Understanding the true extent of the COVID-19 pandemic requires estimates for the true number of infections over time. COVID-19 case counts from hospital records and government testing programs produce tip-of-the-iceberg lower bound estimates for the total number of active cases in a region. This undercounting has several causes, including limited testing volumes and the existence of COVID-19 carriers who do not show symptoms. On the other hand, when blood samples are available, seroprevalence surveys are able to provide more accurate estimates of the true numbers of cases by analyzing the presence of COVID-19 antibodies in blood. The disease analytic models developed in this paper allow for estimation of the true number of active cases over time given three sets of count data which are readily and publicly available during a pandemic situation: observed case counts, observed case recoveries, and observed deaths attributed to the disease. These statistical models can be applied around the world to provide regional estimates where data exists. The authors apply the new methods to estimate under-reporting of COVID-19 in the Northern Health Authority region of British Columbia, Canada. When accounting for changes in weekly testing volumes, and for changes in public policy, they found under-reporting rates varying from 60.2% to 84.2% over the period 2020-03-26 to 2020-10-15. The results match those that have been obtained through a seroprevalence survey in British Columbia during May 2020. This work allows policy makers to make better informed decisions regarding current and future pandemics.