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Many complex networks exhibit vulnerability to spreading of epidemics, andsuch vulnerability relates to the viral strain as well as to the networkcharacteristics. For instance, the structure of the network plays an importantrole in spreading of epidemics. Additionally, properties of previous epidemicmodels require prior knowledge of the complex network structure, which meansthe models are limited to only well-known network structures. In this paper, wepropose a new epidemiological SIR model based on the continuous time Markovchain, which is generalized to any type of network. The new model is capable ofevaluating the states of every individual in the network. Through mathematicalanalysis, we prove an epidemic threshold exists below which an epidemic doesnot propagate in the network. We also show that the new epidemic threshold isinversely proportional to the spectral radius of the network. In particular, weemploy the new epidemic model as a novel measure to assess the vulnerability ofnetworks to the spread of epidemics. The new measure considers all possibleeffective infection rates that an epidemic might possess. Next, we apply themeasure to correlated networks to evaluate the vulnerability of disassortativeand assortative scalefree networks. Ultimately, we verify the accuracy of thetheoretical epidemic threshold through extensive numerical simulations. Withinthe set of tested networks, the numerical results show that disassortativescale-free networks are more vulnerable to spreading of epidemics thanassortative scale-free networks.

Generalized individual-based epidemic model for vulnerability assessment of correlated scale-free complex networks