A number of epidemics, including the SARS-CoV-1 epidemic of 2002-2004, have been known to exhibit superspreading, in which a small fraction of infected individuals is responsible for the majority of new infections. The existence of superspreading implies a fat-tailed distribution of infectiousness (new secondary infections caused per day) among different individuals. Here, we present a simple method to estimate the variation in infectiousness by examining the variation in early-time growth rates of new cases among different subpopulations. We use this method to estimate the mean and variance in the infectiousness, β, for SARS-CoV-2 transmission during the early stages of the pandemic within the United States. We find that σβ/μβ ≳ 3.2, where μβ is the mean infectiousness and σβ its standard deviation, which implies pervasive superspreading. This result allows us to estimate that in the early stages of the pandemic in the USA, over 81% of new cases were a result of the top 10% of most infectious individuals.
An actomyosin network is an active mesoscopic material, formed by actin and myosin motors, that gives structure to cells and plays a key role in cell locomotion, transport, cell deformation, and mechanical sensing. Several actinbinding proteins such as a-actinin and Arp2/3 allow the myosin motors to produce large-scale motions by linking together and branching actin filaments. The type and degree of connectivity regulates the dynamical behavior of the motorized actomyosin network. Percolation of connectivity in actomyosin networks has previously been studied experimentally and using Coarse-Grained molecular simulations. In this work, we present a simple analytical model, based on Flory-Stockmayer theory, that describes the conditions under which connectivity percolation of the network occurs. We compare the results of this new model to a Coarse-Grained mechanochemical model of actomyosin networks. We find that Arp2/3 modulates the connectivity of the actin network in a non-monotonic way. Finally, we relate connectivity percolation to rigidity percolation and show how the relative concentrations of actin-binding proteins change the behavior of the network from a sol, to a contracting gel, to a rigid gel.
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