Our aim is to provide model-based estimates of the number of individuals aged 65 and greater who will become infected with COVID-19 during the period April 7 to June 30, 2020, 2020 who also have one or more combinations of three prior medical conditions: hypertension, cardiovascular disease, and lung diseases. We provide a breakdown of cases by each possible combination of a medical condition. We estimate that there are 13 million individuals aged 65+ who have one or a combination of three major prior medical conditions or a combination of these medical conditions aged 65+ in the U.S. who have one or at risk of acquiring COVID-19 during April and June, 2020 if proper precautions are not implemented and adhered. The model-based estimate of COVID-19 numbers for those aged 65+ is predicted to be between 34,000 to 104,000; a higher estimate attributable to inadequate precautions is predicted at 477,000 during April and June, 2020. Hospitalizations of patients both with and without ICU-admissions with more prevalent underlying conditions could range between 37,000 to 94,000 cases during the same period. These estimates may aid us in better understanding the potential volumes of patients requiring inpatient care.