Qualitative analysis for a Wolbachia infection model with diffusion

被引：55
作者：
Huang MuGen [1 ,2 ]
Yu JianShe [1 ]
Hu LinChao [1 ]
Zheng Bo [1 ]
机构：
[1] Guangzhou Univ, Sch Math & Informat Sci, Guangzhou 510006, Guangdong, Peoples R China
[2] Guangzhou Univ, Sch Econ & Stat, Guangzhou 510006, Guangdong, Peoples R China
来源：
SCIENCE CHINA-MATHEMATICS | 2016年 / 59卷 / 07期
基金：
中国国家自然科学基金;
关键词：
dengue fever; Wolbachia infection dynamics; cytoplasmic incompatibility mechanism; attractive region; Turing instability; non-constant steady-states; CYTOPLASMIC INCOMPATIBILITY; MOSQUITO; ESTABLISHMENT; INVASION; DYNAMICS; SYSTEMS; SPREAD; DENGUE;
D O I：
10.1007/s11425-016-5149-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider a reaction-diffusion model which describes the spatial Wolbachia spread dynamics for a mixed population of infected and uninfected mosquitoes. By using linearization method, comparison principle and Leray-Schauder degree theory, we investigate the influence of diffusion on the Wolbachia infection dynamics. After identifying the system parameter regions in which diffusion alters the local stability of constant steady-states, we find sufficient conditions under which the system possesses inhomogeneous steady-states. Surprisingly, our mathematical analysis, with the help of numerical simulations, indicates that diffusion is able to lower the threshold value of the infection frequency over which Wolbachia can invade the whole population.
引用
收藏
页码：1249 / 1266
页数：18
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