Diffusion-induced Spatio-temporal Oscillations in an Epidemic Model with Two Delays  

作　　者：Yan-fei DU Ben NIU Jun-jie WEI 

机构地区：[1]School of Mathematics,Harbin Institute of Technology,Harbin 150001,China [2]School of Mathematics&Data Science,Shaanxi University of Science and Technology,Xi'an 710021,China [3]Department of Mathematics,Harbin Institute of Technology,Weihai 264209,China [4]School of Science,Jimei University,Xiamen 361021,China

出　　处：《Acta Mathematicae Applicatae Sinica》2022年第1期128-153,共26页应用数学学报（英文版）

基　　金：supported by National Natural Science Foundation of China(No.11901369,No.61872227,No.12071268 and No.11771109);Natural Science Basic Research Plan in Shaanxi Province of China(grant No.2020JQ-699);Shandong Provincial Natural Science Foundation(No.ZR2019QA020)。

摘　　要：We investigate a diffusive,stage-structured epidemic model with the maturation delay and freelymoving delay.Choosing delays and diffusive rates as bifurcation parameters,the only possible way to destabilize the endemic equilibrium is through Hopf bifurcation.The normal forms of Hopf bifurcations on the center manifold are calculated,and explicit formulae determining the criticality of bifurcations are derived.There are two different kinds of stable oscillations near the first bifurcation:on one hand,we theoretically prove that when the diffusion rate of infected immature individuals is sufficiently small or sufficiently large,the first branch of Hopf bifurcating solutions is always spatially homogeneous;on the other,fixing this diffusion rate at an appropriate size,stable oscillations with different spatial profiles are observed,and the conditions to guarantee the existence of such solutions are given by calculating the corresponding eigenfunction of the Laplacian at the first Hopf bifurcation point.These bifurcation behaviors indicate that spatial diffusion in the epidemic model may lead to spatially inhomogeneous distribution of individuals.

关 键 词：epidemic model stage structure delay DIFFUSION Hopf bifurcation spatio-temporal oscillation 

分 类 号：O175[理学—数学] R181.3[理学—基础数学]