考虑随机与扩散对传染病系统动力学的影响任务书

 2021-10-13 08:10

1. 毕业设计（论文）的内容和要求

研究一类含空间扩散和随机扰动的传染病系统的动力学行为。

通过分析系统特征方程以及构建Lyapunov 函数，证明确定性传染病系统的地方病平衡点的局部和全局稳定性。

对于空间扩散传染病系统，给出地方病平衡点的全局稳定性的条件。

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2. 参考文献

1.Cantrell R, Cosner C. Spatial ecology via reaction-diffusion equations. Wiley; 2003.2.Wang K, Wang W, Song S. Dynamics of an HBV model with diffusion and delay. J Theor Biol 2008;253(1):3644.3.Mulone G, Straughan B, Wang W. Stability of epidemic models with evolution. Studies Appl Math 2007;118(2):11732.4.Bandyopadhyay M, Chattopadhyay J. Ratio-dependent predator-prey model: effect of environmental fluctuation and stability. Nonlinearity2005;18(2):91336.5.Dalal N, Greenhalgh D, Mao X. A stochastic model for internal HIV dynamics. J Math Anal Appl 2008;341(2):1084101.6.Tornatore E, Buccellato S, Vetro P. Stability of a stochastic SIR system. Phys A 2005;354:11126.7.Yu J, Jiang D, Shi N. Global stability of two-group SIR model with random perturbation. J Math Anal Appl 2009;360(1):23544.8.Jiang D, Ji C, Shi N, Yu J. The long time behavior of DI SIR epidemic model with stochastic perturbation. J Math Anal Appl 2010;372(1):16280.9.Xiao D, Ruan S. Global analysis of an epidemic model with nonmonotone incidence rate. Math Biosci 2007;208(2):41929.10.Liu M, Wang K. Global stability of a nonlinear stochastic predator-prey system with Beddington-DeAngelis functional response. Commun Nonlinear SciNumer Simulat 2011;16(3):111421.11.Lv J, Wang K. Asymptotic properties of a stochastic predator-prey system with Holling II functional response. Commun Nonlinear Sci Numer Simulat2011;16(10):403748.

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