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 nonstandard 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 behavior using human population-density data, a previously developed fitting algorithm, and gravity-like mobility kernels. We define a basic reproductive number [Formula: see text] for this system, analogous to that used for compartmental models. Controlling for [Formula: see text], 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 subexponential 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 neighborhoods, identifying very strong correlations between fourth-order clustering and nonstandard epidemic dynamics. Our results motivate the observation of both incidence and socio-spatial human behavior during epidemics that exhibit nonstandard incidence patterns.
Highlights
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
Semi-empirical networks that arise from detailed simulations [8] may have complex higher moments; their impact on epidemic dynamics is obscured by the variance of their offspring distribution
Epidemics can be understood in terms of compartmental models, which are more tractable mathematically and are equivalent to large network models with very simple topologies [10]
Summary
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. For a limited set of network types, we can use analytical expressions for higher moments of the degree distribution to calculate key properties of their potential epidemics, such as the probability of epidemic establishment and cumulative incidence [6, 7]. These higher-order moments are tractable for some special cases, they are seldom the primary target of theoretical studies.
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