Inferring network structure from secondary and tertiary infections on complex networks

Abstract

Numerical experiments on the spread of infection on the three standard models of random and complex networks: Erd¨os-R´enyi (ER), Barab´asi-Albert (BA), and Watts-Strogatz (WS), to determine how the secondary R₀ and tertiary R₁ infections appear using different constant infection probability ρ. The number R₀ of new infections arising from random introduction of one infected individual (patient zero) into an uninfected system is also known as the basic reproduction number. We utilize the number R₁ of new and unique agents that are successively infected by the R₀ individuals, given the same ρ-value. We show that the dependence of R₁ on R₀ can determine whether one is closer to, or farther from, ER-like networks. We further show that the deviation of WS and BA networks away from the ER network appears to be towards opposite directions. This basic result is used to infer the structures of real-world networks.