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

• 作者: Yan-fei DU Ben NIU Jun-jie WEI
• 来源期刊: 应用数学学报（英文版）
• 年，卷（期）: 2022,（1）
• 页码范围: 128-153
• 页数: 26页
• 语种: 英文

摘要

We investigate a diffusive,stage-structured epidemic model with the maturation delay and freely-moving 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.