周期演化域上一个禽流感模型的动力学分析

Dynamic Analysis of an Avian Influenza Model on Periodically Evolving Domain

本文研究了周期演化区域上一个禽流感模型.首先假设区域的增长为各向同性,将模型转换为固定区域上的反应扩散问题.然后利用相关的特征值问题和上下解方法得出模型解的渐近性态.研究结果表明,周期性区域的演化对疾病的传播与抑制取决于区域的周期演化速率ρ(t)的积分平均值ρ-2=1/T∫0T1/ρ2(t)dt.若ρ-2>1,则周期性区域的演化可抑制疾病的传播;若ρ-2<1,则周期性区域的演化可加速疾病的传播;若ρ-2=1,则周期性区域的演化对疾病的传播没有影响.

An avian influenza model on a periodically evolution region is studied in this paper.First,by assumping that the growth of the region is isotropic,the model is transformed into a reaction-diffusion problem over a fixed region.Then,the asymptotic behavior of the model is obtained by using the related eigenvalue questions and the up-down solution method.The results show that the impact of periodic evolution regions on the spread and inhibition of disease depends on the integral average value ρ-2=1/T∫0T1/ρ2(t)dt of the periodic evolution rate ρ(t) of the region.If ρ-2> 1,the evolution of periodic regions can inhibit the spread of disease;if ρ-2<1,the evolution of periodic regions can accelerate the spread of disease;if ρ-2=1,the evolution of periodic regions has no effect on the spread of disease.