一类具有饱和发生率和恢复率的生态流行病模型  

An Eco-epidemiological Model with Saturation Incidence and Recovery Rate

作　　者：冯宇星 雒志学 胡永亮 梁丽宇 FENG Yu-xing;LUO Zhi-xue;HU Yong-liang;LIANG Li-yu(School of Mathematics and Physics,Lanzhou Jiaotong University,Lanzhou 730070,China)

机构地区：[1]兰州交通大学数理学院

出　　处：《兰州交通大学学报》2020年第1期124-129,141,共7页Journal of Lanzhou Jiaotong University

基　　金：国家自然科学基金(11561041);甘肃省自然科学基金(1506RJZA071)

摘　　要：研究了一类食饵具有传染病的捕食-食饵模型,考虑食饵的庇护作用,以及染病食饵和捕食者的恢复作用.利用Hurwitz判据、LaSall不变集原理和微分不等式,证明了系统解的有界性,分析了系统非负平衡点的存在性,最后通过特征根法讨论了非负平衡点的局部稳定性.结果表明:存在一个使疾病灭绝平衡点全局渐进稳定且系统持续共存的阈值.A kind of predator-prey model with infectious disease considering the protective effect of preys,and predators is studied.The boundedness of the system solution is proved by using the criterion,invariant set principle and differential inequality,and the existence of non-negative equilibrium point is analyzed.Finally,the local stability of the nonnegative equilibrium point is discussed by using the characteristic root method.The results show that there is a threshold that makes the disease extinction equilibrium point globally asymptotically stable and the system coexists continuously.

关 键 词：食饵-捕食者 平衡点 局部稳定 流行病 Hurwitz判据 

分 类 号：O175.1[理学—数学]