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Models of disease spreading are critical for predicting infection growth in a population and evaluating public health policies. However, standard models typically represent the dynamics of disease transmission between individuals using macroscopic parameters that do not accurately represent person-to-person variability. To address this issue, we present a dynamic network model that provides a straightforward way to incorporate both disease transmission dynamics at the individual scale as well as the full spatiotemporal history of infection at the population scale. We find that disease spreads through a social network as a traveling wave of infection, followed by a traveling wave of recovery, with the onset and dynamics of spreading determined by the interplay between disease transmission and recovery. We use these insights to develop a scaling theory that predicts the dynamics of infection for diverse diseases and populations. Furthermore, we show how spatial heterogeneities in susceptibility to infection can either exacerbate or quell the spread of disease, depending on its infectivity. Ultimately, our dynamic network approach provides a simple way to model disease spreading that unifies previous findings and can be generalized to diverse diseases, containment strategies, seasonal conditions, and community structures.
In this work we study a modified Susceptible-Infected-Susceptible (SIS) model in which the infection rate $lambda$ decays exponentially with the number of reinfections $n$, saturating after $n=l$. We find a critical decaying rate $epsilon_{c}(l)$ abo
Percolation theory is an approach to study vulnerability of a system. We develop analytical framework and analyze percolation properties of a network composed of interdependent networks (NetONet). Typically, percolation of a single network shows that
We propose a maximally disassortative (MD) network model which realizes a maximally negative degree-degree correlation, and study its percolation transition to discuss the effect of a strong degree-degree correlation on the percolation critical behav
We analyze the dynamics of a population of independent random walkers on a graph and develop a simple model of epidemic spreading. We assume that each walker visits independently the nodes of a finite ergodic graph in a discrete-time markovian walk g
We study a general epidemic model with arbitrary recovery rate distributions. This simple deviation from the standard setup is sufficient to prove that heterogeneity in the dynamical parameters can be as important as the more studied structural heter