Some directly transmitted human pathogens such as influenza and measles generate sustained exponential growth in incidence, and have a peak incidence that is consistent with age-groupspecific depletion of susceptible individuals. Many do not. While a prolonged exponential phase typically arises in traditional disease-dynamic models, quantitative descriptions of nonexponential growth are either highly abstract, phenomenological or ignore well-described social structuring. Here, we create large socio-spatial human contact networks using population density data, a previously developed fitting algorithm, and gravity-like mobility kernels. We define the basic reproductive number for this system to be analogous to the traditional compartmental model definition. 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 the strength of spatial correlation required to induce sub-exponential outbreak dynamics with lower, later peaks. We investigate the topological properties of our networks via a generalized clustering coefficient that extends beyond immediate neighbourhoods, identifying topological properties of these networks that correlate with strictly sub-exponential spread. 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.