Characterization of Complex Networks for Epidemics Modeling

Complex networks have certain properties that characterize them. These inherent properties can be measured and applied in other fields of research. To this end, we characterize several complex networks from different domains using concepts from graph theory. In particular, the node degrees, graph spectral radius, degree assortativity, and the entire topological structure of selected complex networks are studied on the Susceptible, Infectious, Recovered (SIR) epidemic model. The results show that various complex networks properties affect the epidemic model differently. For instance nodes with high average degrees with corresponding high clustering coefficients are seen to be effective in spreading epidemics. Also the degree distribution patterns have an effect on the spreading rate of epidemic, that is dis-assortative networks are good conduits for the epidemic spreading if low degree nodes are in turn connected to high degree nodes. These results have given us a new dimension on how epidemic spreadings can be studied using complex networks as these networks possessed in them certain properties that resemble that of human society. To the best of our knowledge, this is the first work that simulated the SIR model using heterogenous complex network properties in order to study their cumulative effects on epidemic spreading.