Epidemic Spread on Weighted Networks

The contact structure between hosts shapes disease spread. Most network-based models used in epidemiology tend to ignore heterogeneity in the weighting of contacts between two individuals. However, this assumption is known to be at odds with the data for many networks (e.g. sexual contact networks) and to have a critical influence on epidemics' behavior. One of the reasons why models usually ignore heterogeneity in transmission is that we currently lack tools to analyze weighted networks, such that most studies rely on numerical simulations. Here, we present a novel framework to estimate key epidemiological variables, such as the rate of early epidemic expansion () and the basic reproductive ratio (), from joint probability distributions of number of partners (contacts) and number of interaction events through which contacts are weighted. These distributions are much easier to infer than the exact shape of the network, which makes the approach widely applicable. The framework also allows for a derivation of the full time course of epidemic prevalence and contact behaviour, which we validate with numerical simulations on networks. Overall, incorporating more realistic contact networks into epidemiological models can improve our understanding of the emergence and spread of infectious diseases.Author Summary: Understanding how infectious diseases spread has public health and ecological implications. The contact structure between hosts strongly affects this spread. However, most studies assume that all types of contacts are identical, when in reality some individuals interact more strongly than others. This is particularly striking for sexual-contact networks, where the number of sex acts is not identical for all partnerships. This heterogeneity in activity can either speed up or slow down epidemic spread depending on how strongly the individuals' number of contacts coincides with their activity. There are two limitations to current frameworks that can explain the lack of studies on weighted networks. First, analytical results are difficult to obtain, which requires numerical simulations. Second, inferring weighted networks from survey data is extremely difficult. Here, we present a novel framework that allows to alleviate these two limitations. Building on configuration type network epidemic approaches, we manage to capture disease spread on weighted networks from the distribution of the number of contacts and distribution of the number of interaction events (e.g. sex acts). This allows us to derive analytical estimates for the epidemic threshold and the rate of spread of the disease. It also allows us to readily incorporate survey data, as illustrated in this study with data from the National Survey of Sexual Attitudes and Lifestyles (NATSAL) carried out in the UK.