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Understanding Medicine

Problems and tasks from a variety of sources intended to illustrate the way mathematics arises in life and work.

Masking Pain. A painkiller taken orally is absorbed into the body in proportion to the difference between its concentration in the intestine and the blood stream, is metabolized at a constant rate once in the blood stream, and is eliminated through the kidneys in proportion to its concentration. Use a spreadsheet to determine the level of painkiller in the blood in terms of dosage and frequency. What conclusions can you draw about optimum protocol for relieving pain with minimum use of drugs?

AIDS Epidemic. Examine multiple-year data on the annual number of new cases of AIDS to see if the data follow the typical pattern of other epidemics. Look especially at the ratios of cases from year to year, and at the ratios of these successive ratios. Repeat this analysis with data on HIV infections. What conclusions can be drawn?

Transmitting Disease. The transmission of the HIV virus poses many epidemiological problems both because of the way it is transmitted and the long latency period before symptoms occur. Standard models need to consider individuals with or without HIV, with or without AIDS, with HIV whose behavior or circumstance makes them not infectious; as well as those who die from AIDS and those who die from other causes. Moreover, such models need to examine the rates of conversion from one category to another, differences between men and women, differences among races, and the probabilities of infection. Build a flow chart that shows the relationships among these many factors, and then translate that chart to a spreadsheet in which month-to-month changes can be examined according to various assumptions of transmission rates.

Hospital Quality. Data on high- and low-risk surgery patients in two hospitals show that patients who choose the hospital with the lower overall death rate are more likely to die than those who choose the hospital with the higher rate. It seems that the "better" hospital, perhaps because of its reputation, receives and cares for many more high-risk patients. But this produces a lower ranking in the "deaths per admission" statistic used to rank hospitals, even though its record with both high and low risk patients is outstanding. Given this paradoxical result, suggest means of comparing hospitals that will be fair to both the potential patient and to the hospitals.

False Negatives. Explore the likelihood of false negatives and false positives in public health tests such as STD (sexually transmitted diseases) or PSA (prostate-specific antigen). Compare with the public health risks of widespread vaccination programs. Discuss the implications of this analysis for public health policy and on costs of health insurance.

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Last Update: 12/29/98