Effects Of Individual Diversity On Network Evolution And Epidemic Spreading

Many complex systems, such as biological, social and communication systems, are composed of a large number of interacting individuals, which often exhibit a rich di-versity in many aspects. Since the end of the last century, the emerging interdisciplinary science of complex network, where nodes represent individuals and edges stand for in-teractions, has become a powerful approach to understanding many real-world complex systems and provided extensive applications in related fields. This thesis, in the frame-work of complex networks, focuses on the effects of diversity between individuals on the dynamics of network evolution and epidemic spreading on networks. Depending on the detailed description and definition of the individual diversity, the thesis is divided into the following three parts:1. Enlightened by the idea of "rich-get-richer", we have proposed two fitness de-pendent evolving network models:mutual selection model and deactivation model. In the first model, the probability of connection between any two nodes is determined by their fitnesses, independent of their degrees. We find that the stationary degree distri-bution of the network depends on the fitness distribution of the nodes. We obtain a structured exponential network when the fitness distribution of the individuals is homo-geneous and a structured scale-free network with heterogeneous fitness distributions. In addition, we show that the mutual selection model exhibits small-world properties with the scaling laws of the average clustering coefficient and the average shortest path length. In the second model, both the growth and aging of nodes have been considered in the network evolving. The probability of deactivation of a node is determined by its fitness. On the one hand, we find the large influence of the node fitnessses on the connectivity distribution. The homogeneous fitnesses generate exponentially decaying degree distri-butions, while the heterogeneous fitnesses result in power-law ones. On the other hand, we recover two universal scaling laws of the clustering coefficient, regardless of the fit-ness distributions. These results are consistent with what has been empirically observed in many real-world networks, and so the fitness dependent models provide a simple way to understand complex networks where intrinsic features of individual nodes drive their popularity.2. To understand how the diversity of node degrees influences the disease spread-ing, we have developed an SIV epidemic model including susceptible, infected and imperfectly vaccinated compartments on Watts-Strogatz (WS) small-world, Barabasi-Albert (BA) scale-free and random scale-free networks, respectively. The epidemic threshold and prevalence are analyzed. In the WS small-world network, the effective vaccination intervention is suggested and its influence on the threshold and prevalence is analyzed. In scale-free networks, the threshold is found to be strongly related both to the effective vaccination rate and to the degree distribution. Moreover, so long as vaccination is effective, it can linearly decrease the epidemic prevalence in small-world networks, whereas for scale-free networks it acts exponentially. These results can help in adopting pragmatic treatment upon diseases in structured populations.3. There is usually a diversity between connection densities of different com-munities in community networks. Regarding each community as a single entity, we further study an SIS epidemic model on a community network in order to show how the diversity of community structure influences the epidemic pattern. For simplicity, we consider a random network with two communities, where the disease is endemic in the dense community but alternates between outbreaks and extinctions in the sparse one. We provide a detailed characterization of the temporal dynamics of epidemic patterns in the sparse community. In particular, we investigate the time duration of both outbreak and extinction, and the time interval between two consecutive inter-community infections, as well as their probability distributions. Our mean-field theory determines these three timescales and their dependence on the average node degree of each community, the transmission parameters and the number of inter-community links, which are in good agreement with numerical simulations, except when the probability of overlaps between successive outbreaks is too large. These results can aid us in better understanding the bursty nature of disease transmission in a local community, and thereby suggesting effective time-dependent control strategies.