摘要
基于传染病动力学建模方法,综合性地研究了双蠕虫交互的AH-SIBV传播模型.利用微分方程定性理论对模型进行了分析和谱半径理论求出了模型的基本再生数,并利用李雅普诺夫函数和劳斯-霍尔维茨稳定性判据证明了模型的双平衡点在可行域内的全局渐进稳定性.研究了双蠕虫交互的传播规律,得到控制蠕虫传播的阈值.最后,MATLAB仿真实验结果验证了理论分析结果,证明了本模型的正确性、有效性和实用性,为采取有效措施控制蠕虫的大规模传播提供了有价值的理论依据.
Based on the dynamic epidemical models,it comprehensively studies a two-worms interactive propagation model. By using the qualitative theory of differential equation,the propagation dynamics of worms is researched. It gets the model＇s basic reproduction number by using the theory of spectral radius,and proves the globally asymptotical stability of the two equilibrium by using Lyapunov functions and Routh- Hurwitz stability criterion. The propagation laws of two-worms interaction are discussed,and the threshold of controlling worms is gained. Finally,MATLAB numerical simulation verifies our theoretical results and proves the validity,effectiveness and practicability of this model,providing valuable theoretical basis for taking effective measures to control the large-scale propagation of worms.
出处
《福建师范大学学报（自然科学版）》
CAS
CSCD
北大核心
2015年第6期24-31,共8页
Journal of Fujian Normal University：Natural Science Edition
基金
国家自然科学基金资助项目(61202450
U1405255)
福州市科技局项目(2013-G-84)
福建师范大学创新研究团队(IRTL1207)
关键词
传染病动力学
基本再生数
平衡点
全局渐进稳定
阈值
dynamic epidemical models
basic reproduction number
equilibrium
globally asymptotical stability
threshold
