title: Wolbachia spread dynamics in stochastic environments.
abstract: Dengue fever is a mosquito-borne viral disease with 100 million people infected annually. A novel strategy for dengue control uses the bacterium Wolbachia to invade dengue vector Aedes mosquitoes. As the impact of environmental heterogeneity on Wolbachia spread dynamics in natural areas has been rarely quantified, we develop a model of differential equations for which the environmental conditions switch randomly between two regimes. We find some striking phenomena that random regime transitions could drive Wolbachia to extinction from certain initial states confirmed Wolbachia fixation in homogeneous environments, and mosquito releasing facilitates Wolbachia invasion more effectively when the regimes transit frequently. By superimposing the phase spaces of the ODE systems defined in each regime, we identify the threshold curves below which Wolbachia invades the whole population, which extends the theory of threshold infection frequency to stochastic environments.
authors.affiliation: College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, PR China; Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, PR China.
authors.forename: Linchao
authors.initials: L
authors.lastname: Hu
authors.affiliation: College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, PR China; Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, PR China.
authors.forename: Mugen
authors.initials: M
authors.lastname: Huang
authors.affiliation: Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.
authors.forename: Moxun
authors.initials: M
authors.lastname: Tang
authors.affiliation: College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, PR China; Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, PR China. Electronic address: jsyu@gzhu.edu.cn.
authors.forename: Jianshe
authors.initials: J
authors.lastname: Yu
authors.affiliation: College of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, PR China; Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, Guangzhou, 510006, PR China; Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.
authors.forename: Bo
authors.initials: B
authors.lastname: Zheng
mesh_terms: D000330:Aedes / Q000382:microbiology*; D000818:Animals; D003715:Dengue / Q000517:prevention & control*; D053476:Extinction, Biological; D005260:Female; D006801:Humans; D008297:Male; D008954:Models, Biological; D011157:Population Dynamics; D012282:Rickettsia Infections / Q000401:mortality / Q000635:transmission; D013269:Stochastic Processes; D020577:Wolbachia / Q000472:pathogenicity*
keywords: Cytoplasmic incompatibility; Dengue fever; Population replacement; Stochastic dynamics; Wolbachia