A wolbachia infection model with free boundary

TL;DR

This paper develops a reaction-diffusion model with a free boundary to analyze Wolbachia-infected mosquito spread, providing criteria for invasion success and insights for disease control strategies.

Contribution

It introduces a novel free boundary model for Wolbachia-infected mosquito invasion, offering new mathematical criteria for spreading and vanishing outcomes.

Findings

Criteria for Wolbachia invasion success

Conditions for mosquito population eradication

Insights into mosquito releasing strategies

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.