Rearch On The Transmission Dynamics On Complex Networks

Transmission dynamics of complex network research is a very new and broader issue, and it is a new direction in the complexity of scientific research section. At present, it has been widely used in many areas. In this paper we study the transmission dynamics of disease and public opinion on the complex networks.We summarize the basic concept and typical mechanism model of complex networks, and we especially introduce some main transmission models and the spreading behavior of transmission model on complex networks, and we pay more attention to the newest investigation of spreading behavior in small world and scale free networks.At first we establish an epidemical model of mobile individual, which takes into account births and deaths of people as well as seasonal variation of the transmission probability. And we study the propagation behaviors and the people's distribution trait of epidemic spreading in mobile individuals. Simulation results show that there exists a critical value of infected rate fluctuating amplitude, above which the epidemic can spread in whole population. Moreover, with the value of infected rate fluctuating amplitude increasing, the spatial distribution of infected population exhibit the spontaneous formation of irregular spiral waves and cluster phenomena, at the same time, the density of different population will oscillate automatically with time. What's more, the traits of dynamic grow clearly and stably when the time and the value of infected rate fluctuating amplitude increasing.Then we introduce noisy population to above model, and establish epidemic spreading model in diffusion population considering the effects of noisy population. A node can contain more than one people in system. It is investigated that how to influence the epidemic spreading in diffusion population by the noisy. It is found that infected population density changing with time evolution occurre a clearly cyclical synchrotron self-oscillation phenomenon under steady state in epidemic spreading, and the synchrotron self-oscillation behavior is strengthen along with the noisy increasing, which is confirmed through analyzing phase pattern and collective synchronization order parameter. At the same time, the different population density spatial distribution are more disorder with noisy increased, which induce to the infected population and susceptible population contacting more frequently, and it lead to the number of infected population and the death for infected are increased with the noisy increased.We investigate the critical behavior of an epidemical model in a diffusive population mediated by a static vector environment on 2D network using Finite-size and short-time dynamic scaling relations. We find that this model presents a dynamical phase transition from disease-free state to endemic state with a finite population density. Finite-size and short-time dynamic scaling relations are used to determine the critical population density and the critical exponents characterizing the behavior near the critical point. The results are compatible with the universality class of directed percolation coupled to a conserved diffusive field with equal diffusion constants.At the same time, public opinion evolution model is investigated on scale free network in which the topology structure is always changing in this paper. In the model we consider the influence of a constant external fieldφ₀ and node's inertia e^γk_h on publicopinion evolution, here we define the public opinion evolution parameter asφ₀e^γk_h. It is indicated that public opinion evolution and network topological structure interact with each other, and they are all influenced by the external fieldφ₀, and the node's inertiafactorγ.Without considering the influence of node's inertia, it is found that the time evolution of the public opinion not only is controlled by the topological structure , but also induces the change of the topological structure: The network structure is no longer the initial scale-free network, but Poisson distribution. With the time evolution in system, there is obvious convergenve effect of the public opinions. The dozens of opinions in initial state evolve with the time, Most of them perish and only a few of them remain and development after a long time. The trend is coincident with the evolution of the public opinion, views and beliefs in the society.Considering the influence of node's inertia, it is found that degree distribution gradually gets away typical power law distribution with the public opinion time evolution in our model. The number of public opinion will decrease by the time evolution without considering node's inertia. In other words, the evolution of network itself must obliterate some public opinion value. The result will take on colorful changes with time evolution.when considering node's inertia. As the parameterγ= 0.3, no matter how the time evolves, both the opinion's number and distribution are changeless. But when the parameterγ=-10, the number of opinion decrease sharply at the beginning, then this tendency slow down, until there is only one opinion value remaining. We draw the conclusion that adjust of node's inertia factorγcan control the opinion value's number, which even controls the rate of change.