The COVID-19 pandemic is widely studied as it continues to threaten many populations of people especially in the USA, the leading country in terms of both deaths and cases. More and more reports show that the spread of COVID-19 involves infected individuals first passing through a pre-symptomatic infectious stage in addition to the incubation period and that many of the infectious individuals are asymptomatic. 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 presymptomatic and asymptomatic infectious in the states of Florida, Arizona, New York, Wisconsin and the entire United States. We emphasize the benefit of lockdown by showing that for all four states, earlier and later lockdown dates decrease the number of cumulative deaths. This benefit of lockdown is also evidenced by the decrease in the infectious cases for Arizona and the entire US when lockdown is implemented earlier. When comparing the influence of the symptomatic infectious versus the presympomatic/asymptomatic infectious, it is shown that, in general, the larger contribution comes from the latter group. This is seen from several perspectives (1) in terms of daily cases, (2) in terms of daily cases when the influence of one group is targeted over the other by setting the effective contact rate(s) for the non-targeted group to zero, and (3) in terms of cumulative cases and deaths for the US and Arizona when the influence of one group is targeted over the other by setting the effective contact rate(s) for the non-targeted group to zero. The consequences of the difference in the contributions of the two infectious groups is simulated in terms of testing and these simulations show that an increase in testing and isolating for the presymptomatic and asymptomatic infectious group has more impact than an increase in testing for the symptomatic infectious. For example, for the entire US, a 50% increase in testing for the presymptomatic and asymptomatic infectious group results in a 35% decrease in deaths as opposed to a lower 6% decrease in deaths when a 50% increase in testing rate for the symptomatic infectious is implemented. We also see that if the testing for infectious symptomatic is kept at the baseline value and the testing for the presymptomatic and asymptomatic is increased from 0.2 to 0.25, then the control reproduction number falls well below 1. On the other hand, to get even close to such a result when keeping the presymptomatic and asymptomatic at baseline fitted values, the symptomatic infectious testing rate must be increased considerably more - from 0.25 to 1.7. 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 (the most recent epicenter) and we find that such a strategy requires a significant number of deaths and as such is questionable in terms of success. We conclude with a brief summary of our results and some implications regarding COVID-19 control and mitigation strategies.