S evere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) is the etiologic agent of the current rapidly growing outbreak of coronavirus disease (COVID-19), originating from the city of Wuhan, Hubei Province, China (1). Initially, 41 cases of "pneumonia of unknown etiology" were reported to the World Health Organization by the Wuhan Municipal Health Committee at the end of December 2019 (2). On January 8, 2020, the pathogen was identified (1), and human-to-human transmission was reported soon after. By January 21, most provinces of China had reported COVID-19 cases. By March 16, the outbreak had led to >170,000 total confirmed cases and >6,500 deaths globally. In a period of 3 months, an outbreak of apparent idiopathic pneumonia had become the COVID-19 pandemic.Studying dynamics of a newly emerged and rapidly growing infectious disease outbreak, such as COVID-19, is important but challenging because

124 Main text including references and figure captions: 3,945 All rights reserved. No reuse allowed without permission. author/funder, who has granted medRxiv a license to display the preprint in perpetuity. AbstractThe novel coronavirus (2019-nCoV) is a recently emerged human pathogen that has spread widely since January 2020. Initially, the basic reproductive number, R0, was estimated to be 2.2 to 2.7. Here we provide a new estimate of this quantity. We collected extensive individual case reports and estimated key epidemiology parameters, including the incubation period. Integrating these estimates and high-resolution real-time human travel and infection data with mathematical models, we estimated that the number of infected individuals during early epidemic double every 2.4 days, and the R0 value is likely to be between 4.7 and 6.6. We further show that quarantine and contact tracing of symptomatic individuals alone may not be effective and early, strong control measures are needed to stop transmission of the virus.

Although the use of phylogenetic trees in epidemiological investigations has become commonplace, their epidemiological interpretation has not been systematically evaluated. Here, we use an HIV-1 within-host coalescent model to probabilistically evaluate transmission histories of two epidemiologically linked hosts. Previous critique of phylogenetic reconstruction has claimed that direction of transmission is difficult to infer, and that the existence of unsampled intermediary links or common sources can never be excluded. The phylogenetic relationship between the HIV populations of epidemiologically linked hosts can be classified into six types of trees, based on cladistic relationships and whether the reconstruction is consistent with the true transmission history or not. We show that the direction of transmission and whether unsampled intermediary links or common sources existed make very different predictions about expected phylogenetic relationships: (i) Direction of transmission can often be established when paraphyly exists, (ii) intermediary links can be excluded when multiple lineages were transmitted, and (iii) when the sampled individuals' HIV populations both are monophyletic a common source was likely the origin. Inconsistent results, suggesting the wrong transmission direction, were generally rare. In addition, the expected tree topology also depends on the number of transmitted lineages, the sample size, the time of the sample relative to transmission, and how fast the diversity increases after infection. Typically, 20 or more sequences per subject give robust results. We confirm our theoretical evaluations with analyses of real transmission histories and discuss how our findings should aid in interpreting phylogenetic results.HIV-1 | transmission | paraphyly | coalescent | phylogeny

Pathogen phylogenies are often used to infer spread among hosts. There is, however, not an exact match between the pathogen phylogeny and the host transmission history. Here, we examine in detail the limitations of this relationship. First, all splits in a pathogen phylogeny of more than 1 host occur within hosts, not at the moment of transmission, predating the transmission events as described by the pretransmission interval. Second, the order in which nodes in a phylogeny occur may be reflective of the within-host dynamics rather than epidemiologic relationships. To investigate these phenomena, motivated by within-host diversity patterns, we developed a two-phase coalescent model that includes a transmission bottleneck followed by linear outgrowth to a maximum population size followed by either stabilization or decline of the population. The model predicts that the pretransmission interval shrinks compared with predictions based on constant population size or a simple transmission bottleneck. Because lineages coalesce faster in a small population, the probability of a pathogen phylogeny to resemble the transmission history depends on when after infection a donor transmits to a new host. We also show that the probability of inferring the incorrect order of multiple transmissions from the same host is high. Finally, we compare time of HIV-1 infection informed by genetic distances in phylogenies to independent biomarker data, and show that, indeed, the pretransmission interval biases phylogeny-based estimates of when transmissions occurred. We describe situations where caution is needed not to misinterpret which parts of a phylogeny that may indicate outbreaks and tight transmission clusters.

Erik Volz and colleagues use HIV genetic information from a cohort of men who have sex with men in Detroit, USA to dissect the timing of onward transmission during HIV infection. Please see later in the article for the Editors' Summary