He graduated with a B. A. from Emory College in 1909 and was admitted that year to the Johns Hopkins Medical School. Rivers was physically strong and had led gymnastic classes in college, but during his second year in medical school he developed a weakness of the left hand that was diagnosed as an often fatal neuromuscular degeneration. After leaving medical school he went to the Panama Canal Zone and became a laboratory assistant at San Tom s hospital. However, his illness ceased to progress and he returned to Johns Hopkins in 1912. He received the M. D. in 1915.
After a year's internship at Johns Hopkins, Rivers became assistant resident in pediatrics.
In 1918 he was commissioned first lieutenant in the army medical corps and was attached to a special unit investigating an outbreak of pneumonia at an army post. In 1919 he returned to Johns Hopkins to do research in bacteriology. Three years later he was invited to join the hospital staff of the Rockefeller Institute for Medical Research (now Rockefeller University) in New York City to head the infectious disease ward and conduct research on viral diseases.
Beginning his studies on viral disease, then a new field of research, Rivers made valuable observations on the latency of certain pathogenic viruses and on passive immunity induced by viral infection.
In 1926 he announced that viruses, unlike most bacteria, are obligate parasites: their reproduction depends upon living cells of the host. This fundamental principle has since been firmly established but was then contrary to findings of his chief, Simon Flexner, and his colleague, Hideyo Noguchi. Rivers' stubborn insistence on this point of difference between bacteria and viruses did much to establish virology as a separate division of microbiology.
In 1928 he published an article in which he clearly described for the first time the major pathological effects of virus infection, namely cell necrosis and cell proliferation. In 1928 he edited Filterable Viruses, summarizing current knowledge about virus infections.
In 1929 a dangerous disease, psittacosis ("parrot fever"), appeared in New York and California. It was so contagious, especially among public-health laboratory workers, that research on its cause was abandoned everywhere except at the Rockefeller Institute. Rivers studied this disease with two young colleagues, George P. Berry and Francis F. Schwentker, both of whom became seriously ill.
An experienced clinician as well as laboratory experimenter, Rivers made the first thorough clinical studies of several other rare viral diseases, including "louping ill" of sheep, Rift Valley fever, and lymphocytic choriomeningitis. His work and that of the men who gathered around him made the Rockefeller Institute in the 1930's and 1940's a leading center of virus research. Rivers was promoted in 1927 to full membership in the Rockefeller Institute.
In 1937, when Rufus Cole retired from the directorship of the hospital, Rivers succeeded him. A dozen of the leading virologists of the next generation were trained by Rivers.
When the National Foundation for Infantile Paralysis was organized in 1933 he became chairman of its committee on research. He was later chairman of the foundation's vaccine advisory committee, which conducted the clinical trials of Jonas Salk's vaccine. Rivers was a member of the New York City Board of Health and took an active part in organizing the Public Health Research Institute of the City of New York.
In 1943 the surgeon general of the navy called Rivers to discuss the problems of infection faced by the armed forces in the Pacific area. Subsequently, Rivers directed the formation of Naval Medical Research Unit Number 2, made up largely of Rockefeller Institute physicians and scientists. The unit conducted an antimalaria program in Peleliu and Okinawa, fought an epidemic of paratyphoid fever on Okinawa, and battled hookworm on Guam.
He retired from the Naval Reserve Medical Corps with the rank of rear admiral. After returning to the Rockefeller Institute, Rivers edited Viral and Rickettsial Infections of Man (1948). In 1953, when Detlev W. Bronk became president of the Rockefeller Institute, Rivers was appointed vice-president, retaining his directorship of the hospital. After retiring from the institute in 1956, he joined the National Foundation as medical director.
In 1958 he became vice-president for medical affairs and held the post until his death, in New York City.
Rivers was a member of the National Academy of Sciences and the American Philosophical Society, and served as president of several national professional societies in his field.
A kindly man, Rivers was sympathetic with patients and totally without pretense. But as a scientist he was opinionated and pugnacious. His prodigious memory and sharp tongue made him a formidable adversary in debate.
He married Teresa Jacobina Riefle on August 5, 1922; they had no children.