Beyond network structure: How heterogenous susceptibility modulates the spread of epidemics

The compartmental models used to study epidemic spreading often assume the same susceptibility for all individuals, and are therefore, agnostic about the effects that differences in susceptibility can have on epidemic spreading. Here we show that–for the SIS model–differential susceptibility can make networks more vulnerable to the spread of diseases when the correlation between a node’s degree and susceptibility are positive, and less vulnerable when this correlation is negative. Moreover, we show that networks become more likely to contain a pocket of infection when individuals are more likely to connect with others that have similar susceptibility (the network is segregated). These results show that the failure to include differential susceptibility to epidemic models can lead to a systematic over/under estimation of fundamental epidemic parameters when the structure of the networks is not independent from the susceptibility of the nodes or when there are correlations between the susceptibility of connected individuals. The contact networks that underlie the spread of diseases, behaviors [1] and ideas have heterogenous topologies [2–4], but also, exhibit heterogeneity in the susceptibility of individuals [7–11]. In recent years the compartmental models used to study the spread of behaviors have been generalized to include the effects of network topology, but not the effects of both topology and differences in the susceptibility of individuals [4,12,13]. Generalizations including the network topology have revealed an intimate connection between the spectral properties of the contact network, and the basic reproductive number of infectious diseases, showing that for a network described by an arbitrary degree distribution the basic reproductive number of an infection (R0), is proportional to the largest eigenvalue of the contact network’s adjacency matrix [13]. For highly heterogenous networks, this eigenvalue is always larger than 1 meaning that network heterogeneity can reduce and even eliminate the existence of an epidemic threshold. Our understanding of the role of heterogeneous network topologies in epidemic spreading, however, has not been matched by a comparable development in our understanding of the role of heterogeneity in the susceptibility of individuals. Yet, differential susceptibility, defined as the variation in the susceptibility of individuals is as widespread as network heterogeneity. For example, genetic conditions are known to cause heterogenous reactions to HIV [7,8], H5N1 influenza [9], and the Encephalomyocarditis virus, [10] . Differential susceptibility can also be the result of differences in age as it has been shown in the case of Hantaan Virus in mice [11]. Other mechanisms leading to differential susceptibility include previous disease history, obesity, stress, history of drug abuse, physical trauma or differences in healthcare quality, which could emerge from discriminatory practices or individual self-selection. The biological prevalence of differential susceptibility, therefore, invites us to ask whether relaxing the assumptions of homogeneous susceptibility has consequences for the spread of epidemics that are tantamount to the relaxation of assumptions of homogeneity in the connectivity of the contact network. The incorporation of differential susceptibility into epidemic models, however, also introduces a new dimension to epidemic modeling, since there are multiple ways for individuals with differences in susceptibility to be arranged in a network. For instance, the mixing patterns and segregation of populations [14] imply that differential susceptibility can be structured through non-trivial correlations. Examples here include schools, nursing homes and hospitals, where children, senior citizens and patients, who can be more susceptible to diseases, spend more time together. These mixing patterns imply that a complete ar X iv :1 40 3. 27 08 v1 [ ph ys ic s. so cph ] 1 0 M ar 2 01 4