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. The mosquito population infected with Wolbachia 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 that infects the whole mosquito population with Wolbachia and eradicates the mosquito-borne diseases eventually.
Highlights
Several public health projects were launched in China [27], USA [1] and France [22], with an aim to fight mosquito populations that transmit Zika virus, Dengue fever and Chikungunya
A factory in Southern China is manufacturing millions of ‘mosquito warriors’ to combat epidemics transmitted by mosquitoes [27]
We studied a reaction-diffusion model with a free boundary in one-dimensional environment
Summary
Yunfeng Liua,b, Zhiming Guoa, Mohammad El Smailyc and Lin Wangd aSchool of Mathematics and Information Sciences, Guangzhou University, Guangzhou, People’s Republic of China; bSchool of Mathematics & Statistics, Qiannan Normal University for Nationalities, Duyun, People’s Republic of China; cDepartment of Mathematics & Statistics, University of Northern British Columbia, Prince George, Canada; dDepartment of Mathematics & Statistics, Statistics, University of New Brunswick, Fredericton, Canada
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