Social networks with strong spatial embedding generate non-standard epidemic dynamics driven by higher-order clustering

Abstract

Some directly transmitted human pathogens such as influenza and measles generate sustained exponential growth in incidence, and have a high peak incidence consistent with the rapid depletion of susceptible individuals. Many do not. While a prolonged exponential phase typically arises in traditional disease-dynamic models, current quantitative descriptions of non-standard epidemic profiles are either abstract, phenomenological or rely on highly skewed offspring distributions in network models. Here, we create large socio-spatial networks to represent contact behaviour using human population density data, a previously developed fitting algorithm, and gravity-like mobility kernels. We define a basic reproductive number R0 for this system analogous to that used for compartmental models. Controlling for R0, we then explore networks with a household-workplace structure in which between-household contacts can be formed with varying degrees of spatial correlation, determined by a single parameter from the gravity-like kernel. By varying this single parameter and simulating epidemic spread, we are able to identify how more frequent local movement can lead to strong spatial correlation and thus induce sub-exponential outbreak dynamics with lower, later epidemic peaks. Also, the ratio of peak height to final size was much smaller when movement was highly spatially correlated. We investigate the topological properties of our networks via a generalized clustering coefficient that extends beyond immediate neighbourhoods, identifying very strong correlations between 4th order clustering and non-standard epidemic dynamics. Our results motivate the joint observation of incidence and socio-spatial human behaviour during epidemics that exhibit non-standard incidence patterns. Author SummaryEpidemics are typically described using a standard set of mathematical models that do not capture social interactions or the way those interactions are determined by geography. Here we propose a model that can reflect social networks influenced strongly by the way people travel and we show that they lead to very different epidemic profiles. This type of model will likely be useful for forecasting.