Nadin Grégoire, Strugarek Martin, Vauchelet Nicolas
Sorbonne Universites, UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, 4 place Jussieu, 75005, Paris, France.
Sorbonne Universites, UPMC Univ Paris 06, CNRS UMR 7598, Laboratoire Jacques-Louis Lions, Inria Equipe MAMBA, 4 place Jussieu, 75005, Paris, France.
J Math Biol. 2018 May;76(6):1489-1533. doi: 10.1007/s00285-017-1181-y. Epub 2017 Sep 22.
We study the biological situation when an invading population propagates and replaces an existing population with different characteristics. For instance, this may occur in the presence of a vertically transmitted infection causing a cytoplasmic effect similar to the Allee effect (e.g. Wolbachia in Aedes mosquitoes): the invading dynamics we model is bistable. We aim at quantifying the propagules (what does it take for an invasion to start?) and the invasive power (how far can an invading front go, and what can stop it?). We rigorously show that a heterogeneous environment inducing a strong enough population gradient can stop an invading front, which will converge in this case to a stable front. We characterize the critical population jump, and also prove the existence of unstable fronts above the stable (blocking) fronts. Being above the maximal unstable front enables an invading front to clear the obstacle and propagate further. We are particularly interested in the case of artificial Wolbachia infection, used as a tool to fight arboviruses.
我们研究当一个入侵种群扩散并取代具有不同特征的现有种群时的生物学情况。例如，这可能发生在存在一种垂直传播感染的情况下，这种感染会导致类似于阿利效应的细胞质效应（例如伊蚊中的沃尔巴克氏体）：我们所建模的入侵动态是双稳态的。我们旨在量化繁殖体（入侵开始需要什么条件？）和入侵能力（入侵前沿能推进多远，以及什么能阻止它？）。我们严格证明，一个诱导出足够强种群梯度的异质环境能够阻止入侵前沿，在这种情况下入侵前沿将收敛到一个稳定前沿。我们刻画了临界种群跳跃，并证明了在稳定（阻挡）前沿之上存在不稳定前沿。处于最大不稳定前沿之上能使入侵前沿清除障碍并进一步扩散。我们对人工沃尔巴克氏体感染的情况特别感兴趣，它被用作对抗虫媒病毒的一种工具。
