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In this paper we create a compartmental, stochastic process model of SARS-CoV-2 transmission, where the process's mean and variance have distinct dynamics. The model is fit to time series data from Washington from January 2020 to March 2021 using a deterministic, biologically-motivated signal processing approach, and we show that the model's hidden states, like population prevalence, agree with survey and other estimates. Then, in the paper's second half, we demonstrate that the same model can be reframed as a branching process with a dynamic degree distribution. This perspective allows us to generate approximate transmission trees and estimate some higher order statistics, like the clustering of cases as outbreaks, which we find to be consistent with related observations from contact tracing and phylogenetics.

Background: The first confirmed case of SARS-CoV-2 in North America was identified in Washington state on January 21, 2020. We aimed to quantify the number and temporal trends of out-of-state introductions of SARS-CoV-2 into Washington., Methods: We conducted a phylogenetic analysis of 11,422 publicly available whole genome SARS-CoV-2 sequences from GISAID sampled between December 2019 and September 2020. We used maximum parsimony ancestral state reconstruction methods on time-calibrated phylogenies to enumerate introductions/exports, their likely geographic source (e.g. US, non-US, and between eastern and western Washington), and estimated date of introduction. To incorporate phylogenetic uncertainty into our estimates, we conducted 5,000 replicate analyses by generating 25 random time-stratified samples of non-Washington reference sequences, 20 random polytomy resolutions, and 10 random resolutions of the reconstructed ancestral state., Results: We estimated a minimum 287 separate introductions (median, range 244-320) into Washington and 204 exported lineages (range 188-227) of SARS-CoV-2 out of Washington. Introductions began in mid-January and peaked on March 29, 2020. Lineages with the Spike D614G variant accounted for the majority (88%) of introductions. Overall, 61% (range 55-65%) of introductions into Washington likely originated from a source elsewhere within the US, while the remaining 39% (range 35-45%) likely originated from outside of the US. Intra-state transmission accounted for 65% and 28% of introductions into eastern and western Washington, respectively., Conclusions: There is phylogenetic evidence that the SARS-CoV-2 epidemic in Washington is continually seeded by a large number of introductions, and that there was significant inter- and intra-state transmission. Due to incomplete sampling our data underestimate the true number of introductions.