This paper surveys estimates of the transmission features of the novel coronavirus, and then proposes a model to address sample-selection bias in estimated determinants of infection. Containment assumptions of the infection forecasting models depend on assumed effects of policies and self-regulating behavior. In the commons dilemma of the pandemic, the perceived ‘low risks’ of unregulated marginal choices do not reflect the full social cost, implying non-pharmaceutical interventions (NPI) to reduce mortality can enhance social welfare. As more economic activity renews with liftings of restrictive NPI (RNPI), a critical question concerns the ability of milder NPI (MNPI) and voluntary precautions to mitigate the risk of greater infections and deaths while also limiting the pandemic’s economic damage and its social costs. Ineffective NPI could lead to continued COVID-19 waves and new types of crises, worsened expectations and delayed economic recoveries. From the central range of surveyed estimates of transmission and alternative herd-immunity-threshold estimates, a ‘worst-case’ virus guidepost suggests eventual deaths of around 25 to 41 million worldwide and 1.1 to 1.7 million in the U.S. needed to reach herd immunity with no vaccine or treatment. The most optimistic study surveyed (theoretical model from a non-reviewed preprint study) combined with the low end of the range of the estimated mortality rate suggests 6 to 9 million deaths worldwide and 250 to 370 thousand in the U.S. to reach herd immunity. Successes in the mix of NPI, treatments, and vaccine can limit the eventual global death toll of the virus. Improved estimation models for forecasting and decision making may assist in better targeting the local timings and mix of NPI. Diagnostic tests for the virus have been largely limited to symptomatic cases, causing possible sample selection bias. A recursive bivariate probit model of infection and testing is proposed along with several possible applications from cross-section or panel-data estimation. Multiple potential explanatory variables, data sources, and estimation needs are specified and discussed.