Contagion is the spreading of a particular event, such as infectious disease, fashion, product adoption, financial shock, riot or any other contagious events, behaviors and opinions, by one susceptible entity directly or indirectly contacting another infectious entity. For example, like the spreading of infectious disease, fashion contagion happens when someone adopts a style of clothing or a way of behaving of another one. Financial contagion occurs when other institutions are affected by certain financial shocks following some initially affected institutions. It suggests that massive contagion may be driven not only by infectious individuals but also by a critical mass of susceptible individuals (Watts and Dodds 2007), while the former have more impact on the speed of the contagion process, the latter may have more impact on final size” (Goldenberg, Han, Lehmann and Hong 2009). The infectivity and susceptibility of humans, animals or other entities for an infectious disease can be individually heterogeneous, as different hosts might have different worm burden, genes, pathogenicity and immune levels (Keeling and Rohani 2008). For social contagion, individual entities' ability to influence or to be influenced can be variant due to certain personal traits such as being attractive, convincing, charismatic, magnetic, innovative, information-seeking, confident, and assertive, etc (Katz 1957; Weimann 1991; Chaney 2001; Thoburn, 2004; Goldenberg, Han, Lehmann and Hong 2009). Fast measuring and ranking infectivity and susceptibility for biological and social contagion at individual level can help control the contagion process more precisely and efficiently. For example, with infectivity and susceptibility estimates and ranks of each individual entity, one can identify those key individuals who might have the potential of disproportionally affecting the spread of contagion, and thus implement more efficient vaccination and quarantine, or more in-depth and relevant genetic examinations and pathological research, to optimize our use of limited medical or business resources for contagion control and prevention. In recent years, many firms are picking and relying on contagious consumers as natural trendsetters, rather than expensive celebrities or models, to efficiently influence consumers' product adoption.
In epidemiology, infectivity is usually measured at the population level by incidence, which is the probability of occurrence of a given medical condition in a population within a specified period of time, but not the ability of a specific individual to establish an infection. In social fields, questionnaires based on individual's personality are used to measure individuals' ability to infect others, but the self-report methods of questionnaires take what people claim themselves (or others) to be, and may involve high cost as the number of the surveyed people increases. Here arises a problem: how to measure or infer individual-level infectivity and susceptibility to various contagions for large number of entities?
Today, with the advancement of information technology and data mining techniques, more and more individual-level behavioral and relationship data can be collected and analyzed. That could be a promising direction for solving the problem. However, most quantitative works related to contagion have primarily focused on population-scale epidemic rather than individual-level dynamics. Usually these works only test the empirical existence of certain contagion, or describe and simulate the diffusion processes in contagion using aggregate and non-individually heterogeneous parameters such as outbreak thresholds and state transferring probability via artificial agents, but seldom estimate heterogeneous individual-level parameters for real people from real world events. Nowadays, the well-known degree centrality concepts in social network analysis are often used to measure individuals' centrality characteristics via observed or inferred relations among people. But the “centrality” measurements based on the number of connections one have, measure “exposure” rather than “virulence”. Although the more connections one has, the more exposure he or she can get. But the final impact is given by the multiplication of exposure with virulence. For the purpose of big impact, a virus of high virulence should be identified and be offered more exposure. At individual level, some work has been done on inferring whether or not an individual entity influences his/her specific friend's certain behavior, but it measures dyad “yes-or-no” relationships between people rather than individual specific traits. Capable of inferring underlying trait and ability, item response theory based latent trait models are used for examinee-test interactions in psychometrics, but they commonly do not include environmental covariates for control. (Birnbaum 1968; Freeman 1979; Case 1991; Hambleton and Swaminathan 1985; Dodds and Watts 2005; Rossi, Allenby and McCulloch 2005; Keeling and Rohani 2008; Hartmann et al. 2008; Trusov et al 2009, Luo et al 2013)