  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.
