Inclusion Criteria:  Each subject must meet the following criteria to be enrolled and randomized into the study:  Willing and able to provide written informed consent to participate prior to commencing any study-related activities. Must be able to attend all visits (scheduled and unscheduled, as applicable) for the duration of the study and comply with all study procedures. Healthy adult males and females 18 to 64 years of age, inclusive, at Screening Visit (Visit 1). Negative to SARS-CoV-2 (COVID-19 disease) at screening and at each dosing, without evidence of recent of exposure or viral respiratory disease not identified as influenza or respiratory syncytial virus (RSV) (febrile or lower respiratory tract infection). Must be in general good health before study participation with no clinically relevant abnormalities that could interfere with study assessments at investigator's discretion. Subjects may have stable comorbidities (no change in medications, exacerbations, or hospitalizations in past three (3) months).  Women of childbearing potential (WOCBP) and men whose sexual partners are WOCBP must be able and willing to use at least one (1) highly effective method of contraception (i.e., including hysterectomy, bilateral salpingectomy, and bilateral oophorectomy, hormonal oral [in combination with male condoms with spermicide], transdermal, implant, or injection, barrier [i.e., condom, diaphragm with spermicide]; intrauterine device; vasectomized partner [six months minimum], clinically sterile partner; or abstinence) during the study.  A female subject is considered a WOCBP after menarche and until she is in a postmenopausal state for 12 consecutive months (without an alternative medical cause) or otherwise permanently sterile.  Subjects not of childbearing potential are not required to use any other forms of contraception during the study. Non-childbearing potential is defined as subject confirmed:  Surgical sterilization (e.g., bilateral oophorectomy, bilateral salpingectomy, bilateral occlusion by cautery, hysterectomy, or tubal ligation). Postmenopausal (defined as permanent cessation of menstruation for at least 12 consecutive months prior to screening); if postmenopausal status is unclear, pregnancy tests will be performed prior to vaccinations.  WOCBP must have a negative pregnancy test before each vaccination. If menopausal status is unclear, a pregnancy test is required.  Inclusion into the open label safety extension  Receipt of at least one (1) vaccination prior to Day 42.  Exclusion Criteria:  Subjects will not be eligible for study participation if they meet any of the exclusion criteria:  History of an acute or chronic medical condition that, in the opinion of the investigator, would render vaccination unsafe or would interfere with the evaluation of responses. History of ongoing clinical condition or medication or treatments that may adversely affect the immune system. Subjects with pulse oximetry <90% at screening and prior to each vaccination. Individuals who are antigen positive, seropositive or reverse transcriptase polymerase chain reaction (RT-PCR) positive for SARS-CoV-2, including prior to a second dose of PTX-COVID19-B. Individuals who are at increased risk of exposure to SARS-CoV-2 (e.g., healthcare workers, emergency responders). Close contact of anyone known to have SARS-CoV-2 infection within 30 days prior to vaccine administration. Individuals with any elevated (Grade 1 or higher) laboratory test assessed as clinically significant for age/sex by the investigator at screening. Individuals known to have anti-platelet antibodies. Individuals with myocarditis and/or arrythmias. Active neoplastic disease (excluding non-melanoma skin cancer that was successfully treated) or a history of any hematological malignancy. ("Active" is defined as having received treatment within the past five years). Long-term (> two (2) weeks) use of oral or parenteral steroids or high-dose inhaled steroids (> 800 μg/day of beclomethasone dipropionate or equivalent) within six months before screening (nasal and topical steroids are allowed). History of autoimmune, inflammatory disease, or potential immune-mediated medical conditions (PIMMCs). Women currently pregnant, lactating, or planning a pregnancy between enrollment and Day 42. History of immune thrombocytopenic purpura (ITP). History of Guillain-Barré Syndrome or any degenerative neurology disorder. History of anaphylactic-type reaction to any injected vaccines. Known or suspected hypersensitivity to one or more of the components of the vaccine. Known history of alcohol abuse, illicit drug use, physical dependence to any opioid, or any history of drug abuse or addiction within 12 months of screening. Acute illness or fever (temperature >37.5C) within three (3) days before study enrollment (enrollment may be delayed for full recovery if acceptable to the investigator and within Protocol-defined windows). Individuals currently participating or planning to participate in a study that involves an experimental agent (vaccine, drug, biologic, device, or medication); or who have received an experimental agent within one (1) month (three (3) months for immunoglobulins) before enrollment in this study; or who expect to receive another experimental agent up to Day 90 in this study. Receipt of immunoglobulin or another blood product within the three (3) months before enrollment in this study or those who expect to receive immunoglobulin or another blood product during this study. Individuals using prescription medications for prophylaxis of SARS-CoV-2. Individuals who plan to receive another vaccine within the first three (3) months of the study (except influenza vaccine which should not be given within two (2) weeks of vaccine). Receipt of any other SARS-CoV-2 or other experimental coronavirus (MERS, SARS etc.) vaccine at any time prior to or during the study. Receipt of any investigational vaccine or investigational drug within one (1) month of enrollment and through the end of the study (one (1) year after the last vaccination). Planning international travel from enrollment through Day 43. History of surgery or major trauma within 12 weeks of screening, or surgery planned during the study. Significant blood loss (> 400 mL) or has donated one or more units of blood (within 56 days for males and 84 days for females) or plasma (within two (2) weeks) prior to study participation. Positive urine drugs of abuse screen test result. Positive screen for HIV-1 and HIV-2 antibodies, HBsAg, or HCV antibody. Involved in the planning or conduct of this study.  Unwilling or unlikely to comply with the requirements of the study.  Exclusion from the open label safety extension:  Participation in a study that would affect potential immunogenicity evaluation during ongoing participation in this study. Participation in any other study is allowed after Day 90.