Is there a correlation between incidence and/or recovery from flus and cancer

It seems that currently there is again a high incidence of flu-like symptoms in the population. Recovery from flus is variable some recover quickly while others may take several weeks. Flus are basically virus infection, and resolution seems to be dependent in part on the efficacy of the immune system.
It is also generally accepted that it is the immune system which kills many cancer cells before they become established as clinical tumors and that many individuals develop cold sores (Herpes simplex virus infection) because such individuals were under physical or mental stress conditions conditions known to decrease the effectiveness of the immune system. I also recall in my medical practice that we were told to be on guard to search for the presence of early (preclinical ) cancers in those patients with the development of shingles caused by the herpes zoster or chicken pox virus.
It occurred to me based on such argumentative evidence that there might be a correlation in such patents with flu occurrence and recovery time from the viral flu infections and the subsequent development of and/or the presence of cancers. Variations of such an epidemiological study could also include the incidence of flus in their early years of life and cancers developing later.