Studies In The Epidemical Model Of Mobile Individuals On Finite-size Regular Lattice Networks

Complex networks describe a wide range of systems in nature and society. Frequently cited examples include internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, et al. Studies show that these complex networks exhibit some characters, such as Small-World effect and scale free property and so on. These characters can not be explained by regular or random networks theory. The research of epidemical model in complex networks has also attracted many researchers'attention. It is shown that there is smaller threshold of disease spreading in other complex networks compared with regular lattice, even more the absence of thresholds of percolation and epidemic.We summarize the basic concept and typical mechanism model of complex networks, and we especially introduce some main epidemical models and the spreading behavior of epidemical model on complex networks, and we pay more attention to the newest investigation of disease spreading in small world and scale free networks.On this base, we establish the epidemical model of mobile individuals in regular lattice. The behaviors of steady states of epidemic propagation are studied using large scale simulations. The influence of these parameters (the automata density, the jumping probability etc.) on epidemic spreading is studied, and the critical jumping probability and the critical population density are observed.Second, we establish the Mean-Field equations which are good agreement with our network model. Here the efficient contact rate is not a constant but a function of the population density, the point is different with conventional Mean-field equations. Through an approximate equivalence relation between network model and mean-field equations, the concrete form of the efficient contact rate is obtained.At last, the critical behaviors of epidemic propagation are studied using large scale simulations. The ration of new infected population exponentially increases with time above the critical population density. The exponential coefficient shows power-law relations with the jumping probability, and its exponent decreases non-linearly with the population density. And we also found that the mean-field equation can't describe the critical behavior of epidemic spreading, which is different with steady state.