一类具有非线性发生率的生态-流行病模型分析

Analysis of an Eco-Epidemiological Model with a Nonlinear Incidence Rate

对仅在捕食者中传播且具有非线性发生率的一类生态-流行病进行了研究.考虑了系统解的有界性、边界平衡点与正平衡点的存在条件及稳定性;利用分支理论与方法讨论了正平衡点的Bogdanov-Takens分支产生的条件,得到了相应的鞍结点分支曲线、Hopf分支曲线和同宿分支曲线;对正平衡点的Hopf分支,讨论了分支的方向及稳定极限环的存在性.

An eco-epidemiological model with a nonlinear incidence rate in the predator is considered.We analyze the boundedness of solutions and stability of equilibria.By using bifurcation methods and techniques,we study the Bogdanov-Takens bifurcation near a positive equilibrium,and obtain a saddle-node bifurcation curve,a Hopf bifurcation curve and a homoclinic bifurcation curve.The direction of Hopf bifurcation and the existence of a stable limit cycle near a positive equilibrium are also discussed.