不同扩散策略下SI传染病模型的行波解  

Traveling Wave Solutions of SI Epidemic Modelunder Different Diffusion Strategies

作　　者：焦战 JIAO Zhan(Complex System Research Center,Shanxi University,Taiyuan 030006,China)

机构地区：[1]山西大学复杂系统研究所,太原030006

出　　处：《吉林大学学报（理学版）》2022年第3期494-506,共13页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:61873154);山西省重点专项基金(批准号:2020XM18).

摘　　要：考虑具有标准发生率的不同扩散策略下SI传染病模型的行波解,其中易感者采用随机扩散策略,染病者采用非局部扩散策略.利用上下解方法结合Schauder’s不动点定理,证明当R_(0)>1,R_(d)>1,c>c^(*)时系统行波解的存在性,并应用两边夹定理、Lyapunov泛函及Lebesgue控制收敛定理讨论该模型行波解的渐近行为.[HQK]The author considered the traveling wave solutions of the SI epidemic model under different diffusion strategies with standard incidence rates.The susceptible individuals adopted the random diffusion strategy,and the infected individuals adopted the non-local diffusion strategy.By means of the upper and lower solution method combined with Schauder’s the fixed point theorem,the existence of the traveling wave solutions of the system was proved when R_(0)>1,R_(d)>1,and c>c^(*).The asymptotic behavior of traveling wave solutions of the model was discussed by applying squeeze theorem,Lyapunov functional and Lebesgue dominated convergence theorem.

关 键 词：SI传染病模型 行波解 非局部扩散 标准发生率 

分 类 号：O175.1[理学—数学]