论文标题
Wolbachia感染模型具有自由边界
A wolbachia infection model with free boundary
论文作者
论文摘要
科学家一直在寻求使用沃尔巴基亚消除传播人类疾病的蚊子的方法。 Wolbachia可以成为控制蚊子传染病的决定因素吗？为了数学上回答这个问题，我们在一维环境中开发了具有自由边界的反应扩散模型。我们将女性蚊子种群分为两组：一组是未感染的蚊子种群，在整个地区生长，而另一个是感染了沃尔巴基亚的蚊子种群，占据了有限的小区域，并以众所周知的一阶段的史蒂芬（Stefan）条件占据了一个有限的小区域，并以散布的前线侵袭了环境。对于由此产生的自由边界问题，我们建立了发生扩散和消失的标准。我们的结果为设计可行的蚊子释放策略提供了有用的见解，以侵入沃尔巴奇感染的整个蚊子种群，从而最终消除蚊子 - 传播的疾病。
Scientists have been seeking ways to use Wolbachia to eliminate the mosquitoes that spread human diseases. Could Wolbachia be the determining factor in controlling the mosquito-borne infectious diseases? To answer this question mathematically, we develop a reaction-diffusion model with free boundary in a one-dimensional environment. We divide the female mosquito population into two groups: one is the uninfected mosquito population that grows in the whole region while the other is the mosquito population infected with Wolbachia that occupies a finite small region and invades the environment with a spreading front governed by a free boundary satisfying the well-known one-phase Stefan condition. For the resulting free boundary problem, we establish criteria under which spreading and vanishing occur. Our results provide useful insights on designing a feasible mosquito releasing strategy to invade the whole mosquito population with Wolbachia infection and thus eventually eradicate the mosquito-borne diseases.
