School of Science, Xi'an University of Technology, Xi'an 710048, China.
Comput Math Methods Med. 2019 Jul 9;2019:1989651. doi: 10.1155/2019/1989651. eCollection 2019.
In this paper, an infection model with delay and general incidence function is formulated and analyzed. Theoretical results reveal that positive equilibrium may lose its stability, and Hopf bifurcation occurs when choosing delay as the bifurcation parameter. The direction of Hopf bifurcation and the stability of the periodic solutions are also discussed. Furthermore, to illustrate the numerous changes in the local stability and instability of the positive equilibrium, we conduct numerical simulations by using four different types of functional incidence, i.e., bilinear incidence, saturation incidence, Beddington-DeAngelis response, and Hattaf-Yousfi response. Rich dynamics of the model, such as Hopf bifurcations and chaotic solutions, are presented numerically.
本文构建并分析了一个带有时滞和一般发生率函数的传染病模型。理论结果表明，当选择时滞作为分岔参数时，正平衡点可能失去稳定性，并且会发生 Hopf 分岔。此外，还讨论了 Hopf 分岔的方向和周期解的稳定性。进一步地，为了说明正平衡点局部稳定性和不稳定性的众多变化，我们通过使用四种不同类型的发生率函数，即双线性发生率、饱和发生率、Beddington-DeAngelis 反应和 Hattaf-Yousfi 反应，进行了数值模拟。模型的丰富动力学，如 Hopf 分岔和混沌解，也通过数值呈现出来。
