finally, we verify our findings by numerical simulations.

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Section: Introductionmentioning

confidence: 70%

ModelingWolbachiaDiffusion in Mosquito Populations by Discrete Competition Model

Guo

Xing

2020

Discrete Dynamics in Nature and Society

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“…A deep understanding of mosquito population dynamics can help identify the most influential factors for designing the most effective mosquito control policy. In past few years, we have studied the mosquito population dynamics interfered by Wolbachia, focusing on various aspects such as the population replacement by using delay differential equations [12,13,32,36], the inhomogeneous spatial distribution through reaction-diffusion equations [14,15], the impact of random climate changes through stochastic differential equations [9,10,11], and the maternal transmission leakage of Wolbachia [33,34,37]. However, we included only the terrestrial (adult) stage in most of our models.…”

Section: Mugen Huang Moxun Tang Jianshe Yu and Bo Zhengmentioning

confidence: 99%

A stage structured model of delay differential equations for <i>Aedes</i> mosquito population suppression

Huang¹,

Tang²,

Yu³

et al. 2020

Discrete &Amp; Continuous Dynamical Systems - A

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Tremendous efforts have been devoted to the development and analysis of mathematical models to assess the efficacy of the endosymbiotic bacterium Wolbachia in the control of infectious diseases such as dengue and Zika, and their transmission vector Aedes mosquitoes. However, the larval stage has not been included in most models, which causes an inconvenience in testing directly the density restriction on population growth. In this work, we introduce a system of delay differential equations, including both the adult and larval stages of wild mosquitoes, interfered by Wolbachia infected males that can cause complete female sterility. We clarify its global dynamics rather completely by using delicate analyses, including a construction of Liapunovtype functions, and determine the threshold level R 0 of infected male releasing. The wild population is suppressed completely if the releasing level exceeds R 0 uniformly. The dynamical complexity revealed by our analysis, such as bistability and semi-stability, is further exhibited through numerical examples. Our model generates a temporal profile that captures several critical features of Aedes albopictus population in Guangzhou from 2011 to 2016. Our estimate for optimal mosquito control suggests that the most cost-efficient releasing should be started no less than 7 weeks before the peak dengue season.

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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%

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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Qualitative analysis for a Wolbachia infection model with diffusion

Cited by 55 publications

References 30 publications

ModelingWolbachiaDiffusion in Mosquito Populations by Discrete Competition Model

ModelingWolbachiaDiffusion in Mosquito Populations by Discrete Competition Model

A stage structured model of delay differential equations for <i>Aedes</i> mosquito population suppression

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

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