and air pollution. Although we find significant variables in each locale, we find no variable that meets all of our criteria for the core model: universally available and relevant, statistically significant, and identically signed. Further exploration may well identify additional core variables, and this is an important domain for future research. For the purposes of this paper, however, we believe that presentation of diverse country-specific results that cannot be replicated elsewhere would distract attention from our central themes.

# **8.  Summary and Conclusions**

This paper has been motivated by the urgent need for a model of Covid-19 transmission between locales that can be applied anywhere in the developing world. To meet this challenge, we focus on developing a model that is (1) implementable anywhere spatially-disaggregated Covid-19 infection data are available; (2) scalable for entities of arbitrary size, from individual regions to countries of continental scale; (3) reliant solely on data that are free and open to public access; (4) grounded in a rigorous, proven methodology; and (5) capable of forecasting future hotspots with enough accuracy to provide useful alerts.

After a review of existing approaches and technical resources, we opt for a model that combines a gravity-type specification of spatial interaction; the use of travel time rather than geographic distance as a measure of spatial friction; and a model of growth dynamics based on the Gompertz variant of the generalized logistic model. Using free, publicly-available data for the United States, the Philippines and South Africa’s Western Cape province, we estimate a core model of infection growth in a locale that proxies local interactions with population density (D) and incorporates interactions with other locales in a theoretically-derived variable (W) that is the summation of their infections, weighted inversely by an exponential transformation of travel time. We find high significance and the appropriate signs for D and W for all three countries, and for changes over 14 and 28 days. After extensive experimentation, we find no other variable that is common to the three countries, publicly available, statistically significant and identically signed. We also find that the exponential transformation of travel time is less than unitary in all three cases, which indicates that infection growth in a locale is affected by the scale of infections in relatively distant locales.

We assess the accuracy of the model by forecasting 14 and 28 days in advance, using only information available on the first day of the forecast. For the United States, we find that 52.5% of model-identified hotspots are top-5% actual hotspots for 14-day predictions; 41.3% are actual top5% hotspots for 28-day predictions. For the Philippines, we find that 42.5% of model-identified hotspots are actual top-6% hotpots for 14-day predictions and 22.5% for 28-day predictions. In Western Cape province, the model identifies the actual top-10 sub-districts with 70% accuracy for 14-day predictions and 50% accuracy for 28-day predictions. We conclude that the accuracy levels are sufficient to warrant use of this approach for community alerts, with appropriate caveats about expected accuracy. Among these is the notable bifurcation of predictions that we have discussed above.

To conclude, we believe that this exercise has demonstrated the feasibility and accuracy of a modeling approach that relies solely on free, publicly-available data and can be applied in any developing country or region that reports spatially-disaggregated Covid-19 infection data. We do 17