Modeling<i>Wolbachia</i>Spread in Mosquitoes Through Delay Differential Equations

Zheng, Baodong; Tang, Moxun; Yu, Jianshe

doi:10.1137/13093354x

Cited by 122 publications

(100 citation statements)

References 28 publications

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“…Similarly, Zheng et al (2014) proved that there existed a threshold for the success of Wolbachia invasion. They also investigated the relationships of the minimal releasing of infected mosquitoes and the waiting time with the time delay, and the waiting time in relation to the sex ratio of released populations.…”

Section: Model Formulationmentioning

confidence: 96%

“…In recent years, different mathematical models have been proposed to analyze the spread of Wolbachia in populations, including discrete time models (Turelli , 1994;Vautrin et al , 2007;Haygood and Turelli , 2009), continuous time models (Farkas and Hinow , 2010;Keeling et al , 2003;Schofield , 2002;Hughes and Britton , 2013;Zheng et al , 2014), stochastic models (Jansen et al , 2008) and impulsive models (Zhang et al , 2015b,c). From Keeling et al (2003), the total density of mosquito populations P is subdivided into four classes, uninfected females F U , infected females F I , uninfected males M U and infected males M I .…”

Section: Model Formulationmentioning

confidence: 99%

“…In order to study the effect of mosquito augmentation on the control of dengue transmission, the dynamics of mosquito populations with continuous augmentation of Wolbachia infected mosquitoes was developed by Zheng et al (2014) using delay differential equations. They denoted F R and M R as the densities of Wolbachia infected female and male mosquitoes released, respectively.…”

Section: Model Formulationmentioning

confidence: 99%

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Modeling the Effects of Augmentation Strategies on the Control of Dengue Fever With an Impulsive Differential Equation

et al. 2016

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Dengue fever has rapidly become the world's most common vectorborne viral disease. Use of endosymbiotic Wolbachia is an innovative technology to prevent vector mosquitoes from reproducing and so break the cycle of dengue transmission. Note that the success of different strategies, such as population eradication and replacement, needs to choose different augmentations of Wolbachia infected mosquitoes, and not all field trials of mosquito releases can succeed. So a four dimensional pulse differential system, incorporating the effects of cytoplasmic incompatibility (CI) and the augmentation of Wolbachia infected mosquitoes with different sex, is proposed to describe the spread of Wolbachia in mosquito populations. We evaluated a series of relevant issues regarding the system, including tackling questions such as (a) how each parameter value contributes to the success of population replacement? (b) how different release quantities of infected mosquitoes with different sex affect the success of the two strategies? And (c) how the success of population suppression or replacement can be fulfilled to block the transmission of dengue fever? The analysis of stability, bifurcation and sensitivity reveals the existence of forward and backward bifurcations, multiple attractors and the contribution of each parameter on the success of the strategies. The results indicate that initial density of mosquitoes and the quantity of mosquito augmentation on different sex have impacts on whether or not the strategies of population suppression or replacement can be achieved. Therefore, successful strategies rely on selecting suitable strains of Wolbachia and carefully designing the programme of mosquito augmentation.

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Section: Model Formulationmentioning

confidence: 96%

Section: Model Formulationmentioning

confidence: 99%

Section: Model Formulationmentioning

confidence: 99%

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Modeling the Effects of Augmentation Strategies on the Control of Dengue Fever With an Impulsive Differential Equation

et al. 2016

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“…Many mathematical models have been investigated for the spread of Wolbachia infection [23,28,29,30,31,32,33,34]. A continuous-time model for the behaviour of one and two strains of Wolbachia within a single well-mixed population has been studied which demonstrated the Allee effect and founder control.…”

Section: Two Strategies To Develop Wolbachia For Biological Control Omentioning

confidence: 99%

“…Patchy persistence of the two strains has been shown in a discrete spatial model [23,28]. Delay differential equations analyze how the reproductive advantage offsets the fitness costs for the success of population replacement [32].…”

Section: Two Strategies To Develop Wolbachia For Biological Control Omentioning

confidence: 99%

Models to assess how best to replace dengue virus vectors with Wolbachia -infected mosquito populations

Zhang

Tang

Cheke

2015

Mathematical Biosciences

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__________________________________________________________________________________________Please note that where the full text version provided on GALA is not the final published version, the version made available will be the most up-to-date full-text (post-print) version as provided by the author(s). Where possible, or if citing, it is recommended that the publisher's (definitive) version be consulted to ensure any subsequent changes to the text are noted. Citation for this version held on GALA:Zhang, X, Tang, Sanyi and Cheke, Robert (2015) This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.ACCEPTED MANUSCRIPT A C C E P T E D M A N U S C R I P T Highlights• Now various strains of Wolbachia-infected vectors are released in dengue areas.• Models with and without augmentation for dengue control are proposed.• Stability analysis shows there are backward bifurcations and multiple attractors.• Initial values and release methods affect the success of population replacement.• Suitable Wolbachia and release methods are needed for the control of The results show that successful population replacement will rely on selection of suitable strains of Wolbachia and careful design of augmentation methods.

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Controlling Aedes aegypti populations by limited Wolbachia‐based strategies in a seasonal environment

Rafikov

Meza

Correa

et al. 2019

Math Methods in App Sciences

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In this work, the linear feedback limited control strategy is proposed to indicate how the Wolbachia‐infected mosquitoes should be introduced in the seasonal environment to reduce the non‐Wolbachia mosquito population. The numerical simulations show that the proposed strategy reduces the population level of non‐Wolbachia mosquitos, avoiding mosquito spread and, consequently, reducing the number of cases of vector‐borne diseases.

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ModelingWolbachiaSpread in Mosquitoes Through Delay Differential Equations

Cited by 122 publications

References 28 publications

Modeling the Effects of Augmentation Strategies on the Control of Dengue Fever With an Impulsive Differential Equation

Modeling the Effects of Augmentation Strategies on the Control of Dengue Fever With an Impulsive Differential Equation

Models to assess how best to replace dengue virus vectors with Wolbachia -infected mosquito populations

Controlling Aedes aegypti populations by limited Wolbachia‐based strategies in a seasonal environment

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