Farkas József Z, Gourley Stephen A, Liu Rongsong, Yakubu Abdul-Aziz
Division of Computing Science and Mathematics, University of Stirling, Stirling, FK9 4LA, UK.
Department of Mathematics, University of Surrey, Guildford, Surrey, GU2 7XH, UK.
J Math Biol. 2017 Sep;75(3):621-647. doi: 10.1007/s00285-017-1096-7. Epub 2017 Jan 17.
Wolbachia is possibly the most studied reproductive parasite of arthropod species. It appears to be a promising candidate for biocontrol of some mosquito borne diseases. We begin by developing a sex-structured model for a Wolbachia infected mosquito population. Our model incorporates the key effects of Wolbachia infection including cytoplasmic incompatibility and male killing. We also allow the possibility of reduced reproductive output, incomplete maternal transmission, and different mortality rates for uninfected/infected male/female individuals. We study the existence and local stability of equilibria, including the biologically relevant and interesting boundary equilibria. For some biologically relevant parameter regimes there may be multiple coexistence steady states including, very importantly, a coexistence steady state in which Wolbachia infected individuals dominate. We also extend the model to incorporate West Nile virus (WNv) dynamics, using an SEI modelling approach. Recent evidence suggests that a particular strain of Wolbachia infection significantly reduces WNv replication in Aedes aegypti. We model this via increased time spent in the WNv-exposed compartment for Wolbachia infected female mosquitoes. A basic reproduction number [Formula: see text] is computed for the WNv infection. Our results suggest that, if the mosquito population consists mainly of Wolbachia infected individuals, WNv eradication is likely if WNv replication in Wolbachia infected individuals is sufficiently reduced.
沃尔巴克氏体可能是节肢动物物种中研究最多的生殖寄生虫。它似乎是某些蚊媒疾病生物防治的一个有前途的候选者。我们首先为感染沃尔巴克氏体的蚊子种群建立一个性别结构模型。我们的模型纳入了沃尔巴克氏体感染的关键影响，包括细胞质不相容性和雄性致死。我们还考虑了生殖产出降低、母系不完全传播以及未感染/感染的雄性/雌性个体不同死亡率的可能性。我们研究平衡点的存在性和局部稳定性，包括生物学上相关且有趣的边界平衡点。对于一些生物学上相关的参数范围，可能存在多个共存稳态，非常重要的是，其中一个共存稳态是感染沃尔巴克氏体的个体占主导。我们还使用SEI建模方法扩展模型以纳入西尼罗河病毒（WNv）动态。最近的证据表明，一种特定的沃尔巴克氏体感染菌株能显著降低埃及伊蚊中WNv的复制。我们通过增加感染沃尔巴克氏体的雌蚊在暴露于WNv的区室中停留的时间来对此进行建模。计算了WNv感染的基本再生数[公式：见原文]。我们的结果表明，如果蚊子种群主要由感染沃尔巴克氏体的个体组成，那么如果感染沃尔巴克氏体的个体中WNv的复制充分减少，WNv根除是有可能的。
