Epidemic Spreading Model With Virus Variation And Its Stability

Recently, with the rapid development of complex network science, the studies concern ing the behavior network transmission dynamics have been deeply explored. The spreading of epidemic is common behavior of complex network, and biological and computer epidemic are in particular as two forms of network system existing in the nature and the Internet widely. As an interdisciplinary science, the complex network can be utilized to describe such a network system and in-depth investigation of the features and spreading of disease can be investigated from the perspective of network transmission dynamics.As tremendous negative side of the epidemic to human beings together with easy variation due to its simple structure, the complexity has been consequently increased. In this dissertation, we study and propose three epidemic spreading models and discuss the existing conditions and the stability of equilibrium by using the theory of differential dynamic system, meanwhile, the theorem and results are further verified by simulations. The major contents and contributions of the dissertation are as follows.Firstly, we develop an SIS epidemic spreading model with virus variation, and the existing conditions of dieses-free equilibrium and endemic equilibrium are deduced by the calculation of basic reproductive rate with two given epidemics.The existing conditions and the stability of equilibrium are explored by using the theory of differential dynamic system.Moreover, the theorem and results are further verified by simulations. The results indicate that, the outbreaks of epidemic are highly correlated with its basic reproductive rate.Secondly, we establish an SEIR epidemic spreading model with virus variation, specifically, the existing conditions of dieses-free equilibrium and endemic equilibrium are deduced by the calculation of basic reproductive rate with next generation generator matrix methods.The globally asymptotical stability of equilibrium is explored by Lyapunov fuction modeling. Moreover, the obtained results are proved by some simulations. The results show that, the outbreaks of epidemic can be effectively controlled by enhancing its recovery rate or cure rate before the variation of epidemic.Lastly, the SEI1I2 RS epidemic spreading model in mobile environment is proposed by considering the mobility of node in real network, specifically, the existing conditions of dieses-free equilibrium and endemic equilibrium are deduced by the calculation of basic reproductive rate with next generation generator matrix method s.Besides, the globally asymptotical stability of equilibrium is explored by the theory o f differential system dynamics, and further verified by simulations. The results show that, effective measures can be taken to isolate and control the spreading of the epidemic from its spreading source and radius.