Abstract：In this paper, the stability of a fractional order ecological epidemic model with stage structure and predator delay time during pregnancy was studied. By calculating the characteristic roots of the model and using Routh-hurwitz criterion, it is obtained that the predator extinction equilibrium point, disease-free equilibrium point and endemic equilibrium point are locally asymptotically stability, a sufficient condition for the generation of Hopf bifurcation near the endemic equilibrium is obtained. At the same time, the influence of fractional order on the bifurcation point decreases is discussed, and it is found that the bifurcation point of the system decreases as the order increases. Finally, the validity of the theoretical conclusion is verified by numerical simulation.
豆中丽. 阶段结构分数阶生态流行病模型的稳定性分析[J]. 复杂系统与复杂性科学, 2025, 22(4): 133-138.
DOU Zhongli. Stability Analysis of Fractional Order Ecological Epidemiological Model with Stage Structure[J]. Complex Systems and Complexity Science, 2025, 22(4): 133-138.
[1] ANDERSON R M, MAY R M. Infectious Disease of Human Dynamics and Control[M]. Oxford: Oxford University Press, 1991. [2] XIAO Y N, CHEN L S. Modeling and analysis of a predator-prey model with disease in the prey[J]. Nonlinear Analysis: Theory, Methods and Applications, 1999,36(6):747766. [3] 房鑫. 用疫苗减轻登革热传播的建模[D].哈尔滨:哈尔滨工程大学,2019. FANG X. Modeling of vaccinating strategies for mitigating dengue transmission[D]. Harbin: Harbin Engineering University, 2019. [4] 李录苹,贾建文.一个捕食者具有传染病的生态——流行病模型的分析[J].山西大同大学学报(自然科学版), 2009, 25(6): 13,30. LI L P, JIA J W. Analysis of one predator-prey model with epidemic in the predator[J].Journal of Shanxi Datong University(Natural Science),2009,25(6):13,30. [5] 王玲书,张雅南,苏欢.一类具有阶段结构和饱和发生率的生态流行病模型的稳定性[J].工程数学学报, 2019, 36(4): 406418. WANG L S, ZHANG Y N, SU H. Stability of an eco-epidemiological model with stage structure and saturation incidence[J]. Chinese Journal of Engineering Mathematics,2019,36(4):406418. [6] 张梅,王玲书,贾美枝.一个捕食者染病、食饵具有阶段结构的生态流行病模型的稳定性[J].工程数学学报, 2022, 39(02): 224236. ZHANG M, WANG L S, JIA M Z. Stability of an eco-epidemiological model with disease in the predators and stage-structure for the prey[J].Chinese Journal of Engineering Mathematics,2022,39(2):224236. [7] ALMEID A R, CRUZA M C, MARTINSN B, et al. An epidemiological MSEIR model described by the caputo fractional derivative[J].International Journal of Dynamics and Control, 2019(3):776784. [8] RIHAN F A, LAKSHMANAN S, HASHISH A H, et al. Fractional-order delayed predator-prey systems with holling type-II functional response[J]. Nonlinear Dynamics, 2015, 80(1): 777789. [9] 钱蓉,肖敏,王璐.不同阶次下分数阶SIR传染病模型的稳定性分析[J].吉林大学学报(理学版),2021,59(4):796806. QIANG R, XIAO M, WANG L. Stability analysis of fractional-order SIR epidemic models with different orders[J].Journal of Jilin University(Science Edition),2021,59(4):796806.
