Global dynamics of a mathematical model for the propagation of <italic style="font-style: italic">Wolbachia</italic> bacteria in mosquito populations

WU Dan; GUO Zhiming

doi:10.13471/j.cnki.acta.snus.2020A063

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Global dynamics of a mathematical model for the propagation of Wolbachia bacteria in mosquito populations

Research articles | 更新时间：2023-11-01

- Global dynamics of a mathematical model for the propagation of Wolbachia bacteria in mosquito populations
- Acta Scientiarum Naturalium Universitatis Sunyatseni Vol. 61, Issue 5, Pages: 133-143(2022)
- 作者机构：
  
  广州大学数学与信息科学学院，广东广州510006
- 作者简介：
- 基金信息：
- DOI：10.13471/j.cnki.acta.snus.2020A063
  CLC： O175.1
- Published：25 September 2022，
  
  Published Online：07 January 2022，
  
  Received：17 November 2020，
  
  Accepted：06 January 2021
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武丹,郭志明.一类Wolbachia氏菌在蚊群传播数学模型的全局动力学[J].中山大学学报(自然科学版),2022,61(05):133-143.

WU Dan,GUO Zhiming.Global dynamics of a mathematical model for the propagation of Wolbachia bacteria in mosquito populations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):133-143.
武丹,郭志明.一类Wolbachia氏菌在蚊群传播数学模型的全局动力学[J].中山大学学报(自然科学版),2022,61(05):133-143. DOI： 10.13471/j.cnki.acta.snus.2020A063.

WU Dan,GUO Zhiming.Global dynamics of a mathematical model for the propagation of Wolbachia bacteria in mosquito populations[J].Acta Scientiarum Naturalium Universitatis Sunyatseni,2022,61(05):133-143. DOI： 10.13471/j.cnki.acta.snus.2020A063.

摘要

蚊媒传染病指的是由蚊子来传播的传染病，主要包括登革热、寨卡、疟疾等。一种新型的控制和预防蚊媒传染病的方式是利用内共生菌

Wolbachia

（沃尔巴克氏）来阻断病源体的传播。本文建立了一个新的常微分方程模型研究

Wolbachia

氏菌在蚊群中的传播。应用常微分方程定性理论，证明了模型解的非负性和有界性，给出了平衡点存在条件；在各种不同的参数条件下，得到了平衡点的全局稳定性态；讨论了

Wolbachia

氏菌能够成功入侵野生蚊群的条件；在特殊参数的情况下得到

Wolbachia

能够成功入侵的初值阈值，为释放携带

Wolbachia

氏菌的蚊子提供新的策略。最后用数值模拟验证了相关结论。

Abstract

Mosquito-borne diseases are infectious diseases transmitted by mosquitoes， including dengue fever， Zika and malaria. A new way to control and prevent mosquito-borne infectious diseases is to use the endosymbiotic bacterium

Wolbachia

to interrupt the transmission of the pathogen. A new ordinary differential equation model is established to study the transmission of

Wolbachia

in mosquito population. By using the qualitative theory of ordinary differential equations， the nonnegativity and boundedness of solutions of the model are proved， and the existence condition of the equilibrium points is given. The globally asymptotic stability of the equilibrium is obtained in different situations. The conditions of

Wolbachia

successfully invading wild mosquito population are discussed. In special case for parameters， the threshold for initial values of

Wolbachia

invasion is given， which provides a new strategy for releasing mosquitoes carrying

Wolbachia

. Finally， main conclusions are verified by numerical simulation.

关键词

常微分方程种群动力学Wolbachia登革热全局渐近稳定

Keywords

ordinary differential equation modelpopulation dynamicsWolbachiadengueglobally asymptotic stability

references

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马知恩，周义仓，李承治. 常微分方程定性与稳定性方法［M］. 北京：科学出版社， 2015.

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Global dynamics of a mathematical model for the propagation of Wolbachia bacteria in mosquito populations

DOI：10.13471/j.cnki.acta.snus.2020A063

摘要

Abstract

关键词

Keywords

references