This modeling approach held sway for decades,<sup>1</sup> and some recent studies of Covid-19 spread in China have incorporated it (e.g. Kang et al. 2020; Li and Ma 2020). However, two significant weaknesses have been clear from the outset. First, geographic distance is often a poor proxy for travel cost, principally related to travel time, because of great variation in topography and transport infrastructure quality. The difference is most pronounced in the developing countries that are the focus of the present exercise. Fortunately, this weakness has been overcome by global-scale collaborative work in the OpenStreetMaps (OSM 2020) and Open Street Routing Machine (OSRM 2020) projects, which enable realistic estimation of point-to-point road distances and travel times for an arbitrary number of locales at no cost. Recent studies of Covid-19 spread in the European Union have employed road distances (e.g., Felbermayr, Chowdhry and Hinz 2020). This approximation for travel time is unlikely to introduce significant measurement errors in the European Union, given the density of its road network. For global applications, however, we believe that travel time should be the new measurement standard.

The second weakness of epidemic gravity models is structural: They capture the ultimate results of human travel and interaction, but with composite parameters that incorporate five unobserved elements: travel by individuals from locale A to locale B; their infection rate; the frequency of their interaction with people in locale B; the infection rate in locale B; and the likelihood that each interaction of an infected person with an uninfected counterpart will transmit an infection. In principle, technical progress in communications and infection testing has made four of the five elements susceptible to direct measurement. Where the requisite cell phone data are available, they can enable tracking of individuals between locales and (with sufficiently-precise coordinates and timestamps) identification of co-locations that are close enough for transmission to occur. Mass testing in each locale can produce relatively precise estimates of infection rates. If cell phone data and testing are fully mobilized, the five unknown elements of the composite gravity parameter are reduced to one for statistical estimation: the likelihood of infection per interaction. Even if testing data are not available, the statistical problem is reduced to finding a composite measure for the likelihood of infection. The need for a distance measure is eliminated, since travel and interactions are observed directly.

By implication, gravity-type studies of Covid-19 transmission in networks of places can be supplanted by models that use aggregative cell phone data when the following conditions hold: (1) Travelers carry cell phones with high probability; (2) access to the full set of time-and-locationstamped cell phone data for the entire network is free and open; and (3) local technical resources can accommodate the programming and computational demands imposed by very large-scale analysis of cell phone data. No setting currently meets these conditions, to our knowledge, but more limited Covid-19 studies are appearing within geographic domains bounded by the researchers’ access to cell phone data (e.g. Pullano et al. (2020) for transmission within France; Jia et al. (2020) for transmission from Wuhan, China).

Having reviewed the available options, we return to our motivating conditions: An optimal modeling approach must be _implementable immediately_ ; in any network of places where Covid19 infection data are available; scalable for entities of arbitrary size; solely reliant on free, publiclyavailable data; rigorously grounded in proven methodologies; and, far from least, _capable of_

> 1 For a detailed review of applications in epidemiology, see Truscott and Ferguson (2012).

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