The blood cell changes were seen in this, and other COVID cases are not typical of most viral infections. Viral infections are often marked by an increase, not a decrease, in lymphocytes. Of particular concern is the decrease in large granular lymphocytes, typically NK cells and Cytotoxic T Cells, essential for viral clearance. According to some sources, the cytokine storm that occurs in some patients, especially pro-inflammatory cytokines like TNF-α and IL-6, is responsible for the lymphopenia and the impairment of cytotoxic activity of T cells and NK cells. This pro-inflammatory environment could also trigger the elevated neutrophil levels. The neutrophils themselves are perpetrators of tissue damage.
Also, a COVID-19 infection can deplete both CD4 and CD8 T cells. It has even been proposed that the virus might infect T cells. One source claims that lymphocyte counts that remain low after the first week of symptom onset in the hospital are very predictive of death.
Although this is a white blood cell course, the red cell distribution width (RDW) is worth mentioning. An elevated RDW also seems to be a marker of severity and poor prognosis. The cause could be the pro-inflammatory environment affecting red cell formation and erythropoietin secretion. Also, proposed injury to the RBCs both peripherally and during development is a possibility and lower clearance of old RBCs.