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arXiv · 2006.04073

A wolbachia infection model with free boundary

yunfeng Liu·Zhiming Guo·Mohammad El Smaily·Lin Wang
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Abstract

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.

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yunfeng Liu, Zhiming Guo, Mohammad El Smaily, Lin Wang. 2020-06-07. A wolbachia infection model with free boundary. https://doi.org/10.1080/17513758.2020.1784474

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