In this study, we design and use a mathematical model to primarily address the question of who are the main drivers of COVID-19 - the symptomatic infectious or the pre-symptomatic and asymptomatic infectious in the state of Wisconsin and the entire United States. To set the stage, we first briefly simulate and illustrate the benefit of lockdown. With these lockdown scenarios, and in general, the more dominant influence of the the pre-symptomatic and asymptomatic infectious over the symptomatic infectious, is shown in various ways. Numerical simulations for the U.S. show that an increase in testing and isolating for the pre-symptomatic and asymptomatic infectious group has up to 4 times more impact than an increase in testing for the symptomatic infectious in terms of cumulative deaths. An increase in testing for the pre-symptomatic and asymptomatic infectious group also has significantly more impact (on the order of twice as much) on reducing the control reproduction number than testing for symptomatic infectious. Lastly, we use our model to simulate an implementation of a natural herd immunity strategy for the entire U.S. and for the state of Wisconsin (once an epicenter for COVID-19). These simulations provide specific examples confirming that such a strategy requires a significant number of deaths before immunity is achieved, and as such, this strategy is certainly questionable in terms of success.