Case Studies and Project Ideas: Measles

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Measles: Present-day Afghanistan

Sources

Zia, Amir. "Afghan Measles Epidemic death toll soars beyond 900." India Times. Mar 29 2000.

United States Center for Disease Control

Background

Measles is the most infectious disease known. It is a viral infection which is spread in respiratory droplets. When inhaled, the virus multiplies in the airways The symptoms of measles are high fever, red irritated eyes, runny nose,cough, and a bumpy red rash, measles are often complicated by middle ear infection or bronchopneumonia. After recovering from measles, people are immune to getting the disease again. Approxamitely 1 million people die from measles each year, in the United States, approxamitely 3.2 in 1,000 people die from the disease (although very few ever contract it). There is an effective vaccination for measles, and in the United States, it has been almost eradicated. Despite the vaccine, measles is still common in many parts of the world, even developed countries in Europe and Asia.

Case Study

In northern Afghanistan, a place where most people are not vaccinated from the measles, an epidemic spread this March. Because of the difficulty in getting medical attention and supplies through the mountainous areas of northern Afghanistan, the disease was allowed to run it's course without the intervention of medicine. In addition to the difficult terrain, fighting is taking place in Samangan, one of the most affected provinces between the Taliban and anti-Taliban forces, complicating attempts to get medicine to the region. The area was hard hit by the epidemic, the World Health Organization put the death toll at more than 900 people.

Building the Model

In this model, there are four stocks of people, Susceptible, Exposed, Infected and Recovered. Susceptible people become exposed relative to the number of infected people there are. Exposed people become infected at a constant rate. Infected people recover within 7-10 days. Once someone has recovered, they are immune from infection again. In this model, we only have people dying of natural causes at a constant rate, regardless of infection (although as you have read, people do die of measles). The birth rate is constant-- when a baby is born, what population do they join? The following differential equations represent the flow in and out of the populations:

The following are values for the constants:

Run this model for 50 years with a time step of .125, some ideas to consider when running this model: