Challenge Team Interim Report


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    Team Number: 002

    School Name: Almogordo High School

    Area of Science: Mathecial Biology

    Project Title: Outbreak: The Raging Diseases of The US

Abstract
Interim
Final Report

Making the Model

"Diseases that have the potential to affect large segments of a population is called epidemics (from the Greek words epi, upon + demos, the people)."Jim Callahan 1996. As our group builds the project around the S, I, and R equation, the whole program is totally based about epidemics. What about the S, I, and R equation? Well, for starters Mr. Callahan gave our group a good in depth detail about the equation he used and how to build our model around it.

"First, we can try to draw out of the situation its essential features and describe them mathematically. This is calculus as language. We substitute an "ideal" mathematical world for the real one. This mathematical world is called a model." Jim Callahan 1996.

"Second, we can use mathematical insights and methods to analyze the model. This is calculus as tool. Any conclusion we reach about the model can then be interpreted to tell us something about the reality. To give you an idea how this process works, we'll build a model of an epidemic. Its basic purpose is to help us understand the way a contagious disease spreads through a population--to the point where we can even predict what fraction falls ill, and when. Let's suppose the disease we want to model is like measles. In particular, *it is mild, so anyone who falls ill eventually recovers; *it confers permanent immunity on every recovered victim." Jim Callahan 1996.

Upon learning Jim Callahan^s equation to finding the rate of catching the disease the group learned that in a city or group filled with disease can be categorized in to these three distinctive classes in our project.

Susceptible: normal day to day people who can receive the disease or diseases;

Infected: the people who are already sick or contagious;

Recovered: people whom are already immune to the disease or diseases / bacterium.

S, I, and R are the variables for the number of people in each of these three classes. Put best by Mr. Callahan in 1996 "the classes are all mixed together throughout the population: on a given day, we may find persons who are susceptible, infected, and recovered in the same family describes the variance of the three classes. Think of the world^s population having only these three "compartment" S, I and R. Then think how can the scientist fit S, I, and R into their very own project?" Also some thinks to think about before programming with this are these four simple steps.

1.How many people are there going to be, population?

2.How much time do you give the virus or bacterium to spread to see results?

3.What are the rates of death, catching, and healing from these diseases?

4.Are there any survivors?

By setting these three and simple basic rules it is possible to build upon this and create a program and mathematical model. The goal of the model is to determine what happens to the numbers S, I, and R over time (catchables, infected, and recovered ). "Let's first see what our knowledge and experience of childhood diseases might lead us to expect. When we say there is a "measles outbreak" we mean that there is a relatively sudden increase in the number of cases, and then a gradual decline. After some weeks or months, the illness virtually disappears. In other words, the number I is a variable; its value changes over time." Jim Callahan 1996.

During the time of the epidemic, the susceptible are constantly falling ill or getting sick. Now we probably would expect the number "S" to show a steady decline. If we don^t know more about the illness, we would make the program to so every one eventually catches it in the controlled area. "In graphical terms, this means we don't know whether the graph of "S" levels off at zero or at a value above zero. Finally, we would expect more and more people in the recovered group as cannot decide time passes." Jim Callahan 1996. If we had the graphs that Mr. Callahan had made on his webpage he would then show us that in the graph of R will or should climb left to right.

Mr. Callahan also stated " Suppose we know the values of S, I, and R today; can we figure out what they will be tomorrow, or the next day, or a week or a month from now?" To show what happens in a year, day, or week we must have the rates of catching the diseases of bacterium , but id we had a virus or something it would look like this....

As we can both see the chart shows us that t, time or today, can be set when ever. The increase of infected goes up by how many times the virus of bacterium multiplies. In the chart you can see it goes up 470 ever time which indeed the infected increases the susceptible or "S". In which, "R" also gets higher as "S" rises. With this information anyone should be able to build a program.

Most information found at Http:\\www.math.smith.edu\Local\cicchap1\node2.html (model for measles) and http:\\www.zoology.ubc.ca\~otto\Dio301\Lectures\Lecture\1\Overheads.html(model for primary AIDS).


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