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

作　　者：梁建秀 张雪霞 石漂漂 LIANG JIANXIU;ZHANG XUEXIA;SHI PIAOPIAO(Department of Mathematics,Jin Zhong University,Jinzhong 030619,China)

机构地区：[1]晋中学院数学系,晋中030619

出　　处：《应用数学学报》2021年第1期61-68,共8页Acta Mathematicae Applicatae Sinica

基　　金：山西省高等学校科技创新项目(2020L0613);山西省高等学校教学改革创新项目(J2020319);晋中学院优秀数学建模团队项目资助。

摘　　要：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.

关 键 词：禽流感模型 扩散 周期演化区域 主特征值 全局渐近性 

分 类 号：O175.2[理学—基础数学]